How To Learn Math and Do Proofs Blog

Teaching Test

2009-03-31T11:33:00.000-07:00

A local university was looking to hire a new faculty member. Part of the selection process was to give a teaching demonstration to evaluate the teaching skills of the new hire. The only issue is that that teaching demonstration was giving only to members of the faculty. Though faculty members might be able to discern teaching skills, it is still difficult to determine if the students will benefit from his/her teaching skills.

Since the faculty already knows the material and has taught the material for so long, it is difficult to determine if the average student would have difficulty understanding the lecture. Since the faculty member already knows the material he/she uses his/her knowledge and understanding to fill-in any gaps in explanation or presentation. -Explanation bias once again.

The solution is to test the instructor in front of actual students. Here are the details, suppose the school has 10 candidates, then the school will then choose 10 classes all at the same level (for example Math 50 or whatever numbering system). Since each class has different students, the school can control for student performance by choosing classes with the same overall standardized test scores (standardized tests given by the school). Since different subjects in math may be more or less difficult for students, all the classes chosen to test the candidate will be at the same section in the book.

Now that the school has controlled for several variables, the candidate is then asked to prepare a lecture and to instruct one of the chosen classes. After maybe one or two classes the students are then given an mini-test to determine the quality of instruction, AND are given a questionnaire to determine what the students think of the candidate.

This is probably the most objective way to test the instruction skills of a candidate.

John G.

Focus Groups

2009-03-31T11:00:00.000-07:00

In my previous posts, I suggested the idea that focus groups with students might be a good idea, the only issue is that it is difficult to get students to participate, even with nice incentives.

There are several solutions:

1. Offer the students extra credit if they attend the focus group.

2. Print up a questionnaire, and have every instructor in the school give the questionnaire to their students in class and have the students answer the questionnaire in class. Schools may opt to make the questionnaire scantron based to make tabulation easier. Since all students must register for classes, a school may opt to require answering the questionnaire before the student can register for classes. This may be done by computer, since many students register via computer.

3. If a questionnaire is unsuitable then you may have to find other ways to get students to participate. The guiding principle behind this is to "catch" students into participating by combining the focus group into activities which the students have no other choice but participate. For example, since students must attend class most of the time, a school may choose certain classes, at random, to participate in the focus group. The instructor will be notified, that his/her class was selected to take part and a focus group leader will lead the session in the classroom.

John g.

Practice Exam Score Analysis

2009-03-24T09:41:00.000-07:00

It would be ideal if a scantron machine where developed that could automatically upload test results to a central computer, basically a networked scantron machine. In this manner the principal or whoever manages the student test outcomes of the school can, on a daily basis, get a view of the practice test scores throughout the school.

Everyday the person in charge can determine if test scores are increasing and are on track to meet their goals by the end of the year. In addition the administration can determine if certain programs are working or not working by looking at the overall school test scores. In this manner the administration is not surprised with low test scores at the end of the year. Now, in order to accurately guage student performance the school will need a standard by which to compare the test scores. Not in terms of test itself, rather in terms of the percentage of students who score above a certain amount. Even if these standards are exceedingly high, it is better to set high standards and miss than to set low standards and meet them.

John G.

Teaching Pt. 18 Addendum

2009-03-21T15:54:00.000-07:00

As an addendum to my previous post on studying, it may also be helpful to teach and constantly emphasize time management techniques. In many respects a large part of studying is time management. Without effective time management, productive studying becomes difficult, if not impossible. Without sufficient time to study and correctly do the homework, doing well at school becomes difficult.

Time management allows the student to organize their time such that they do well at school, spend quality time with friends and family, and work (if need be). In this manner the student is not constantly worrying about studying during their free time or constantly wishing he or she had more free time during study time.

So it may be helpful if middle schools, high schools, and even colleges suggest and constantly emphasize some of the most effective time management techniques. Some schools may even go so far as to produce actual study and life schedules of some of their most effective students. This way it becomes easier for the student to structure their time so that they can have a life AND do well at school. In fact some colleges actually instruct their students on time management and studying.

Effective time management is even more critical as the student approaches adulthood and enters the workforce. As a student leaves high school and enters college time management and studying is even more important since the room for error is smaller and the classes more demanding. As the student graduates college, and enters the workforce time management will allow him/her to do quality work without excessive effort.

If a student can master time management and studying, then success is almost assured.

John G.

Tutoring Center

2009-03-14T10:49:00.000-07:00

In a recent meeting of colleges throughout the southwest, the value of on campus tutoring centers was discussed. On campus tutoring centers, for the most part, help increase student achievement and retention.

Another idea that most colleges find useful is, supplemental instruction. Supplemental instructors are students who have either already taken the class, or can tutor the material in the class. They sit in during the lecture and after class or at some other time, they meet with the class to review the material and answer questions. One college took it one step further, during the supplemental instruction period they first watch a video that pertains to the material covered in class, then they help the students with questions.

Some of the issues with supplemental instruction are finding qualified people and constant turnover since supplemental instructors graduate high school, college, or go to a 4 year university.

Some of the issues with the tutoring center are staffing and attendance. It is not sufficient to have a tutoring center if it is not staffed with qualified, capable people. Most tutoring centers hire high performing students to tutor other students, the only problem is that there may not be sufficient students willing to tutor to make the tutoring center effective. Not to mention that the best student-tutors graduate high school, or go on to a 4 year university, so tutoring centers are constantly losing their best tutors. One way to address this problem is to require instructors in the college or high school to tutor at the center a couple of hours per week.

The number of hours can be dependent on the number of units the instructor teaches (at a college) or some other method (at a high school). Now, teacher's unions may have an issue with this, since the instructors are made to tutor. This problem can be resolved without alienating the teacher's unions. It's all a matter of incentives, money is not the only incentive, what good is money if much of your free time is taken up grading papers? Grading papers-an equally powerful incentive. So if requiring instructors to tutor at the center causes problems with the union, a school may make it voluntary BUT offer a grading service as a powerful incentive.

So a college or high school can offer to grade a certain percentage of a teacher's papers, dependent upon the number of hours the instructor tutor's at the center. The more hours the instructor tutors at the center the higher the percentage of paper's the school grades.

Since most textbooks have complete solution manuals, it is much easier to find qualified graders than it is to find qualified tutors. Also, it is much easier to replace graders than it is to replace tutors, and at a lower cost. Furthermore the effect of a "bad" grader is far less damaging than the effect of a "bad" tutor.

The second issue is attendance, what good is staffing a tutoring center with qualified people IF the students who most need it don't use it? First a school will constantly advertise the tutoring center, if a student needs help - he/she will know where to go. Instructors can offer extra credit to students who do attend the tutoring center and finally a school may make it a requirement for students to go to the tutoring center, with the option to not attend for high performing students. Before a student decides to take a class, they must be absolutely sure they have sufficient time to take the class AND attend the tutoring center - this can be reinforced when they sign up for classes - do you have sufficient time outside of work to attend the tutoring center??

We can modify this even further, before a student signs up for a class a software program will analyze their grades to determine if tutoring should be a requirement. If the student is high performing then no tutoring requirement will be necessary, if the student is average performing then he/she will need to attend only a certain number of hours, if the student is low performing then he/she will need to attend even more hours.

This can also be made real time, if the software system detects that the student's grades in a class fall below a certain level then tutoring will be mandatory until his/her grades go above the level.

There may be details to work out, but the main ideas have been proven to be effective.

John G.

Teaching Pt. 19

2009-03-07T10:04:00.000-08:00

Crowd control in schools is also critical, given that some schools in some neighborhoods, may have many students and may have many incidents. So what is needed are organizational methods that reduce or eliminate student incidents. The following ideas may help:

First we must look at student density and student flux. Student flux is defined as the number of students passing through a cross section of one part of the school hall per min. (similar to electromagnetic flux.) We must do a study of the incidents that have occurred in the past. Look at the students involved, student density, student flux, look at the locations where most incidents take place, look at what time most incidents take place, look at what days most incidents take place.

Now once we have all the statistics we can begin organizing the school in a manner to reduce the number of incidents. The basic approach comes from operations research, our goal is to reduce the probability that student incidents will occur.

Each student may be assigned an incident probability number that measures the likelihood that the student may cause trouble. This number can be calculated based on grades, attendance, and previous behavior of the student. This number may change as the student's grades and behavior record changes.

Obviously if the student density is down to 1 student per 20 sq meters, and the student flux is up to 10 students/min no incidents will occur, but of course it is impractical. If the student density is at a maximum and the student flux is at a minimum then incidents will have a high probability of occurring. So our goal is to find the optimum student density and optimum student flux to reduce the probability of incidents occurring while at the same time being practical.

One way to reduce student incidents, student density, and increase student flux, is to stage the school day. For example a certain group of students will start school at 8am, another group will start school at 9am, yet another at 10 am, and so on. Instead of hour intervals it can separated by half hour intervals, this can decided by operations research. Students who have a record of starting incidents can be separated in time and space, so they will never be in the same place at the same time. Groups of friends who have a record of starting incidents can be separated so as to reduce the likelihood that they will be involved in incidents.

Another idea is to place monitors in strategic locations throughout the school during the school day, this can be decided by operations research as well. Operations research can also decide if it is better have the monitor stand in one place, or is it better for the monitor to walk in a circuit around the halls. What is the minimum number of monitors, is there a monitor density or flux we should aim for?

Operations research can decide which students should go in which classrooms and at what time so as to reduce the probability that incidents both in class and in the halls may be minimized. What operations resarch can also decide is the optimum mix of students with a low incident probability number and students with a higher than average incident probability number so as to reduce the overall incident probability inside the classrooms.

Classroom seating can also be studied, students with high incident probability number will always sit in the front, the rest of the students can choose their own seating.

To further decrease the probability of student incidents motivational material can be played on the PA system throughout the day, everyday so as to continuously deliver positive messages to the minds of the students.

Another advantage of school staging is that minimizing the probability of in-school incidents also may have an effect on after-school incidents. Since students will not have the opportunity to follow up on incidents started in school.

Another idea separate from school organization is school path safety. School districts can statistically analyze how the students get to school, which streets, bus lines, subways, do most of the students use most of the time. So in the morning and afternoon these streets, bus lines, and subways can be monitored so as to ensure student safety. An advantage of this system is that students can more or less be guaranteed safety if they use the streets, bus lines, and subways that are more heavily monitored.

We can construct models so as to simulate student behavior both inside and outside of class, these models will be field tested so as to correspond with a high degree of accuracy with actual student behavior.

Once all or nearly all students are at school, the school is organized to minimize student incidents, motivational material is played continuously, and the students are made to study then real learning can take place.

John G.

Teaching Pt. 18

2009-03-01T11:33:00.000-08:00

Once, all or nearly all the students are in school, now we can start working on them. It is not enough to attend school, the student must actively partake in the educational process. One key part of the educational process is studying. The following is best for use in middle schools and high schools.

It is difficult to learn and master complex material in 45-60 min, most students can learn only so much in a given amount of time. So it is imperative that students be taught how to study and use the study techniques everyday.

To ensure that students do study, schools may consider making studying a part of the school day. For example, after the student's last class, each student will be sent to another classroom to study and do homework - correctly.

Both the classroom and the students in the classroom will be randomized. During the last class of the day the instructor will receive a list indicating where each student in class will be studying. For example student 1 - Room bbb, student 2 - Room cbb, student 3 - Room aaa and so on. The choice will be made by computer using a random number generator. It may be helpful if boys and girls are sent to separate study rooms, this can be programmed into the computer.

It may also be helpful if instead of programming where each student goes, to choose a specific room and choose at random which students will go in the room. It may be helpful if the program has options to keep certain groups of students apart, for example groups of friends that have a record of causing trouble. During the study session cell phones, gaming systems, ipods, or any other source of distraction will be placed in a safe box to ensure the student focus on one thing and one thing only - studying.

In addition it may be helpful if motivational material is played over the PA system, during the study session, to encourage students to achieve. The volume must be low enough to make sure it does not disturb the students while studying.

John G.

Teaching Pt. 17

2009-02-27T10:11:00.001-08:00

As an addendum to the previous posting, we might need to take some additional issues into account.

Illness:
Given that students do get ill, it may be necessary to perform a statistical analysis of the number of days that the average student at your particular school experiences an illness throughout the year. The student will be given those number of "sick-days" along with an extra 2 or 3 days. The student can use these "sick-days" anytime during the year, with restrictions put on the number of consecutive sick days (no more than a week). It must be made clear that if the student is not honest about his/her illness he/she will be made to go to school on days when the truly are sick. If the student is truly ill, and has used all their sick days then they must bring a doctors note, and the school will call the doctor directly to verify the authenticity.

Applicability:
Not every student in the school will need the program, this program should be reserved for the chronically truant, those that are truant almost everyday or every week. This program also may not be necessary at every school in every neighborhood. High performing schools may not need such a program, average performing schools may opt to use the program only when necessary and low performing schools may decide they need the program. Also, not every level of education may need this program, elementary and universities obviously don't need the program, but some high schools and middle schools may need the program.

Program Review:
After a couple of months of the program, students will be allowed to opt out of the program based on grades, behavior, and extra curricular activities. If the student begins to show signs of chronic truancy, the program will begin again.

Effects:
This program will decrease truancy, decrease drop out rates, decrease crime rates, and increase graduation rates. Some schools in some neighborhoods have nearly 2/3 of their student population truant on Mondays and Fridays, this make is difficult for the instructors, other students, and administration since they have to slow the class down when the truant students decide they would like to show up. Not to mention that chronic truancy is highly correlated with drop out rates and future criminal activity.

People might scoff at the "severity" of the program, but consider this:

1 in 100 adults are in prison:

http://www.nytimes.com/2008/02/28/us/28cnd-prison.html

The prison programs are far more severe than anything I have proposed here and yet people find it completely normal. Granted not everyone in prison is in for a violent crime yet, this fact does not explain why they committed the crime in the first place.

Given that education is the key to social mobility and a well paying job-without too much physical effort, it is imperative that we develop ways to ensure students attend and do well in school.

Teaching Pt. 16

2009-02-11T20:53:00.000-08:00

I heard a report on the radio regarding one challenging school's efforts to combat truancy, which I believe are commendable. I also heard details indicating that most students, in that school, "skip" school on Mondays and Fridays along with their reasons why. Hopefully the following ideas may help:

There are several ways to combat truancy listed in descending order of cost and effort:

1. Truancy could be nearly eliminated if the students lived on the school grounds, basically a boarding school. Obviously this is an extreme example that may be untenable, but at least the idea has been publicized.

2. The school can statistically analyze which students are most likely to "skip" school on Mondays and Fridays and where they live. So early on Monday and Friday mornings around 5 am school buses will be sent out on routes to pick up those students one after the other. Each bus will carry several truant officers, just in case the students need a little extra motivation to go to school on Mondays and Fridays. The bus routes will be chosen for efficiency of time and energy. Students will be picked up in random order, within certain limits, every Monday and Friday. Both the schedule and the route will be randomized, within certain limits, to forestall any attempts to plan against the pick up.

3. Another idea is to call potential truants, on their landline phone, on Mondays and Fridays around 5:30 am to remind them to attend school. With a follow up call every 10 - 15 min. If the telephone call is not answered, answered by a machine, answered by voice mail, or if any other indication that the student may not attend immediately a truant officer is dispatched. This works in three ways: the direct message to remind the student to attend school, the nuisance factor to the parents and family having to wake up and answer the phone so early in the morning, finally the prospect of having a truant officer show up at 5 am to get you ready for school. Once again the timing and frequency of the phone calls will be randomized. Truant officers may be strategically placed around the school district to ensure no less than a 10 min lag between notification and arrival on scene.

Once the student answers the phone he or she will be given a certain amount of time to arrive to school based on how long it takes to travel to school depending upon the mode of transportation.

4. Given that most students use cellphones, the school may use Google latitude to track the position of students as they make their way to school. Students that may be potential truants will be identified and located. In fact the phone call from part 3 may actually direct the student to turn on his/her cell phone just for this purpose.

5. Student will be encouraged to attend classes, and reminded everyday the importance of school and of consistently attending school.

John G.

Teaching Pt. 15

2009-02-09T09:42:00.000-08:00

As an addendum to the gradekeeper system proposed in my eariler post, once a negative grade trend is detected the server can alert the student's parents via email, snail mail, twitter, or phone, whichever form each parent uses as primary communication. It is probably best to send all email, snail mail, twitter messages, or phone messages to each parent's place of employment. This way the school avoids student tampering with email accounts, snail mail, phone messages, or twitter messages.

John Gonzalez

Teaching Pt. 14

2009-01-25T09:50:00.000-08:00

The effectiveness of item analysis of standardized exams was demonstrated recently. At a meeting of instructors we reviewed the results of a standardized student learning outcome exam. We performed item analysis and found that most students were performing poorly on certain questions.

The purpose of the exam was to determine exactly how much the student learned and mastered by the end of the class. So if they performed poorly on certain questions the conclusion is that they must not have learned it that well.

So what's the solution? Its easy, make all your quizzes and exams comprehensive. Quite possibly the best idea of the meeting, brought up by another instructor. Given that we have limited test time and that students can only study for so many things at once, we can modify this great idea and make sure to include at least one or two questions in each quiz and exam that pertain to the questions that most students miss on the student learning outcome exam.

For example suppose most students missed questions about order of operations and linear equations, so each exam and quiz will contain at least one or two questions regarding order or operations and linear equations. We can take this further and make it part of the homework. Every homework assignment will contain questions that most students miss in the student learning outcome exam. Of course you can only give these questions on exams and homework only AFTER you covered them in the course. The idea is great, constant reinforcement of difficult concepts.

There may be some instructor resistance to accepting and implementing effective ideas from others. I always remind myself of past professors that were some of the best in their field whose instruction definitely needed improvement. This goes to show that simply because someone understands and has mastered the material, doesn't mean they know how to teach it.

So if knowing the material does not imply knowing how to teach the material, then not knowing how to teach the material does not necessarily imply that you don't know the material. Hence any suggestions that may improve one's instruction should not be taken to mean one is incompetent, or ignorant, or unintelligent. Think about it, if professors who are the best in their field often have trouble teaching, doesn't mean they stop being the best in their field.

John G.

Teaching Pt. 13

2009-01-23T09:23:00.000-08:00

Integration of all these ideas is key to creating a robust and effective educational system. Here is one such system:

All teachers will use Gradekeeper or similar software. The benefit of using computerized grading is that software reduces the amount of work and errors incurred in calculating the student grades. In addition gradekeeper or similar software files can be uploaded to a server and the server can perform statistical analysis on each student's grades and look for negative grade trends and other factors. If negative grade trends are detected then the server alerts the instructor via email, the instructor will have a chance to reverse the trend, otherwise if it continues a school counselor will be alerted and will work with the instructor to develop strategies to reverse the grade trend.

Given that at any one time an instructor may have more than one such students, the server will be connected to the national student database, the server will suggest certain strategies to reverse the trends dependent upon profile analytics. The server will look for the most similar grade trends for past students in the most similar schools around the country, then it will look for the most effective solution. The counselor-instructor team will decide if the strategies selected will be effective for their particular situation.

Another advantage is that the server can provide contact information for the instructor or school that developed the strategy, that way they can get real time advice on how to proceed.

In addition since all grades are uploaded to a server, the server can create a webpage for each student that way both the student and the student's parents can view the grades real time. In addition, any negative grade trends will be indicated on the webpage that way the student and the parents can determine exactly where the student needs to improve.

John G.

Teaching Pt. 12

2009-01-21T09:03:00.000-08:00

Another benefit of using scantron grading along with item analysis is that an instructor can compile the results of past classes to get a more accurate view of the strengths and weaknesses of most students and more importantly how understanding and mastery of the material develops through the year.

The instructor can determine the rate of score increase for the average student and look for correlations with specific dates, teaching methodologies, and other factors. This approach will allow the instructor to determine which factors play the biggest role in increasing the score of the students.

In addition temporal test score analysis may help in developing more effective academic calendars and will reveal which subjects require more time and which require less time and more importantly will reveal exactly HOW much time is required for each subject area. The analysis may also reveal where the students begin to lag or stagnate and gives the instructor the opportunity to discover why.

John G.

Teaching Pt. 11

2009-01-18T11:58:00.000-08:00

Given that different schools may have different approaches, we need some method to determine whether or not an effective approach to education will have a good chance of working at a particular school. We need a method to measure how similar or how different two schools are.

Method:

In this respect we may learn something from business. The question is, how do corporations know whether or not a certain franchise will work consistently in a certain location? This may sound odd, but the reasoning is, if businesses can profile something as fickle as consumer demand to determine the best location to set up a franchise, then it should be possible to use similar methods to profile the student base and other factors to determine the most effective approach to education in a particular location.

One such method is advertised in the following website:

http://www.mappinganalytics.com/customer-profiling/customer-profiling.html

This method can be applied to every school in the US and organized into a database, then if a particular school wants to improve student outcomes, it will search the database for the highest performing school with the most similar student profile and most similar factors and copy every single detail of that school.

This method will also help instructors improve student outcomes, because instructors will have a technique by which to decide between competing teaching methodologies, e.g employ the teaching methodologies used by the highest performing schools with the most similar student profile and most similar factors.

This method will also help administrators because they will have a guide as to how to organize every aspect of their school.

Given that no two schools are exactly alike, some problems may arise, this is when the online forum is helpful. Super-instructors and super-administrators will be available to help solve problems that may arise due to profile differences. In addition the case study database will be available to help schools find solutions to common problems. In fact by combining the case study database with the profile analytics, it will be only a matter of time before all problems in education are solved.

There may be problems that no school has found a solution to yet, in this case the online forum is helpful, because everyone can offer different possible solutions. Then each possible solution is rated by instructor and administrators, as to how effective the possible solution is under actual conditions. The highest rated possible solutions are then emphasized and analyzed according to the profile analytics.

Once schools across the country are working at peak performance, for their particular location. Educational research will provide methods by which to continually improve student performance.

John G.

Teaching Pt. 10 P.S.

2009-01-17T10:49:00.000-08:00

Another advantage of using the Scantron machine to score tests is that the instructor can use the Question Item Analysis Form after test scoring to determine which areas of the test most students are weakest. This allows the instructor to then set priorities as to which areas of the test they should focus on.

John G.

Teaching Pt. 10

2009-01-13T20:25:00.000-08:00

I heard several reports on the radio of methods and strategies that schools around the country are trying to improve test scores in challenging environments. Two methods stand out; pay teachers according to the performance of the students along with termination if their students fail to reach the standards.

This experiment does not test theories of education, rather it tests whether incentives motivate teachers, which economics has, in some respects, already shown that it does. The only problem with this approach is that it makes no sense to terminate teachers without instructing the teachers as to the best and most effective teaching systems that work for that particular school.

Given that educational research may take time to produce effective results, a more practical strategy may be more effective in the short term.

Practical Short Term Solutions:

To give teachers the best chances of succeeding it would be best to distill every single detail of the most effective teachers into system that is easy to implement. Here is an example, find the most effective teachers in your school and copy nearly everything about them. Copy their calendar - which indicate which topics are covered and when, copy their tests, quizzes, lecture notes, copy everything they use in their classrooms to the smallest detail - in other words try to replicate the results of the most effective teachers by emulating everything they do, down to the smallest details.

Some of the problems that may arise from this approach is that different teachers have different approaches, so it would be best to perform a delphi survey of the most effective teachers to develop the most effective calendar, the most effective tests, quizzes, and homeworks, the most effective lecture notes, and any other factors that make an effective curricula - for their particular school.

This approach makes it much easier for new teachers to be effective at a challenging school.

The curricula should also detail issues that aren't covered in traditional curricula, for example which sections of the book do students have the most trouble and how to address the problem. Explanations of difficult concepts that most students will understand. How to deal with the problems of many students in one classroom, how to deal with discipline problems, how to arrange the class so that discipline problems don't even have the chance of occurring? Are there any case studies of difficult students that caused problems, along with a strategy to deal with such students? In general - What issues are common to the student base that affect learning and how do we address such issues? The approaches to these issues should be included in the curricula.

Another idea is for teachers to give students tests similar to their local standardized tests on a daily or weekly basis. This way teachers can get an objective measure of the students progress AND focus on problems BEFORE the students are tested under actual conditions. This will give the teachers time to focus on portions of the test that most students find difficult and will help them identify students that may need extra help. The teachers can use a Scantron Machine with 882-E scantron form to quickly and accurately score the practice tests.

In addition practice test scores can help the teacher gauge how effective their practices are and how closely they are replicating the practices of the most effective teachers.

Lecture Analysis:

This is good idea in concept, but some problems may arise in practice. The core problem is that it is difficult for a teacher to analyze his or her lectures, if there is no standard by which it is measured. Without such a standard or at least a method by to find areas that need improvement and practical methods to ACTUALLY address these issues, it becomes nearly impossible to improve. It is not enough to simply point out all the teachers mistakes, practical solutions should be suggested. One should also balance the negative with the positive, after pointing out a mistake, point out what the teacher did correctly. Make it clear to the teacher that the analysis is not meant to punish them, rather to help them improve.

It may be helpful if the most effective teachers review the lectures and offer their advice. They can better guide the teacher to continually improve their teaching methods.

Networking:

These are not the first nor the last schools with challenges, schools such as these have existed for a long time, yet most approaches are still trial and error. To help avoid trial and error it would helpful if the most effective, field tested practices for similar schools were shared around the country and around the world.

It would also be helpful if there was a centralized network where similar schools could exchange information. For example it may be helpful to set up an online forum where teachers around the country and around the world could exchange ideas, anonymously if they wish. One advantage of this method is that the most effective teachers around the country and around the world, for schools in similar situations, could publish their calendars, quizzes, tests, homeworks, lecture notes.

Super-teachers would be available to answer questions, solve problems, suggest methods and strategies. Super teachers would be identified according to their ratings- similar to how the rating systems work at Physicsforums.com.

To help replicate successful student outcomes, every detail of the most effective approaches, for schools in similar situations, would be published on the forum. Ineffective approaches would also be published so that schools in similar situations would AVOID making the same mistakes.

It may also be beneficial to construct a database of Case Studies of difficult students (identity protected) along with effective solutions, difficult classes along with effective solutions, concepts that students find most difficult along with effective explanations, problems with student crowd control along with effective approaches, etc. By effective I mean, field tested solutions to problems.

The most important question is, what have we learned about the best approaches for challenging schools? The practices don't have to be perfect, they simply have to take the best of what is possible in those schools.

John G.

Teaching Pt. 9

2009-01-12T12:21:00.000-08:00

There are more issues to address in regards to education.

Scale

The problem of scale deals with the student to teacher ratio. We can best understand the problem of scale by considering certain examples.

Consider a class with only one student and one teacher, given enough time and effort, most of the time, the teacher can teach the student to perform perfectly on almost any test and to fully understand the material. Consider 2 students, it is still possible to do the same with both students, with a minimal expenditure of additional time. Consider more and more students, little by little the expenditure of additional time and effort increase until the individual approach to education ceases to be practical and in fact is counterproductive. The amount of time to help each student adds up until much of class time is spent simply helping each person.

So what must be researched is how to organize class time, class layout, class groups, to compensate for problems of scale. One idea is for the teacher to give an assessment test at the beginning of the class year to determine which students might need more help than others. The students who scored in the first quartile will be given first priority in help, the second quartile students will be given second priority, and the third quartile students will be given third priority.

In fact the third quartile students can be helpful in groupwork, they can help explain concepts to the second and first quartile students.

Students can be organized into groups of 2 or 3 where each group can contain a mix of 1,2, or 3rd quartile students or it might be more effective to group the first quartile students together in groups and mix the 2 or 3rd quartile students in groups. In any case these are the types of questions that education research can investigate - what are the optimum class organization methods to maximize student performance in large scale classrooms and with students of differing preparation? Maybe the optimum method must vary according the overall preparation of students in the class, meaning if the distribution of well prepared students is that of a bell curve then one method will be best, if the distribution of well prepared students is that of J-curve then another method must be employed. If the distribution is that of a rectangle then another method will be best.

Metrics

Metrics are an important part of educational research because, in theory, they provide objective measures of student performance. The problem is that numbers by themselves do not provide objective information, the methods by which the numbers are obtained must also be investigated.

Some examples of metrics are assessment test, class test, quiz, homework, and classwork scores. These scores can be analyzed statistically to determine if any negative trends exist, giving the teacher prior warning of problems that may arise in the near-future. This way the teacher has time to address the problems before they shows up, which is much easier than addressing the problems when they are in full effect.

John Gonzalez

Teaching Pt 8

2009-01-04T22:34:00.001-08:00

The ideas presented in this blog are mostly directed towards schools that need improvement. A high performing or even average performing school may not need to consider all the ideas, since they have a system that works, more or less.

The scientific approach is not meant to stifle ideas, discussions, or debate. Vigorous discussions are common in all the sciences, it serves as a method by which to determine which theories are worthy to be tested and which don't work, even in the abstract. In the end, though, it is experiment that determines which theory is closer to reality. Without a test to falsify competing theories scientific progress is very difficult.

I suppose this is the ultimate form of optimism, the belief that with enough thought and enough work most problems can be solved.

One criticizes, not to personally offend, but to improve. Problems are identified and analyzed in the light of day, not to embarrass, but to solve them. Failure scenarios are considered, not to be negative, but to design systems to avoid them. Counterarguments are developed, not to bicker, but to vigorously articulate and develop one's ideas. Ideas are rigorously tested, not to stifle creativity or freedom, but to guide us towards truth. Non-falsified theories are standardized, not to dictate how to think, because it is easier to learn, master, and contribute when you have set system of thought, rather than to try to re-derive centuries of thought in one lifetime.

Field Testing

In keeping with the principle of field testing, we should welcome feedback from the teachers and the students. Just as in software testing, it is often difficult to test for every single scenario, and sometimes the theory or approach may not have taken into account certain factors that affect the student learning outcomes. Allowing for honest feedback is a great way to find weak spots in the educational systems approach. Given that teachers may be reluctant to offer honest feedback, due to administrative concerns, we may have to look at online forums where teachers are able to post anonymously.

More Later

John G.

Teaching Pt 7

2009-01-01T16:48:00.001-08:00

The most important part of this new model of education is field testing. Even if people dismiss all the other ideas, the one idea that cannot be dismissed is does it work with actual students, in actual schools, with actual teachers, under actual conditions. No matter how well argued or well conceived a theory may be, if it doesn't work under actual conditions, then it really doesn't improve education.

The main problem is that philosophies, theories, conjectures, principles, guesses, ideas, approaches, strategies, tactics, and methods can all be argued ad infinitum. Almost any approach to education can be made to make sense in an ideal world, but in the actual world some approaches work better than others. The reason why science has progressed and given applicable results in the last 500 years is because the ultimate arbiter of theory is experiment, more importantly experiments that falsify theories.

One problem is that theories are often tested with ideal students, in ideal schools, with ideal teachers, under ideal conditions. Though this may be a good preliminary method to develop and test the theory, it is not rigorous enough to determine if it works at the level of the local school. Certainly not rigorous enough to determine if it works at the level of a challenging school. Hence before an approach to education is standardized it has to be rigorously tested at different types of schools.

This is not to say that theories are unimportant, for in order for science to progress new theories must be developed, but the theory in and of itself is not enough. Another reason why the scientific method has worked so well is because no one has to take the word of scientific authority on its face, anyone with enough equipment can test the theory on their own and determine if the theory works for themselves. Teachers don't have to believe the theory on word of the experimenters. Every teacher can test the theory in their own classrooms and determine for themselves if the theory works as it should.

Any approach to education has to be broad enough to meet the educational needs of the target student base, easy enough so that the average teacher can master and implement it, flexible enough to deal with different conditions, resilient enough to come back from difficulties, and finally must always be seen as a work in progress.

John G.

Teaching Pt. 6

2008-12-27T18:57:00.000-08:00

Yet another factor in teaching is textbooks. Different authors explain the concepts in different ways that different students may or may not understand. One way to develop a good textbook is to continually test the book with focus groups. To help aid the initial construction of the book it may be worthwhile to research books that a large representative group of student consider to be easy to learn from, yet satisfy the teacher's requirements.

It is a good idea to test every aspect of the book with a representational cross section of the target student base. Everything from wording, to phrases, figures, to notation should be finely tuned for maximum student understanding, while at the same time satisfying the goals of the teacher.

John G.

Teaching Pt. 5

2008-12-27T00:11:00.000-08:00

I have been talking in broad terms with regard to the framework of the model of teaching. The core is built around the coaching model, so in order to best help use develop the framework, we need a specific coaching model to work from. One of the best if not the best coaching books available is Successful Coaching by Rainer Martens. The more I read the book the more methods I see that could applied to teaching. The great advantage of the book is that it is self contained and covers nearly all aspects of coaching in a logical format.

This book can help educators develop a set of teaching principles, based on experiment, that can be exported to any school. Though, I believe that we might have to customize the approach to 3 categories, rural, suburban, and urban schools.

An advantage of the book is that it does not give a list of rules to follow, rather a set of guidelines for the coach to develop his own program based on the most effective approaches. This allows the flexibility necessary to adapt teaching to different environments.

Failure Analysis

Any educational program designed according to coaching model should be tested to the breaking point. This is not intended to discredit the approach, rather to analyze where the program failed and how it can be repaired. In this respect it may be good to take the engineering approach, you perform a stress test, when the system fails you perform a failure analysis to determine which part or parts failed and why. One of the best failure analysis methods is Failure mode and effects analysis.

Another idea that might be helpful in educational systems planning is futures techniques. Though I think it may be quite on the fringe, it nevertheless may prove helpful.

The coaching model is the "workhorse" of the educational system, with the other ideas on the periphery meant to help increase the effectiveness of the coaching model. The educational systems analysis is meant to approach education on a broader scale, possibly on the scale of school or several schools.

More ideas later.

John Gonzalez

Teaching Pt. 4

2008-12-22T13:38:00.000-08:00

There is yet, one more factor to discuss; instructor bias in explanations. It often happens that an explanation of a concept that an instructor thinks is clear and easy to understand is difficult for students. Also, it often happens that other instructors think the explanation is clear, so the instructor, even if he/she asks other instructors what they think about the explanation often get highly biased feedback.

The problem is that concepts are easy to those who already understand them and know how to use them. So, when instructors look at a textbook or another instructors explanation of a concept, they tend to use their own mastery of concepts and techniques to "fill in" or "understand" parts that students may find difficult. Hence, what the instructor thinks is easy is actually difficult for the student.

Now this does not mean we have simplify ideas to the point of compromising the main concept, rather it is a balancing act. You have to balance ease of understanding with integrity of the main concept.

For example in regards to textbooks, it is best to let the students decide which textbooks they think are easiest to learn from. Then from that list of textbooks (usually there is more than one) let the instructors decide which textbook(s) satisfies their objectives for the class. This way you satisfy both the student AND the teacher.

In regards to explanations, one way to develop a sense for what constitutes an explanation that is understandable for the student is to practice explaining concepts by tutoring students. After tutoring many students you develop a sense of how to explain concepts in a way that the student understands and leads to mastery of the main concept.

John G.

P.S. It may often happen that tutors have a standard answer for common questions. While this may be efficient, it runs the risk of falling into the trap of explanation bias. So, once a tutor identifies a common question, it may help to have an answer ready, but always try to improve the answer based on experience.

Coaching and Teaching Pt. 3

2008-12-19T11:36:00.000-08:00

There is a problem, educators and administrators tend to gravitate to theories of education that are theoretical and untested. This may affect nearly all of my suggestions, my approach is more experimental - Use the techniques and methods that have proven themselves to get results, not the techniques you think should get results.

This doesn't imply that we can't experiment with new techniques, rather it is saying that the techniques that are to be standardized should be those that have been tested experimentally in similar circumstances and have proven to give good results.

Another issue is National standardization of pedagogy. Like I have said before, much of teaching as it is currently practiced is trial and error. Simply because different school districts or different states approach education differently doesn't mean they are all equal, or give equal results. Some techniques, strategies, tactics, work better than others. It would be irresponsible to use the concept of academic freedom as an excuse not to use techniques, strategies, and tactics that have proven to get results.

I routinely sit in on other teachers classrooms, not because they are perfect, but because I may learn a technique, strategy, concept, or tactic that is effective and that I can use in my own classroom. I sign myself up for SAT and study skills classes, so I can learn different strategies and incorporate them into my system.

Another method that can be used in education is that of focus groups. Instead of testing different advertisements on the students, test different teaching styles and methodologies, and find out which ones the students like the most AND gets good results.

There should be some flexibility built into the standardization to take into account differences in school districts. For example different approaches may be needed for urban, suburban, and rural schools. Maybe a different system of categorization is needed, but as long as the best practices are standardized I think it will greatly benefit education.

More later

John G.

Coaching and Teaching Pt. 2

2008-12-19T09:51:00.000-08:00

There are more differences between coaching and teaching:

1. In coaching you can easily see if the athlete is performing the movements correctly, in education you cannot see if the student is reasoning correctly. This is why I emphasize that the student explain the problem to the teacher and then the teacher analyze and correct the student's reasoning. This method is equivalent to a coach analyzing and correcting the athletes movement.

2. Given that you can't see the student's reasoning, it is sometimes difficult to communicate how a "good" student reasons and organizes his/her work for maximum effect. So it may be beneficial to create videos of "good" students taking a test or doing homework, with the audio dubbed to describe what the student was thinking as he/she was doing the test/homework. The videos should be "shot" from above the student, this way you can see how the student organizes their work on the paper. One advantage of this method is that it is easier to communicate the practices, habits, strategies and tactics of a good student in test taking situations.

In addition, this method can be used with students who need improvement. If you create a video of the student taking a test or doing homework, then you can review the video with the student to gain an understanding of the thought process. During the analysis process, you can correct any thought processes, writing habits, strategies, tactics, etc. Also, you can identify parts of the testing process where the student could be more efficient, do the same work with less time, and where certain strategies could have been used and how they could have been used. The psychological dimension should also be explored to determine how the student can manage anxiety, panic, and overwhelm during the test.

This method can also be applied to studying.

3. Given that some parts of education is mandatory (elementary and high schools), students may have to attend the school involuntarily. Even if student attendance is not completely involuntary, the student's belief that he/she is capable of learning and succeeding may not be there. So you may have to use motivational techniques to instill the belief that they can succeed, both emotionally and rationally.

Even this is not enough, sometimes you will be called on to "sell" education, to convince the student to "buy" what you are "selling", mastery of knowledge. The more challenging the school, the more difficult the sell. As such it may be beneficial to employ techniques used in sales, marketing, public relations, and politics. Our goal is to find out which words, which phrases have maximum effect on the students and incorporate them into the lectures. We want to understand the mind of the students, their desires, their fears, their hopes, and their dreams. We want to know what drives them. In other words we want to know how they think. This way we can determine how to best "sell" education to a sometimes challenging audience. Our goal here is not to manipulate for selfish ends, rather it is to guide the student to a positive goal, without telling inaccruate, distorted, or self serving statements.

It may be helpful for schools to study public relations, sales techinques, and marketing techniques.

4. Another idea, is for the teacher to record each lecture. Afterwards the teacher can then analyze the lecture, and look for improvements. Each explanation, each example, word, phrase, concept, movement, and pose will be analyzed and directed to maximum effect - the communication of concepts in such a manner that most of the students will understand, the motivation of students, and the "selling" of education.

5. Teaching few students is not the same as teaching 30 or even 40 students. The difference is that when you teach a few students you can work on each on individually, you can wear down the exterior and motivate them more effectively. Students act differently in crowds, so we should also study student behavior in crowds, and learn how to control crowds and direct them to postive ends. In this regard it is best to study the work of Edward Bernays and crowd psychology.

More Later

John Gonzalez

Coaching & Teaching

2008-12-10T10:04:00.000-08:00

Update - Many may wonder how the students in the high school exit exam prep class did, well I had 6 students and 5 of the 6 passed the high school exit exam.

The more I think about teaching and teaching methodology the more connections I find with coaching in sports. Coaching is to the physical domain what teaching is to the intellectual domain. We can learn much from the methods of coaching since sports programs are more developed in the US than educational programs. Some of the advantages of focusing on coaching programs is that coaching has been finely tuned over decades to get results, not just winning games, but producing good athletes and good students. Another advantage of studying coaching programs is that they are "holistic", in order for an athlete to perform at their peak, mind, body, and emotions must all be aligned to produce the desired result. So athletic programs developed entire systems of thought and philosophy to address nearly every aspect of the athlete. - If we can adapt these systems, these programs, to education I think we can great improve student outcomes.

Due to competitive pressures, coaching in sports has identified and analyzed every factor that could possibly have an affect on the athlete and the outcome of a game. Then these factors are finely tuned to produce good athletes and to win games. Unfortunately finely tuned factors are not enough, the way the factors are harmonized also has effect on the athlete and the outcome of a game. In other words harmonizing the finely tuned factors is also a factor. This harmonizing is what is known as a philosophy, a program if you will that guides not only what factors are used, but when and how they are used. Harmonizing the factors is an art and different coaches approach it differently, but this does not mean all approaches are equal, different approaches yield different results. So it is best to focus on the coaches that get the best results, not just winning games, but producing good athletes. - This is what is missing in current educational programs.

Most educational programs focus on certain very limited factors, namely explaining concepts, without regard for other factors that affect whether or not the student gains an understanding of the material. Even if other factors are identified and to some extent tuned, they are not harmonized with the environment. More importantly, many educational programs are reluctant to admit that not all approaches are equal, and that some approaches yield better results than others. In many respects teaching as it is currently practiced is trial and error. This makes it difficult for a teacher with a good intentions and a good heart to be effective at challenging schools.

Given the current budget crisis, it may not be possible to increase teacher salaries, so instead make it easy to be a good teacher and get good results - work on the altruistic side of teaching, as opposed to strictly the self-interest side. One way to make it easy to be a good teacher is to distill the practices, the philosophy, the tactics, the strategies, the behaviors, etc of the most effective teachers into a set of principles that are easy to follow. Not as a set of rules that must be followed rather as a set of guidelines to help the teacher. This way teachers don't have to rely on the painful process or trial and error, thereby leading to a more positive environment and increasing teacher retention.

Programs can be specialized to the area that the school is in, for example different programs may be needed for urban, suburban, and rural high schools. The most effective teachers from each category should be interviewed to determine every aspect of their "program" that yields good students and good results.

As any coach will tell you, the preparation, motivation, prior experience, and parental involvement make a difference in the way you approach a group of athletes. Athletes who have never played the game, are not motivated, and have no parental environment will need different approach from athletes who have played the game, are highly motivated, and have much parental involvement. Some people may interpret this as putting the athletes down, but no, rather it is being honest about factors that play a big role in the way you approach the program. The same thing holds true for student, admitting that the student may not be as well prepared, or motivated, or as disciplined as other students is not a put down, rather it is being honest about factors that will shape your approach to teaching them.

Preparation, motivation, and consistency, are aspects that every student can improve, it is not genetic, as such it is not a put down. A true put down, is claiming that students are incapable of learning, or that genes control their achievement, or that they are inherently incapable of abstract problem solving - these are the cruelest put downs. These are the put-downs that some people gravitate to when they don't see improvement in results.

Differences

Now there are differences between sports programs and educational programs. Participation in sports programs is usually voluntary, while going to school is sometimes involuntary. So we might need a different approach in motivating students to participate in the sometimes intellectually rigorous educational process. The solution may lie in marketing - if it is possible for businesses and corporation to "make" people want things they don't need, then it should be possible for educational institutions to "make" students want something they DO need - education. In other words, we should "sell" education - not as a ploy to get a student or the student's parents to spend money, rather as a technique to get the student and the student's parents to undergo the rigorous process of education. The teacher may have to use sales techniques to convince the student that education is important and to undergo the rigors therein. Salesmen and teachers have this much in common, sometimes both are placed in situations where the "sales" are difficult, hence you may have a high turnover rate in difficult "markets".

The Big Picture

I suppose the grand overarching philosophy is this: Every problem in education should first be identified and then analyzed. Then we should realize that these problems have already been solved and finely tuned by some other group or institution. Our goal is to adapt and harmonize them to education.

John Gonzalez

Standardized Tests 2008 Pt. 2

2008-08-18T23:31:00.000-07:00

Teaching to do well on a standardized tests requires a different approach from teaching simply to pass a test designed, given, and monitored by the teacher.

The main difference is that correctly answering the questions on a standardized test need not always require knowing how to answer the questions algebraically. The same tricks and strategies useful on the SAT and ACT is directly applicable to any standardized exam. Any reputable SAT book will provide a list of practical strategies to use during the test. This can help the student answer questions that he/she could not have answered without the strategies, which in turn can help boost the students score.

Another helpful technique is to compile a bank of practice exams, Kaplan provides a series of practice exit exams, so does Barron's and Princeton Review. Since the exit exams are specific to one state the number and variety of practice exams are smaller in number when compared to the SAT or the ACT. So in this case we have to improvise and utilize the exit exams from other states, the standards from state to state are similar enough that their practice exams can be helpful. Once again Kaplan, Barron's, and Princeton Review provide the practice exams for other states as well, in my case I considered using the practice exams from Massacheusetts and New York. In addition the New York Regents exam is also of great use.

Another good suggestion is for the teacher to take the practice exam him or herself under timed conditions. In this manner the teacher can determine which questions might be more difficult than others. Also, the teacher can develop multiple ways to answer the same question-this is one of the most effective techniques for standardized tests. I usually encourage my students to answer the question in more than one way, the most obvious way is using algebra though it is not always the most efficient way. So I encourage the students to develop alternate ways to answer the question; trial and error, eliminate obviously wrong answers and guess, measure with a piece of scratchpaper, test the answers. You can also combine multiple strategies, algebra + trial and error, trial and error+test answers, measure+test answers, etc. The more ways your students can answer a question the higher the chances they can correctly answer a question on the test when the algebra is too difficult. Sometimes I tell my students that they can answer the question using any method they want, except algebra! This really gets them to think.

Sometimes you may want to challenge the students in different ways to see if they can adapt, so sometimes I give them a test at a level higher than would be expected. Sometimes I give them a test with different types of questions, for example comparisons or arithmetic type questions etc.

One should avoid simply teaching the material without teaching the strategies mentioned above. Covering only the material does help improve the student's score but a much slower rate. One should avoid simply reading from a textbook, the best advice is to teach but verify, meaning teach a concept, then give the students a couple of examples to do and go student by student to determine if each student understands. Another techinque is to use progressive understanding; every mathematics problem can be broken down into a series of simple steps. For example suppose a student cannot solve the following problem:

Solve for x: 3x+9 = 18

So you say ok, can you solve this problem: x + 9 = 18, most of the time students can solve it, x = 18-9, so x = 9. If the student can't solve it, usually it is very easy to explain how.

Ok so then you ask, can you solve this problem: 3x = 27, most of the time students can solve it, x = 27/3 = 9. Once again usually it is very easy to explain.

Then you return to the original problem: 3x+9 = 18, then give them a little hint start with the 9 just like you did before in the easier example, worry about the 3x later. So they start 3x = 18-9 so 3x = 9. This looks very similar to the problem before, why not try the same technique, usually the student understands at this point. At this point I usually give the student several of these problems to make sure they understand how to solve it, then I have them explain the solution process to me in detail.

Standardized Tests, Its That Time of Year Again

2008-08-15T20:35:00.000-07:00

Around this time of year the results of the last year's standardized tests are released. Often there is much hand-wringing, due to the poor or fair test results of certain ethnic groups. This year has shown improvement in the test results, though gaps are still persistent. This is expected, since test results usually depend upon the mastery of previous material, any gaps in mastery of knowlege from the previous years tends to continue in the future years.

A while back I decided to test my ideas in actual practice, to determine if they are effective under the most difficult of circumstances. I was given that opportunity at a local school in one of the most challenging cities. By luck I was assigned to teach a class for young adults that were unable to pass the high school exit exam on multiple attempts and in some cases they had taken class multiple times, quite a challenge.

I was given 6 students all of whom failed the high school exit exam, specifically the mathematics portion. I was given an analysis of the each student's score separated into different parts according the different portions of the test. So I began to the review the section where most of the students had trouble. As time went one I continuously modified my approach until I found one that worked. I found the following 4 rules to be the most effective approach.

1. Enforce attendance:
If the students are not there you can't help them improve.

2. Make them study in class:
Many of the students are in the class because they never developed the study skills to ensure a passing score on the high school exit exam. Often I assigned homework and reading assignments which they hardly ever completed, so I made them study in class. I determined that many students have to work to help support their families so they don't have much time to study after class, many also lack the discipline to study consistently. As I have said before, by study I don't mean simply starting at a book, or looking at notes, I make studying interactive.

One time I made them memorize 20 geometrical forumulas in class, then I tested them in class. Then I made them memorize the solutions to a complex mathematics problems, then I tested them in class, by asking each student individually to solve the problem on the board as I peppered them with question after question after question. I found that before you can try this you first have to earn the trust of the students. They have to know that you care about their education and that everything you do is for their improvement.

3. Test them everyday: To ensure they pass the test by the end of the class, it is best they get as much experience with the test situation by simulating test conditions as accurately as you can. All you need is a scantron machine, scantron paper, some #2 pencils, and of course practice exams. (Most schools have a scantron machine) Ensure that they improve their score everyday or at least every week, sometimes I give the same test over to determine if they at least memorized the material.

4. Always keep them busy: If they finish with studying or with a test, make sure you have either another test or more material they should study prepared.

There is much room for indpendent initiative to be creative.

John Gonzalez

Mathematics and the Real World

2008-05-10T07:23:00.000-07:00

I read the following article regarding mathematics education:

Study Suggests Scrapping Balls and Slices

I agree with the fundemantals of research, teaching mathematical concepts through concrete applications doesn't work, but using concrete applications to deepen understanding may work. I agree that teaching the abstract principles should come first, but to fully understand the principles and understand how to use the principles one should use a mix of abstract and concrete problems. Mr. Sloutsky alluded to this in his statement: "[Word] problems could be an incredible instrument for testing what was learned. But they are bad instruments for teaching,".

I believe that the first purpose of word problems is not to teach the principles, but to teach problem solving using the principles. Word problems should be justified as a way to "stretch" your mental problem solving muscle, to challenge your thinking to grow, and to teach and reinforce the type of thinking beneficial in mathematics.

More Empirical Verification

2008-04-30T10:31:00.000-07:00

Hello, some of the ideas presented in the website regarding intelligence has been given additional empirical verification:

Memory Training Boosts Brainpower

Hopefully this helps researchers develop more effective brain training techniques.

John Gonzalez

Elite Training Techniques

2008-04-28T07:04:00.001-07:00

I was perusing the New York Times website when I came across this article:

Elite Korean Schools, Forging Ivy League Skills

It's quite amazing that nearly all of their students go to Ivy League schools, but what is most important to me are the skills they emphasize in the article. Constant studying, motivated students, and more importantly motivated parents. What I would like to see is an analysis of the specific study techniques they employ. For example, "such and such" student reads the paragraph then memorizes it and then goes on to the next paragraph, something like that. Specific time management skills and whatnot.

Overall, I think the article is great it serves as a general plan for any student who wishes to attend and ivy league institution.

Mental Exercises

2008-04-23T16:29:00.000-07:00

One method to create or identify effective mental exercises would be to use the fMRI machine. We could view the brain activity under different "loads". "loads" could be mathematics problems, logic problems, physics problems, reading, arguing, etc. Then we could look for patterns in the areas of the brain used in those "loads".

Then we design a set of mental exercises, we may categorize them according to the different areas of the brain we think it may target, OR the different areas of thinking it may target. In fact the fMRI machine may be able to help us identify which areas of the brain may be involved when thinking about a certain category of problems, then we can use these results to design exercises to target those areas of the brain used in thinking about certain problems. This is similar to a thinking map, where a category of thoughts may be associated to a pattern of brain activity.

Some of the problems may be that different people use different brain patterns to process the same thought, also different people may have a slightly different conception of a thought so it uses a different part of the brain. I suppose this may require further thought, but there may be sufficient similarity in brain activity for similar thoughts to elucidate the brain patterns.

This will help us to develop mental exercises that "elucidate" similar or the same type of brain patterns that are used in solving problems.

More Later

John Gonzalez

The Website

2008-03-26T21:47:00.000-07:00

Many may say that the website is simply study skills. To some extent that is true, some of my website is study skills, but my website goes beyond simply study skills.

First most study skills books tell you when to study and to some extent how to study, my website on the other hand tells you specifically and in detail exactly how to study.
Most study skills books may recommend finding another textbook, but often they do not specify which textbooks, my website gives specific books to refer to, as well as the rating of the book on amazon. In addition, study skills books are static, meaning that if a new textbook is published after the study skills book is published they cannot recommend the book. My website on the other hand is dynamic, I constantly look for highly rated books and change my recommendations accordingly.
Most study skills books emphasize understanding the concepts, with the implicit assumption that if one understands the concepts one will be able to solve the problems. The issue with such reasoning is twofold first, how do you go about understanding a concept? "Understanding" the concepts is necessary but not sufficient to solve problems.
The most significant difference between my website and most study skills books is that I emphasize the reasoning process rather than simply understanding the concepts. For it is the reasoning process that leads one from problem to solution.
Understanding is the result of a reasoning process not the other way around. So if you learn how to reason correctly then understanding a concept is simply a judicious application of the reasoning process.
My website offers specific advice on how to strengthen and refine the reasoning process, which in turn allows one to strengthen and refine the ability to "understand" concepts which in turn modify the reasoning process.
My website offers specific advice on how to test your reasoning processes to determine if your reasoning processes reflect an accurate "understanding" of the concepts.
My website analyzes the reasoning processes, cognitive habits, and planning techniques of notable people in the fields of mathematics and physics. These serve as insights into some of the best reasoning processes.
My website not only emphasizes critical thinking, but also the strategies, tactics, and tools necessary to solve problems in mathematics. These reasoning processes are specific to mathematics and must be practiced everyday in order to be effective.
My approach is not bound to one theory, study, or result, rather my approach is more philosophical. Philosophical principles are ontologically prior to any theory, study, or result, (with some exceptions) hence reach farther than the latter.
Finally my website emphasizes the importance of explaining your reasoning process to yourself, (almost self-referential). This way you can strengthen your own "understanding" of the subject. Also I emphasize the importance of explaining your reasoning process to people who know the subject so you can determine any faults or weaknesses.

John Gonzalez

Net Neutrality and the DOJ

2007-09-08T10:59:00.000-07:00

If you are not informed about net neutrality please read this:

http://www.savetheinternet.com/=faq

As you might have already read the DOJ on September 6, 2007 came out against net neutrality. The reason the DOJ might have ruled as it did is that big business convinced them that the Internet is “hurting business”.

Google News

The Internet is unlike most other forms of communication in that you have nearly an infinite amount of choices to choose from. The Internet expands people's palette, so to speak, meaning because you can access nearly any piece of information easily, you can find out about artists, movies, software, products, and ideas that you would not have been exposed to without the internet. This makes it incredibly difficult for companies to sell products, why buy a piece of software when you can legitimately download an open source program that does the same thing free? Why buy a digital camera on sale from a large company, when you can find a better camera online for less money? Why buy a newspaper when I can look at it for free? Why buy a pop-star's album when I can find a more musically talented artist that fits my tastes exactly? Why should I take so and so's word when I can ask several top experts what they think? Why believe people or institutions biased to tell you a spun version of the truth when you can look at it yourself?

Before the Internet, people where limited by the amount of material you could acquire, read, and compare, but with the internet you can compare almost every online retailer, you can read product evaluations from experts, you can compare and shop like never before. You can contact experts, professors, common-folk, soldiers, etc. You can get facts directly, you can analyze events yourself, you can look at the bare numbers, and the bare equations and say I see something wrong, or my local media missed this or that etc. You can ask several top experts questions regarding the information and come to your own conclusion. No longer is the public limited to information presented by major media outlets, you can read dissenting opinions, different opinions, weird opinions, crazy opinions, and every once in a while an opinion that make more sense than anything you've read in the major media.
End result, it is more difficult for big companies to mold the public to buy their products or support government policy because it makes them money. They hate this.

Much of the push for no net neutrality is that many internet service providers want to make sure there is enough bandwidth for all their products, like internet telephony, on demand video services, etc. The only problem is that it will come at the cost of websites, and web servers that can't afford to pay to have their packets prioritized.

If our internet service providers route different packets with different priority and if the packets we want are not on the top of their priority list then technically they are doing a disservice. Why should someone have their packets routed first if both he and I pay the same amount of money, same package, same provider? What's worse is that they can play this little game with websites they don't like. They can make it easier for someone to access one website over another thereby little by little pushing the public towards the website they want you to see.

Intended Audience

2007-09-03T20:23:00.000-07:00

As one can probably tell, many of my recent posts are not really directed towards those who already are doing well in school nor are they directed toward educators or the management of high performing schools. In fact much of my website is directed and has always been directed to those who need help learning and communities who have always been underrepresented in higher education. Of course anyone is welcome to my website, and if it helps them all the better.

I can easily see the irony here, those who need the most help are the ones least likely to own a computer or use the internet. If they do use the internet they probably won't use it to learn how to learn math. Nevertheless, I believe that if I cast a wide enough net, and I cast it frequently eventually the few people I do reach will add up. Even if my opinions are unpopular and extreme if it helps one more kid and/or parent to get his/her act together to go to college, finish college and become a productive member of society then, it is worth it.

Standarized Tests IV

2007-09-03T11:11:00.001-07:00

I realize the previous post might seem extreme, but it is nevertheless useful. We see that the way children study is equally if not more important than how a subject is actually taught. Given that we live in the US and that educators can only play, at best, a limited role in the child's education, it is best to set exceedingly high standards of studying. This is necessary so that when most children fall below the standard, they will be studying at a level necessary to adequately learn the material and/or do well on standardized exams.

This is akin to a negotiation, given that usually one must compromise and give up certain demands, it is best to start by asking for more than what you want. In the process of teaching one will usually always compromise and give up certain standards, so it is best to start the class by asking for more than what is needed.

Standarized Tests III

2007-09-02T09:14:00.000-07:00

Regarding the following article:

School test scores level off as federal standards get tougher

The biggest problem with the US educational system is that, simply because a child sits in a classroom doesn't mean he/she is learning. Anyone can sit in a chair for an hour; daydream, not pay attention nor fully process the information and give the teacher the impression of learning. What educators should want is the child to internally process the information. The US educational system is set up to maximize the freedom given to the child, of course this means the child has the freedom not to do well in school.

Now 2 hours of math and English a day combined with 3 hours on the weekend for a total of 11 hours of math and English. Let us assume the child gets out of school at 3 pm from 3 to 7 pm is spent doing homework and studying, lets assume the child goes to sleep at 10 pm, for a total of 3 hrs of "freetime". On the weekends lets say the child goes to 3 hours of enrichment on Saturday for a total of 9 hrs of freetime, on Sunday lets say 12 hrs of freetime. If you add the freetime you get 36 hrs of freetime weekly, you see this is directly comparable with the 31 hrs spent supposedly actively learning, doing homework, or studying.

The way this "free time" is spent is the most important factor in education. I teach at an afterschool program for children, most of them are of Asian background ranging from the ages of 5 to 17. Here is a typical day:

They do their math and English homework, tutors help them with any question they have. Tutors also check to see if their homework is done correctly. Afterwards they are given a series of practice standardized tests and they are timed, the tests are scored and then the children must redo the test correcting all the missed questions. After that they are given math and English enrichment packets where they practice the concepts learned in class or learn concepts not yet presented in class. The tutors make sure they do them correctly otherwise they have to correctly rewrite any missed question 5 times each, if they miss the questions again they have to rewrite them 6 times and so on. Oh yea, the children go through this "grilling" 6 days a week, including Saturday and starting from 5 yrs old all the way to 17 yrs old. This center even has Standardized exams for 6 yrs old kids, so just imagine a child taking a scored practice standardized exam nearly everyday for 11 yrs, do you think it will have effect?

The only reason such a program works is because parents make the children go, whether the child wants to or not. Also they give the tutors the right to "grill" their sons and daughters, in addition at home they make them study all the time, and by all the time I mean that nearly all of their freetime is spent studying.

Now in regard to summer vacation, what summer vacation? At the center they offer summer math and English classes where they cover 1 month of material in a week, the homework literally takes up all of their free time.

So you see, it has nothing to do with intrinsic capabilities, it has everything to do with just how much parents are willing to do to educate their kids. If the educators want to surpass this plateau then they will first have to make the children "internalize" the value of education, second they will have to make the children want to study correctly everyday, third they will have to make children think like a person who scores high on standardized exams.

Standarized Tests II

2007-08-28T13:11:00.000-07:00

As an addendum to my last post, another thought conditioning technique is something similar to the Christian saying, "what would Jesus do?", but in our case it would be "how would a high test scorer think?".

First one should think, then one make sure that every thought has an element of problem solving, analytical thinking, and reasoning required on standardized tests, then one should ask "how would a high test scorer think?", then one would think through a high test scorer thought process. Just as asking oneself "what would Jesus do?" becomes a habit, asking oneself "how would a high test scorer think?" should also become a habit. Also, the person should take practice exams everyday with the goal of besting your previous score and then one should analyze the test to see how a high test scorer would have answered every question. Then retake the test using the high test scorers thought process.

If every thought is conditioned by this technique, eventually thinking like someone who scores high on tests will become natural and therefore the child will also score high on standardized exams.

Standarized Tests

2007-08-28T10:08:00.000-07:00

There are only two things that really matter in the US educational system standardized test scores and grades, everything else is rubbish. Yet, people make two fallacious conclusions about different ethnic groups regarding test scores:

1. Differences in test scores are immutable.

2. Differences in test scores are due to racial differences.

1. Both from experience and AI arguements most test scores are changeable, you can improve your score on almost any type of test. Like I have said before if thinking is an epiphenomena of the brain and the brain operates according to the laws of physics then it is possible to emulate the brain processes of someone who does well on a standardized test and use it to also do well on a standardized test. Some may ask if it is possible, then why do we have so many people who don't do well on standardized tests? This is a simple question to answer, the reason why people score differently is because we don't have access to the brain algorithm of people who do well. It is not as if our brains come with a firewire or fiber optic data ports, where we can download our operating system to another brain.

2. This is another conclusion people draw from standardized test scores, the problem is that it is based upon John Stewart Mill's logic:

a) If we have two objects the same in every respect except one, then any difference between the two should be due to that difference.

b) if we have two objects different in every respect except one, then any similarity between the two should be due to that likeness.

Most people draw conclusions using logic a) that if we have two people the same in every respect except they are of different racial backgrounds then any difference in test scores must be due to that difference. The problem is how can you tell if two people are exactly the same, except for a racial difference? Even within races people are not exactly the same, so this logic fails to account for more than one difference. There are tremendous differences in the way different ethnic groups approach discipline, consistency, strategy, and mental training. The reason most people downplay such differences is because they are difficult to analyze and quantify.

Logic b) is the one most people downplay, though it is more positive and more useful. It is much easier to assume that two people of different racial backgrounds are different in every respect, and to attribute any similarity in test scores to a likeness between the two people. Obviously this too has problems for how can we determine if two people are different in every respect? Despite the problems this logic is more useful for if we can find the likeness between people of different racial backgrounds that accounts for a similarity in test scores, we can analyze it and help others to raise their test scores.

Studying:

Possibly the most important factor in both grades and standardized tests, the problem is that people seem to confuse the act of studying with actually studying. Any child can stare at a book or half-read a book to give the impression that they are actually processing information, when in reality they may be daydreaming or whatnot. So here is what I do, after they are done studying I say, so you think you really know this huh? I pick out, at random, a question from one of the pages they should have read and processed, if they can't answer it within a minute then they really didn't study. If they can answer then I pick another more difficult question and so on, increasing the level of difficulty until they can't answer the question at which time they have to restudy the book until they can answer any question, of any difficult, at anytime under 1 min.

Same technique with standardized tests, so you think you can do well on these tests huh? I pick out a series of difficult test questions, which they have not seen, and give them only 1 min per question (about 30s less than required) if they can't answer them all correctly within the alloted time, then they really don't know the test.

It all comes down to whether the child wants to learn or not, it is almost impossible to teach a child who doesn't want to learn while, it is relatively easy to teach a child who does want to learn. Simply because a child sits a in a classroom doesn't mean he/she is learning, simply because a child goes through a program doesn't mean the child has internalized the program, you want the desire not just the action. It many respects the value of education is like an ideology that children must learn and internalize, the problem is that unlike dictatorial states, it is easy in the US to not value education.

High School Exit Exams

2007-08-24T07:04:00.000-07:00

In regards to the following article:

Students strive for passing grade in exit exam

The negative tone of the article is meant to emphasize just who is it that is failing the test.

People who believe in the power of "common sense" always but always in one way or another believe, "anyone can pass this test, why don't these kids, they must be idiots or defective". The problem is that "common sense" is highly dependent upon where you live, and what time you live. At one time it was "common sense" to believe that diseases were brought upon by God trying to punish people, it was "common sense" to believe the earth was flat, it was "common sense" to believe time was absolute etc. Also common sense is highly dependent upon where you live, it maybe common sense for a sailor to know where the star Polaris is while it may not be for a land lubber. It may be common sense for someone raised in a household where academic achievement and competition is normal to know how to study for a standardized exam. These are not meant to be excuses but explanations.

Unlike the sciences, education is one subject that cannot be approached in a reductionist manner. Educators are always looking for that one program that will magically raise the number of children who pass, when in reality one needs a holistic approach. By holistic I mean you will need to take the child's economic situation, cultural beliefs, approach to discipline and consistency, peer group, parents, study techniques, activities outside of school, and mental training techniques all into account. If any one of these parts is lacking the outcome will not be as good as it could be.

Beneficial cultural values should be taught, retaught and reinforced from a young age. Standardized exams should be given everyday from kindergarten onward. In kindergarten the educators should simply get the kids used to the test and working under timed conditions. In the subsequent grades the educators will slowly increase what is expected from the children, while at the same time, children will be encouraged to think about the standardized exam outside of school. The goal will be to make taking timed tests as something normal for the child, much akin to reciting the alphabet.

Thinking in the patterns expected in the exam should become a way of life, every thought, every action, everyday should be directed towards mastering the subjects and the test taking techniques needed to pass the exam. Also, the child will continuously think of ways to improve the aforementioned. Problem solving, analytical thinking, and test taking tricks and techniques should become part of the child's thought process. Their parents and peer group should also reflect this thinking otherwise the child will quickly fall away. The child will think about this test and other standardized exams all the time, while on the bus, driving a car, listening to music, or watching TV, mastering the test(s) will become akin to the air they breath.

Finally we need patience. People want results yesterday, the problem is that education doesn't work that way, it takes time to build the foundation upon which one can achieve success. Also it takes time to modify the system to achieve maximum results, it also takes time to re-engineer cultural values.

The most beneficial cultural beliefs implicit in the cultural practices of the typical American are:

1. It is not enough to say, one must do.

2. It is not enough to do, one must do it correctly.
It may not be possible to do it correctly the first time around, so it is best to always improve, with the goal of one day doing it correctly.

3. It is not enough to do it correctly, one must finish.
Many people say, do, and do it correctly but never finish. Also it is best to correctly finish everything on time.

4. It is not enough to finish one correctly done project, homework assignment, or correctly read book, one must be consistent in finishing whatever one begins.

5. It is not enough to correctly finish anything one begins, one must have a strategy, path, or system to follow. Basically one must have a set of goals and should direct their actions towards them.

6. It is not enough for one person to follow the above steps you need a sizable portion of the population following the steps.

7. It is not enough for a sizable portion of the population to follow the steps for one generation, the population must follow the steps generation after generation.

To sum up: Everything in your life must be rational, analytical, detailed, thorough, consistent, and timely.

Climate Change II

2007-07-31T08:32:00.000-07:00

I have found another great website responding to anthropogenic climate change skeptics:

Brian Angliss:

A Thorough Debunking

John G.

Climate Change

2007-07-28T10:30:00.000-07:00

I have avoided the topic of climate change because of its political ramifications, but I felt impelled to reply to all of the anthropogenic climate change skeptics out there.

Much of the popular media has not presented either the basics of anthropogenic climate change or a balanced analysis of pro and con arguements. Much to popular media's dismay the pro arguements are much stronger than the con arguments, the problem is that we rarely hear any response from climate scientists to the con arguements presented in popular media, leading people to think such arguements don't exist, but they do.

First we start with a website operated by reputable climate scientists that present nearly all the facts dealing with climate change. They present the papers, the theories, and the arguements for anthropogenic climate change. They also present arguements against anthropogenic climate change and rigorously show how nearly every such argument is flawed.This is possibly the best website on climate change:

Real Climate:
http://www.realclimate.org

The website is extensive so here is a link for beginners:
http://www.realclimate.org/index.php/archives/2007/05/start-here/

Here is a website that goes straight to the core of the matter, presenting powerful and devastating counterarguments to nearly every anthropogenic climate change counterargument:

How to Talk to a Climate Skeptic:
http://gristmill.grist.org/skeptics

John G.

Truth and Verification

2007-06-24T11:23:00.000-07:00

There may be many positions on truth in this installment I will focus on two the Hegelian and the existentialist. The Hegelian view holds that there exists a God-like point of view from which it is possible to reason about the world, in other words, absolute truth is possible. The existentialist holds that we are finite beings as such a God-like point of view is not possible. Both are right but, the reason why is contained in neither.

I think Karl Popper gave us an answer. Karl Popper believed that humans are capable of attaining absolute truth but, the problem is verifying that a statement is true. This statement shows that both the Hegelian and the existentialist view are correct and both incorrect.

I suppose a Hegelian could argue that a God-like point of a view presupposes a God-like method of verification, in which case the Hegelian must show that such a method of verification is accessible to finite beings (like us). Until such time we must accept some tenets of the existentialist view, our methods of verification are finite as we are finite beings.

Let us apply the above to physics. The above statements imply that though we may have the ideas and theories that will turn out to be true or close to true, we will not be able to verify that they are true or close to true, ahead of time.

Necessary But Not Sufficient Part III

2007-06-15T12:04:00.000-07:00

I don't want to give the impression that any theoretical physicist is doomed to failure rather I wanted to give an explanation as to why progress in science is not linear and why only a couple of physicists make breakthroughs. Also I wanted to make clear that it has nothing to do with competency, simply because you ended up working on a theory that turned out to be false doesn't mean you are an incompetent physicist.

Once again I must reiterate the probability of making a breakthrough is higher if you try than if you don't try. In lieu of future knowledge as to which ideas or theories will turn out to be correct the best we can do is use critical thinking to determine which theories or directions have a higher probability of being correct. In the very least we can determine which theories or directions that we think will be fruitful. Not every paper will lead to a breakthrough but it will clarify some point of contention or simply show what can be done with certain starting assumptions. On the positive side, someone may have already published a paper with an idea that one day will work.

I take Edison's philosophy to heart after failing nearly 10,000 times to find a light bulb filament that won't burn some news reporter asked him, "how does it feel to fail 10,000 times" Edison said "I haven't failed 10,000 times, I have successfully found 10,000 ways that won't work". Later on he found a way to not burn the filament and yet have the filament glow. We have many physicists who have successfully found ways that either won't work, have trouble working, or one day will work. All in all each paper serves a purpose and each is our best effort to find the truth, or an approximation thereof.

Necessary But Not Sufficient Part II

2007-06-14T11:16:00.000-07:00

Sometimes people believe that sheer intelligence will yield a correct theory in physics, people believe that intelligence gives people the ability to "derive" or "see" the correct theory of physics.

Though ability does help, the biggest problem with this belief is that there are many internally consistent, plausible, and complex theories that can describe or hopefully describe the same phenomena and yet can recover the classical theories of physics. Sometimes plausible theories require much work to develop, sometimes they are developed to the point where an insurmountable problem arises or a contradiction arises, this is another problem. Sometimes the theories yield falsifiable predictions which require new technologies or funding to test. As one can see without the benefit of future knowledge as to which theory will lead to correct predictions, even the most intelligent person on earth can spend his/her days working on a theory that will turn out to be false.

If there was only one logically, mathematically possible theory, it would be easier to develop the "right" theory. The problem is that we tend to view progress in science as a linear process where each proceeding theory is seen, in a loose manner, as obvious and as the only theory logically consistent with the older theory. So we fall under the impression that nearly every theory was obvious, if only the people back then could "reason" or "think" correctly. This is only possible with hindsight for the criteria for correct reasoning, in a certain field, is constrained by the knowledge/insights/results available at the time. The reason the "correct" path was not obvious to people of the past is that at the time what was considered obvious was completely different.

John G.

P.S, P.S.

2007-06-07T10:21:00.000-07:00

As a post script to post script I would like to say, that there are no guaretees but there are probabilities. Some people might reason that if there isn't a guarantee of a breakthrough then why should they make an effort to study theoretical physics? The reason is that the probability of making a breakthrough is much higher if you do try than if you don't try. The probability that you will make a breakthrough is higher if you study hard and go to a good university, the probabilities are higher if you try to develop new ideas or at least new directions.

Sometimes the physical concepts, mathematical concepts, and the technology are available to make a breakthrough, someone simply has to reorient their thinking to see it. Sometimes neither the physical concepts, mathematical concepts, nor the technology is available, the problem is that we as people, constrained by results/insights/knowledge of our time, cannot determine which of the two scenarios obtains. This is why it is crucial that we try, for our attempts and our mini-breakthroughs will eventually add up possibly allowing someone in the future to make a major breakthrough.

P.S.

2007-06-05T00:13:00.001-07:00

As a postscript I should mention that not all ideas are equal, some ideas have a higher probability of being closer to truth than others. My point is that we must strike a balance between complete stifling of free thought and treating all ideas and theories as equal. This is why it is so difficult to develop something new, the idea must be "irrational" enough to be new but "rational" enough to be plausible.

Necessary but Not Sufficient

2007-06-04T19:14:00.000-07:00

People often believe that by simply mastering existing theories and concepts that somehow they will assuredly discover or create something new. Though mastering previous theories and concepts is necessary, it is not sufficient for developing something new. It is one thing to master that which already has been done, it is quite another to discovery/create something new.

The problem is that it is not possible to rigorously derive new theories from old theories, in other words it is not possible to discover/create something new thinking strictly in terms of old structures of thought. For example it is not possible to rigorously derive Quantum Mechanics or General Relativity from Classical Mechanics, though it is possible to derive Classical Mechanics from QM and GR. So, the process of discovery/creation can't be too rigorous simply because the new theory contains ideas and concepts not contained in the old; you can't extract concepts that are not implicit in the fundamental assumptions of the old theory. Sometimes these new ideas may appear irrational, if reasoned from the perspective of the old ideas. A strange inversion occurs the old ideas become irrational when the new ideas are shown to be valid. On the other hand, the reasoning can't be too loose, it must be possible to extract the old theory from the new. This is why high intelligence does not guarantee discoveries/progress; the path to the new theory is not simply a complex derivation from the old, in other words it is not linear. To be fair innate ability does help, though lack of innate ability doesn't imply a lack of discoveries/progress.

Obviously this implies risk because the ideas have not been shown to be valid, the chances you will turn out to be wrong are high. The reason why we take this risk is because the old theories sometimes prove to be inadequate, this is not because previous physicists were incompetent rather, it is because we have information/results/insights they didn't have. Sometimes the new information/results/insights shows there is a problem with their theory. There may be elements of truth in the old theory, but these elements are constrained by the information available to their creators.

Another problem is that people may not want to question old ideas/theories on the basis that old ideas/theories have worked so well and are so well reasoned that they must be true. Sometimes people don't question old ideas/theories on the basis that if people "smarter" than themselves couldn't improve upon the theory, neither could they. At other times people believe that everything that could ever be thought of has already been thought, so what's the use? Sometimes people believe something to be impossible hence they don't consider it further. Some people believe it is not their position in life to develop something new, that is left to "special" people. Others simply don't want to make the effort. Finally any new idea brings the risk of the unknown and of being shown wrong hence, many people do not want to take the risk. The entire paradigm of thought weighs heavy on people's shoulders any attempt to cast it off is difficult.

Many people wish for a life or career of guarantees; guaranteed success, guaranteed position, guaranteed wealth, and for the physicists, guaranteed truth (or approximation thereof). The problem is that there is none; you may spend your entire life working on a theory only to have it turn out to be wrong, you may be the most intelligent person on earth working on what appears to be the correct direction for a new theory only to have it destroyed in an instant.

These prospects sometimes lead people and sometimes entire cultures to rarely take risks, to rarely think of something new, or to even pursue new avenues of thought. According to them, it is much safer to work with theories and ideas that are already established, especially if one desires guaranteed results or success. Sometimes entire societies inadvertently stifle free thought, especially if the cultural structures of thought implicitly impair the development of new ideas. This usually takes form as a belief in certain unquestioned assumptions that may or may not be evident, sometimes it is a belief that every idea must be rational (in common parlance it must make sense), the only problem is that what is considered rational is constrained by available information/insights/results.

To sum up it is necessary to master established theories but it is not sufficient to make new discoveries.

Study Time

2007-06-02T23:25:00.000-07:00

People often get the mistaken impression that by simply sending a child to SAT prep courses or intensive study courses, in any subject, that somehow, magically, the child will show significant improvements in performance. The problem is that 1 or 2 hours of intensive study per week cannot substitute for 1 or 2 hours of intensive study over an extended period of time.

The child may show some improvement if he/she studies 1 or 2 hours per week but, if you desire your child to show significant improvement, he/she must study intensely everyday. In addition your child should strive to improve their study technique in comparison to the previous day. They should strive to understand more or understand things more deeply, they should strive to identify their weak spots and work on them until they become strong. They should strive to understand the logic behind the subject, to understand the subject from a broader perspective, and finally they should strive to improve the very way they improve their study technique.

As you well know sports is my favorite analogy; how can you expect to become a better baseball, soccer, or tennis player if you only practice intensely 1 or 2 hours a week? Also, when you do practice you don't practice with the intent of practicing better than you did last time? Eventually you will reach a plateau of performance that has nothing to do with genes or talent. The only way to break through that "wall" is by pushing yourself to be better than you were last time, to constantly seek ways to practice better, and finally to realize that practicing intensely everyday yields far better results than practicing intensely once or twice a week.

Math and Physics II

2007-05-24T15:17:00.001-07:00

What the previous post implies is that there may exist an area of mathematics that can give rise to "new physics", the only problem is how do we go about it? The basic structures of thought and language have been developed to operate in one direction only, from physics theory to mathematics, this makes talking about or even thinking about the opposite direction difficult. I'll see if I can elucidate this later.

Math and Physics

2007-05-16T11:07:00.000-07:00

Physicists make the assumption that for every theory of physics there exists mathematics (existing or uncreated) that can describe the theory of physics. In reality the construction of a theory or an addendum to an existing theory is guided both by physical and mathematical considerations. In general terms the theory guides the mathematics while the mathematics sometimes guides the theory.

Though one may start reasoning from strictly physical considerations eventually one also uses reasoning from strictly mathematical considerations, sometimes the mathematical considerations have tremendous influence upon the physical considerations. So, if there exists mathematics to describe every physical theory maybe there exists physics to describe every piece of mathematics. Physics can be treated as a universal axiomatic system from which mathematical concepts originate, hence every piece of mathematics will have some connection to physics.

I will post more on this later.

John G.

Prestige and Education

2007-03-01T12:49:00.000-08:00

There has been much discussion, both in talk radio and newspapers, about the supposed overemphasis of national rankings when choosing a college or university. Contrary to what many may say, national rank and prestige does matter, especially in a competitive environment.

Rank matters more when there exist objective or at least partially objective measures/metrics by which to categorize people, this holds particularly true in the sciences, engineering, and law. Rank is not as important in fields where such metrics either don't exist or are not important, you can always argue that since objective measures don't exist objective categorization is not possible.

Rank is most important when applying for jobs and in choosing post-undergraduate education. What is most important is the rank of the school's PhD program. In the sciences rank offers significant advantages; peers within your own field take you more seriously, there are more and better research opportunities along with more funding for research, you interact with people at the top of your field on a daily basis, and you have more/better access to equipment for experiments. In addition rank helps you obtain professorships in universities with good research programs.

The ultimate measure of talent for a theoretical scientist is the quality of his/her published papers and that of an experimental scientist, the quality/results of his/her experiments. After a certain level, the quality of performance matters much more than the rank of your schooling, though the rank of your schooling may in some part determine the quality of performance. Also, the rank of your schooling may determine the opportunities available by which you can perform in the first place. Though you can get a job, even a good job, and do good research with degrees from lower ranked schools, you will have to prove yourself much more and with less opportunities to be considered equal.

Though rank is not everything, it does count for much, especially if you desire to be at the top of your field. In my opinion I would say, go for it, aim for the number one school. Even if you aren't accepted into the number one school, the time and dedication you put into becoming competitive will take you much farther than if you didn't aim for the top school.

Here are the rankings:

Phyiscs

Physics Elementary Particles/Fields/String Theory

Mathematics

I will leave you with a quote from Arthur Miller's play "Death of a Salesman"

He [in reference to Willy Loman] had a good dream. It's the only dream you can have - to come out number-one man.

The Power of the Internet

2006-11-30T13:34:00.000-08:00

The true power of the internet does not lie simply in the access to nearly all of human knowledge but also in the access to people who know how to answer questions regarding that knowledge. In addition, access to people who help others discover that a certain branch of knowledge exists, or that a certain idea exists is equally important. Knowing that a realm of knowledge exists is almost as powerful as actually having the knowledge available.

The internet allows even the most economically disadvantaged person, and/or the least educated access to some of the best minds on earth. Think about that, the best minds not only in their locality, but on earth. The average internet user can also gain knowledge of some of the best sources of knowledge, as ranked by experts and other average users. No longer are we limited by what we see on TV, hear on the radio, read in the newspaper or magazines, or what our local libraries (if any) can afford to pay for. The average internet user has access to the same materials or at least knows about said materials as do top experts and elites.

Before any of this can happen, though, the average internet user must become aware that the internet can be used in this manner in the first place. What good is access to people who can answer your question if you don't know they exist, or that their realm of knowledge exists, or that you can use the internet to access them?

Our knowledge of the world was formed and shaped by those who could afford to pay for or had the power to communicate with large masses of people, as such our knowledge was limited and indeed manipulated to serve certain ends, in the very least we had limited access to alternative sources of knowledge which might have helped us form a more thoughtful opinion.

The biggest difference between old media and new media is that the average person can, with relative ease communicate with thousands if not millions of people. Ideas, opinions, and knowledge can spread based solely on merit and not on how much money they generate, or how much power they give to a certain groups or people, or how well they accord with the reigning paradigm.

Thinking about Thinking

2006-10-20T15:20:00.000-07:00

It is still undecided whether our mind is simply a machine. Quantum mechanics allows for indeterminism, hence physics may allow our minds to break deterministic behavior, if quantum effects are visible at the scale of our brains. Yet to say that our minds follow no patterns is incorrect, for our thinking and behavior does follow certain patterns.

If both the thought and behavior of our ancestors did not follow any pattern then survival becomes difficult hence, one could argue that evolutionary pressures select for thought and behavior that follows certain patterns. In fact, interactions between animals, to a certain extent, depend upon the predictability of behavior and in the case of humans thought as well. Since evolutionary pressures at human scale are highly deterministic, one could argue that certain algorithms loosely govern these patterns, it is these algorithms or patterns we want to emulate.

Personally, I believe that the origin of consciousness is an emergent structure of a complex dynamical system, namely our brain. This would explain why both our behavior and thought follow certain patterns, yet allows us to break old patterns. What makes our dynamical system special is that our system is in constant rapport with an external system namely, whatever is outside of us. As such it is constantly being perturbed to follow certain paths as not determined by itself yet, depending on the state of our internal system the way we follow the path and for how long is not predictable. We can never perfectly emulate another system because we do not have perfect information about that other system and its surroundings yet, we can emulate the system with more and more accuracy given more information we gain about that system, and its surroundings.

John

Correction

2006-10-18T10:47:00.000-07:00

Physics was considered before Aristotle, but it was deemed impossible since Parmendies notion of the entity was immovable. What Aristotle did do is show that motion is possible thereby making physics a possible science. Though Aristotle was wrong as to the principles of motion, he made it possible to study physics as a true science.

Stephen Jay Gould

2006-10-17T00:24:00.000-07:00

Lets consider a passage from Stephen Jay Gould:

Q: In your book you examine the inability of baseball players to hit .400 anymore and argue that it's because hitting has improved.
A: The overall batting average has been about .260 throughout the history of baseball. But the variation around that average has shrunk. It's at least plausible that variation declines because play improves. A batting average is a comparison between hitting and pitching. So if everybody's improving, as long as they improve at the same rate, the batting average will remain constant. But it gets to the point where everyone is so good that there's just not much variation anymore. Hitting .400 in baseball is a good example because there's a "right wall," if you will, of human limits. Given how our muscles work, there's just so much that the human body can do. There will always be a few individuals who, by dint of genetic gifts and obsessive commitment and training, will stand close to that right wall. That's where Ty Cobb was in 1911 and where Tony Gwynn is today. But there is this limiting wall. What has happened in baseball is that all aspects of play have improved enormously. Back in 1911, average play was so far inferior to where Ty Cobb was that his batting average could be measured as .420. Today, Tony Gwynn is just as good, maybe even closer to the wall than Cobb was. But the average player has improved so much that Gwynn's performance -- equal to or better than Cobb's -- is not measured as high.

We can see that innate ability played a much larger role in baseball's past because the difference between the gifted player and the average player was so great but, since training techniques have improved as has our baseball farm system, the ability of the average player rivals the ability of the player with innate ability.

This is analogous to what I saw occurring in the sciences the only problem is what constitutes training techniques for the mind? This is not to say there are no gifted people for there are people who have an innate ability to work in certain fields but, what I am saying is that just like sports we can improve our ability to perform in a certain fields with proper training. This has been given empirical backing in the August 2006 issue of Scientific American:

Scientific American

This also does not imply we should not encourage gifted children to develop their abilities, for just as in sports children with innate abilities should be encouraged throughout their lives to reach their maximum potential. People also have to realize that gifted children do not necessarily become gifted adults, because by the time they reach adulthood many of their "average" cohorts have also improved their abilities. One only need look at the New York Times Article:

Prodigy Puzzle

The problem is that groundbreaking ideas don't occur in a vacuum, what good is it for Barry Bonds to hit a homerun (with no one on base) if the Giants are down by 5, for all his innate talent you need the entire team to perform to win a game. I believe the same thing occurs in science, much of the time ideas that advance a field dramatically are the culmination of years of research, and without that research groundbreaking ideas are not possible.

Newton's laws of motion were possible only after Descartes proclaimed only material causes may affect material objects. In fact the entire idea of Physics as a separate science was only made possible after Aristotle defined its boundaries. Calculus was made possible only after both geometry and algebra were well established. Einstein's General Theory of Relativity could only be rigorously formulated after Tensor Calculus was developed, which by necessity required Newton's or Leibniz's formulation of Calculus. Without the prior developments, Newton or Einstein would have to develop the entire background knowledge necessary before they could even think of formulating their ideas correctly.

Besides background knowledge one also needs the "right" ideas, this is where individual creativity and thought comes in. If one reads the above article "Prodigy Puzzle" one finds that neither William Shockley or Luis Alvarez were deemed prodigies yet both won Nobel prizes, while none of the Termite protege's won a Nobel. This goes to show that sheer intelligence does not a Nobel Laureate make, one needs ideas, especially the "right" ideas.

John

Nobel Prizes

2006-10-11T00:22:00.000-07:00

I would like add that my previous comment was not intended to detract from Mr. Kornberg's spectacular achievement. That is a once in several lifetimes achievement, and any elite scientist could only wish to one day achieve as did Mr. Kornberg. All I was saying is that his achievement isn't due entirely to his genes.

Kudos Mr. Kornberg

Nobel Prizes and Genes

2006-10-05T23:19:00.000-07:00

Looking at the recent spate of Nobel prizes one can see a father who won a Nobel and a son who won a Nobel. The Son Roger Kornberg won the Nobel for Chemistry and his father Arthur Kornberg won the Nobel for Medicine.

Many may say that this shows the powerful influence of genes in science but, if you look deeper you will see that there are many other factors at work.

One is subjectivity, how exactly does one judge which accomplishments warrant a Nobel prize? There are so many fields in one discipline and so many achievements how do you know which one achievement is the most important?

Besides the subjective factor, we are missing one other obvious factor, many of the Nobel families did work in related fields.

Check it out at the Nobel prize website (scroll all the way down):

Family Nobel Laureates

Its interesting how nearly all of the families who share nobel prizes are for the same if not related fields. One reason is because a parent at the cutting edge of a field is in a good position to guide the education of their child from an early age. Not to mention that if the child decides to follow a similar path, the parent will know exactly how to guide the child's research. Doing cutting edge research isn't simply solving problems in a field, rather it is solving the right problems in a field. The key thing is what are the right problems? Since the parent was and probably still is at the cutting edge of the field he/she will know which problems or directions are crucial for that field. Combine this with the fact that from an early age the child was guided with expertise in that field, he/she's got a good chance to solve the right problem.

My old adage also applies, how is it that out of all the brilliant researchers only a select few receive the Nobel? Are they the most brilliant researchers, smarter than everyone else in their field? What about all of the other brilliant researchers who have unfortunately not asked the right questions, or have worked on a theory that turned out to be false, or what if your achievement was not deemed worthy of a Nobel? The very fact that most brilliant researchers don't win Nobel prizes goes to show that sheer brilliance doesn't guarantee success, you need ideas and luck.

Book TV

2006-09-24T00:22:00.000-07:00

Today, Sept 23 I was watching CSpan's BookTV. The show dealt with racial disparities in health care, presented by the American Enterprise Institute. One of the guests explored the effect of "g" on health care disparities, she stated that cognition is not made up of several parts, only "g" matters, which is true. In addition she stated that racial disparities in IQ are very stubborn. Yet, nowhere did she address the fact that if "g" is even partially determined by genetics, then "g" is partially an algorithm.

Most advocates of a hard "g" theory believe that "g" is genetically determined, as such they believe that the mind is in the brain, and processes in the brain constitute the mind. Yet the brain is governed by classical physical laws (quantum mechanics and general relativity have little to no effect) hence it functions like a machine. Since the brain is a machine and processes in the brain constitute the mind then guess what the mind is a machine as well. As such it is an algorithm, hence if one can perform the actions of a universal Turing machine then one can emulate the other algorithm, in principle.

Some advocates of a hard "g" theory, may state that we are more than machines. This implies our mind is not wholly material, hence part of our mind is not determined by the processes in our brains, hence part of "g" is not "in" our brains. Well then where is it? If we are not strict materialists then we must admit supernatural effects on "g", hence "g" cannot be wholly determined by genetics. This also implies that the scientific method may not answer all questions relating to "g".

How the Elite Train

2006-09-22T22:44:00.000-07:00

Just as in sports the creme de la creme in the sciences train from childhood. One only need look at the background of any well known physicist at an elite university. Many have won physics olympiads and mastered undergraduate physics while the regular joe was a freshman in high school. Many graduated with PhD's and have done research all before the average joe has even finished college.

So the lesson here is to start young, if you want your child, or if you want to go to an top ranked university then you must start young.

I suggest we employ the youth sports model, afterschool training in physics and math will yield tremendous benefits. Also we need to build up the social support structure that values this type of training, just as in sports. Without support structures it becomes difficult for the child to continue training if he/she perceives that his/her peer group does not value what they are training for. (why do you think high school football players get so much attention)

Granted it is easier for people to appreciate sports because it functions as entertainment, is easier to understand, and constitutes healthy physical activity. Yet, if we get enough people to value mental training as well as physical training we can develop formidable minds.

John G.

Memorization

2006-09-20T23:39:00.000-07:00

Over and over I hear statements similar to "memorization is not a substitute for learning the material" with the implications that somehow memory is completely separated from learning. Here is my response, try learning the material without memory.

Imagine taking a test in Newtonian physics when you can't remember Newton's 2nd Law, how about taking a Calculus test where you completely forgot what an integral is, or what integration by parts is. What about trying to analyze an event in history without remembering what actually occurred, how about writing an essay where you forgot how to spell simple words. Try programming in any computer language without remembering the commands.

Now of course this doesn't mean that learning is a simple memorization of facts and problems, that is an extreme view, but on the other hand learning in and of itself does not exclude memory and memorization. Memorization provides the raw materials of what we know, but, understanding makes those raw materials become something known.

I propose a balanced view of memorization; understanding is more important than memorization yet, learning something is not simply understanding it, for without memory there is no "it" to understand.

Sports and IQ

2006-09-15T15:30:00.000-07:00

The high IQ individual holds the same relationship with the average person as does a sports star.

The average person can do nearly everything a sports start can do, except the sports star can do it faster, stronger, or with more finesse. Some of these qualities may come about from training and some from genetics. The same holds for intelligence, the average person can do everything a high IQ individual can do except the high IQ individual can do it faster with more finesse, and just like sports some of this ability may come from training and some from genetics.

The key point here is that despite existence of gifted people, intelligence and IQ are not static.

John G.

IQ, Training and Time

2006-09-14T19:32:00.000-07:00

Many may state, if it is very difficult to extract the cognitive algorithm of a high-IQ individual then for all practical purposes it is not possible to emulate their thinking, hence IQ amplification or enhancement is not possible.

Though one may not be able to extract the exact cognitive algorithm of a high IQ individual, there are many properties of problem solving that are general to any cognitive algorithm. In fact an entire field of study is dedicated to this, it is called heuristics.

Others may state anecdotal evidence demostrating that such enhancement is nearly impossible. The key thing about my argument is that if one is a strict materialist, meaning that only material objects may affect other material objects, then one is forced to conclude that if the mind arises from the processes in our brains, and our brains are physical machines then our minds are machines as well, as such one may be able to emulate it in principle.

Since obtaining the algorithm is very difficult our only option is to instead learn the general problem solving techniques general to any cognitive algorithm. Therein lies the difficultly, because to master a technique requires time and the more time you spend mastering it the better you get, hence a person who has spent nearly their entire life solving problems and mastering problem solving techniques will have a tremendous lead on someone just learning problem solving techniques. As such the ability of the novice to solve problems, even after they have trained, will be much less than the ability of someone who has trained their entire life. This is why it is so easy for people to solve problems in adulthood, if they have practiced solving problems and mastered problem solving techniques in childhood.

This of course does not downplay natural ability, because not all native cognitive algorithms are equal, there are people who's native cognitive algorithm is better geared to solving problems, hence they will have an advantage, these people are known as gifted. One can close the gap with proper training and practice, in addition one can emulate the "gifted" algorithm though it might take more time to solve a problem. These advantages really only make a difference at the highest levels of a field, similar to sports.

Yet, simply because one's native cognitive algorithm is optimized to solving problems and understanding concepts within a certain paradigm, it does not necessarily follow that the algorithm is optimized to create new paradigms. This is why despite the abundance of brilliant and gifted individuals working in a field, new ideas and paradigms are rare.

John G.

The mind

2006-08-05T11:49:00.000-07:00

If the mind is "in" the brain and the structures of the brain including the instructions to modify the connection between different parts of the brain are encoded in our genetics either as a DNA sequence, a process guided by a combination of DNA sequences, or a combination of DNA sequence combinations and external biochemistry (the construction of the brain in the fetus must come from somewhere), then we may conclude that the instructions for building a self-conscious machine exists within the interactions of DNA and external biochemistry. Hence we can program a sufficiently powerful computer to implement these instructions to build a self-conscious machine.

John G.

IQ in General

2006-07-31T21:33:00.000-07:00

People tend to think that a barrier to breakthroughs in science is IQ, or sheer intelligence. Lets consider physicsts for example, people seem to think that simply because a physicst has a high IQ or is brilliant somehow he/she will have direct access to the mathematical formulations of the laws of nature, but if you look at history you'll see otherwise.

Just how many brilliant physicsts worked on "ether theory", Rutherford's model of the atom, or on Bohr's theory of the atom, only to find out later that they were on the wrong track. It couldn't have been that only Newton, Maxwell, Einstein, etc. were the only competent physicsts of their time, there must have been hundreds if not thousands of other equally brilliant minds working on similar problems. So what distinguishes Newton, Maxwell, and Einstein from regular brilliance? It wasn't sheer intelligence, but ideas. They had the right ideas at the right time, what does this mean?

They lived at a time when the nacent ideas which were to become groundbreaking theories reached full maturity within their thought. This means two things; the ideas which reached maximium maturity in their thought existed in a certain form before they created their groundbreaking theories and they had the insight to see how to unify these ideas in a coherent and consistent whole.

It almost works in a dialectical process they (Newton, Einstein, Maxwell) could see/create the unity "above" the different ideas. Take note the "unity" occurs "above" the ideas, or better said outside the ideas, outside the old paradigm that's the key. Very rarely has a groundbreaking theory come from nowhere, most groundbreaking theories are firmly based on the hard work of people before oneself, they developed the nacent ideas from the old perspective to a point where someone with an open and creative yet rigorous mind could see the unity behind the ideas, from a new perspective.

Nearly everyone one of those physicsts relied on previously existing ideas to construct their new theories, so we see that groundbreaking theories require more that sheer intelligence, or research, or brilliance, they require philosophical maturity.

John G.

IQ and Genetics III

2006-07-03T00:18:00.000-07:00

I believe that the mind is more that just a complicated machine, the very fact that some part of IQ is due to environment alone and the rest genetics (which can be emulated) goes to show that the mind can't simply be a machine. It appears as if the mind is both material (machine/genetics) and immaterial (environment).

Though it is possible to emulate the machine portion of the mind it may be impossible to emulate the immaterial portion of the mind. It is the immaterial portion of the mind that may distinguish geniuses from "normal" people. What exactly is the immaterial portion of the mind? The functioning of the brain from a strictly materialist point of view is understood to some degree, but the workings of the immaterial portion of the mind is to a large extent unknown.

The idea of emulating at least the superficial aspects of a mind does have benefits, it seems that not only does the brain strengthen its ability to support certain types of reasoning, but the immaterial portion of the mind itself also strengthens its ability to understand and carry out new types of reasoning. It appears as if the immaterial portion of the mind can "unify" itself with the immaterial portion of the mind of former geniuses, though it may be of no use if the reasoning processes of past geniuses where adequate only to solve problems from the past.

John G.

New mental exercise

2006-06-28T00:32:00.000-07:00

I think I may have developed a new mental exercise. A new aspect of IQ previously ignored revealed itself, the ability to "learn" new material. I wonder if the habit of understanding new material can also be cultivated and strengthed. It seems as if children develop the habit of understanding new material when they are constantly challenged to do so and as we grow into adults we are challenged less and less hence this habit falls by the wayside.

So the new mental exercise will be to "understand" or "learn" a new idea, technique, or event everyday. This is a little vague because how do we know if the thing is new? I'm thinking that this new idea should be something unrelated to our daily ideas or thought processes. For instance if we study physics all day then a good canidate for learning a new idea should come from art or music. If the day before our new idea came from art or music then the new idea for the next day should come from politics and so on.

We should try to "learn" as many ideas from as many different fields so that our minds will be in habit of understanding and learning new things. We can even specialize in one field, we can challenge ourselves to ask deep questions from that field that haven't been addressed.

John G.

IQ and Genetics II

2006-06-14T23:55:00.000-07:00

I think I should add to my previous statements regarding IQ. Given that if IQ is partially or even mostly genetic then it implies that the part of the brain/mind responsible for general cognitive ability is simply an algorithm.

The issue will then turn to the ability learn and execute the algorithm. Computer science states there are certain basic computational requirements to emulate another machine, basically the machine must be a Universal Turning Machine:

Universal Turning Machine

Hence any human capable of performing the actions of the Universal Turing Machine will be able to reason at the highest IQ level. Of course in reality the algorithm will be tailored to humans and will not be in binary, but the above argument shows that this is theoretically feasible.

Another question that may arise is; if it is possible to emulate the cognitive algorithm of anyone else, then why aren't there more geniuses? The quick answer is because we don't have the complete cognitive algorithm of any genius. In fact it may be impossible for the genius him or herself to explain their own cognitive algorithm, for it would require a meta-algorithm above and beyond their own cognitive algorithm which falls victim to Godel's incompleteness theorem. The best we can do is read their thoughts in their journals, diaries, and notes, which give us a partial insight into their cognitive algorithm.

Some might ask if it is possible to emulate at least partially the cognitive algorithms of others then why are there so many people with low IQ's? Since we cannot load the algorithm via a CD-ROM or a DVD-ROM into our minds we must content ourselves with guessing at the cognitive algorithm and then trying to execute that algorithm. Since we are really emulating another mind it will be very computationally demanding to input and execute the algorithm. As such it will take time for our brains to make themselves efficient at executing the partial cognitive algorithm.

John G.

IQ and Genetics

2006-04-20T18:33:00.000-07:00

Those who claim that IQ is mostly genetic are making some serious implicit assumptions with some far reaching consequences.

First let us define what IQ means:

IQ:
The measure of intelligence as given by specific tests.

The only ambigouous concept in the previous sentence is intelligence, so we must define it:

Intelligence:
the capacity to acquire and apply knowledge, or the facutly of thought or reason.

The last definition is most revealing for thought or reason is a part of the mind, hence intelligence is also a part of the mind, so IQ is a measure of this part of the mind. Now what does it mean for IQ or intelligence to be mostly genetic? It means that intelligence is mostly determined by the structures and processes in the brain, because this is the only way genetics can possibly influence intelligence. There is an implicit assumption in the last sentence, namely that the mind is in the brain, for if the mind were not in the brain then how could genetics possibly alter it? The brain is simply a physical object hence, it obeys the laws of physics, as such it is nothing more than a very complicated machine. Since the mind is in the brain and brain is nothing more than a machine, the mind is nothing but a machine or an algorithm. Since IQ is a part of the mind and the mind is an algorithim or machine, IQ is nothing but an algorithm or machine. Hence, in principle, anyone can learn this algorithm and "reason" at a higher IQ level. All one needs to do is simply pick the "IQ" algorithm of a person with a higher IQ.

This goes to show that the proponents of the genetic theory have implictly given us the keys to raising everyone's IQ, which is quite paradoxical.

John G.

DIY

2005-09-04T13:35:00.000-07:00

Looking at the destruction left by Hurricane Katrina, looking at the desperation left in the wake of Katrina, one thing is very very clear, you need to save yourself. You cannot rely on slow inefficient beurocracies to help save you at a moment's notice, you need to know how to plan and survive in an enviorment where you might not have government support. This is one of tenets of the DIY (Do It Yourself) philosophy.

It was the DIY philosophy that led me to create this website, you don't need teachers or tutors to learn math or physics you just need the will to do so, you can do it yourself. It has been the less useful side of leftist philosophy that has inculcated in people a total reliance on the government. This make the individual powerless to help himself or others without government assistance, this makesthe nation inherently weak because if the government apparatus is faulty the entire nation is faulty.

We need a balance, we need to be self-reliant, so if the government is not present in our locality you and your loved ones can still survive. At the same time there is only so much one person can do to survive there will come a time when you will need government assistance, but it should only be as a last resort, when you have tried everything in your power to prepare and survive and still need more help.

John G.

Custom GRE Tests

2005-05-03T19:12:00.000-07:00

One way to increase your GRE score is to test yourself above the level at which you will be tested.

The way to do this is to create your own custom GRE tests. First you want to collect as many past GRE tests as you can, and then test yourself with each one to determine which types of questions give you the most trouble. Keep a log of those questions and create your own GRE test that contains only the most difficult questions, with an emphasis on the questions that gave you the most trouble.

One must take special precautions not think about the answers to the questions or the questions themselves before taking the test. To ensure validity, one must time oneself according to ETS regulations.

John G.

Preemptive Thought Execution

2005-04-02T12:16:00.000-08:00

One great way to improve the speed at which one solves problems especially on standardized tests is to perform preemptive thought execution. Preemptive thought execution is presolving basic parts of the problem in question, you will first have to "predict" what type of calculations may be needed and perform them before we start the problem.

Our prediction should be guided by the content of the problem, we should quickly think back to similar problems and presolve portions of it. Though some of our "presolutions" may not be needed it will greatly increase the speed at which the problem is solved.

Preemptive thought execution was dervied from the preemptive code execution technique used in Intel CPU's.

John G.

Thinking Apart From Our Senses

2005-03-06T17:21:00.000-08:00

The country of the blind by H.G. wells, is the story of an explorer who accidentally came upon a land where everyone was blind, and have been blind for many generations. Since the explorer could see and the inhabitants could not and have not seen anything for a long time, there were drastic differences in the concepts of space and time, physics, beauty, and use of language.

Since no one in the land of the blind had sight, the explorer appeared to have a mysterious ability to predict and visualize things which they could not, which at the same time frightened them since they did not understand what this mysterious ability was.

This story brought up an interesting point, our concept of reality is wholly determined by our senses, it is how we interpret and formalize our senses that allows us to construct theories of physics.

Imagine trying to learn math if you where blind, how different would our concept of a the derivative, the curve, the fraction, or any other mathematical concept be. How would we manipulate and solve problems?? Obviously we could not visualize, but we could "visualize" with our fingers, or hearing. How could we learn physics?? How could we understand classical mechanics, or electomagnetics?? How about General relativity??

I bring up this point, not to put down blind people, but to help everyone realize that WE are the blind people. We cannot "see" the 4th dimension like we can the usual 3, yet we have general relativity. We cannot "see" or "feel" an atom, or an electron yet we have quantum physics. Many may say that we build scientific instruments to extend our senses, but we still build our intution of these theories from "classical" concepts based on objects on our scale. It took men of genius to "reason" outside of their senses to realize that reality is much different than what our senses tell us.

Imagine how we would appear to the inhabitants of the land of the blind, imagine how difficult it would be for them to understand the exsistence of other planets, or black holes, or electromagnetic phenomena, yet to us it would be relatively easy. The addition of one more sense makes such a radical difference in the ease of understanding certain phenomena.

When it comes to quantum physics and relativity we are "blind" to an intutitive understanding since we lack the senses to detect effects at those scales. We are like the blind trying to understand a 3-D curve, or a machine. It would be a beneficial exercise to understand a mathematical or physics concept without visualization. We should ask ourselves how would a blind person understand netwonian mechanics or a derivative, thereby allowing us to obtain a radically different world view. This could allow us to realize how our senses limit our ability to intuitively understand quantum mechanics and general relativity and how to overcome or compensate for it. We can begin to reason apart from our senses, and grasp the concept intutively in a radically different manner.

John G.

New Mental Exercise

2005-03-06T16:58:00.000-08:00

Another mental exercise involves visualizing moving objects in our mental space. Many of the most important mental activities involve keeping track of several objects at once. The best way to build up this ability is to visualize one object in our mind then manipulate it, it can be a physical object like an apple, a mathematics or physics problem, or the inner workings of a machine.

At first it may be difficult to visualize and keep track of several objects at once, so one should start off with one object, a simple problem, or a simple machine. Then with time increase the complexity, maybe try to visualize and keep track of two objects, etc.

With practice one may be able to keep track of many objects or thoughts and resolve problems much more quickly.

Efficient Problem Solving

2005-02-09T18:00:00.000-08:00

When one is either writing a proof or solving a problem, one must keep in mind that some proofs and some problems are quite involved and may have many little parts. The most parts it has the higher the chances that you might make a mistake. The worst is when one finally gets an answer only to find that is either wrong, or your proof has a fatal flaw.

This happens more often than not, and finding the culprit is usually a tedious and difficult task. In general one should start with the easier parts first, check your signs and symbols, then move on to the harder stuff like checking that each step is mathematically valid. The last step is usually the most tedious and time consuming and sometimes we constantly overlook any mistakes we make, therefore one should go through each step in detail and verfy it mathematicaly.

John G.

Busy

2005-02-08T21:15:00.000-08:00

Hello everyone, I know I haven't posted in my blog in while, a lot of things have been going on in my life. I started a new job, I'm studying for the Physics GRE, and I'm translating my entire website into Spanish, so I'm quite busy.

I will still post in my blog, though it may be far and few between. In any case you can still contact me via:

mathtutor3141@bigfoot.com

John G.

How to Learn Math and Do Proofs

Luck In Math and Physics

2005-01-13T13:04:00.000-08:00

About a week ago I saw a movie called "Intacto". Here is a description:

With INTACTO, from director Juan Carlos Fresnadillo, a group of people who have "the gift" of being extremely lucky play into a suspenseful world of gambling and superstition. The film begins and ends in the Canary Islands, where ringleader Sam (Max von Sydow), a Holocaust survivor, runs a casino. His right-hand man Federico (Eusebio Poncela) is stripped of "the gift" in a terrifying exchange that Federico sees as worse than death: Sam hugs him and in doing so steals his luck away. Desperate for revenge, Federico latches onto Tomas (Leonard Sbaraglia), the miraculous sole survivor of an airplane crash. He convinces Tomas to test his luck in various games (one involves running full-speed, blindfolded, through a heavily wooded forest to see if he is "lucky" enough to avoid running into a tree.) By training Tomas to be a winner, Federico hopes to eventually have him challenge Sam. Thrown into the complicated mix are an untouchable bullfighter (Antonio Dechent), and an auto accident survivor (Monica Lopez) who want to break up this obsessive gambling ring.

George Polya, the writer of the book "How to Solve it", said that one of the aspects of a good problem solver is luck. You need luck to come up with the ideas that help solve the problem in question. So luck does play a factor in problem solving, but how to do we obtain luck or maximize our luck? We can see luck in two ways, we can either maximize our luck or we can minimize its use.

We can minimize the amount of luck necessary to solve a problem by studying problem solving techniques and studying the subject. This is what my website focuses on.

Now aside from strictly paranormal methods to increase one's luck, we can approach the subject from an experimental basis. For the most part luck has a large subjective component, of course there are some instances when most people would agree a certain person is lucky, but they are few and far between. One way to "maximize" one's luck would be to keep a record of the lucky things that happen to you everyday, try to organize the records according to the field in which you were lucky (lucky in physics, lucky financially, etc..). Then focus on the field of interest, if you want to maximize your luck in physics, make a chart of all the days you where "lucky" in physics and try to find a pattern. You can even analyze the data statistically and find which days, and times when you are most lucky. Once you do this you can plan your studies such that on those lucky days you work on problems you want to solve.

After you have compiled and analyzed enough luck data, you can perform experiments. For instance you can perform certain actions and see if they substantially affect your luck data. If you find that certain actions substantially affect your luck data in a positive manner, then you can maximize your luck.

John G.

A Method for Generating New Ideas

2005-01-10T15:31:00.000-08:00

One way to generate new ideas in both math and physics is to simply take the words used to describe the concepts and arrange them together at random to hopefully form a new concept. For instance if we take the word negative as in "negative number" and combine it with the word dimension, we get negative dimension. As of yet I have not seen any mathematical paper dealing with a concept.

There is no limit to the amount of new concepts we can create using such a method.

John G.

How to Learn Math and Do Proofs

Different world view, different solutions

2005-01-06T13:46:00.000-08:00

During the cold war there were many instances when the Soviet Union made advances in fields where we didn't. High level groups at the white house sat around and asked why couldn't we have invented that or come up with that idea. The reason why the Soviet Union came up with different ideas and different solutions is because they had a different world view.

Our world view plays a part in solving problems both in math and physics. The ability to think differently is very important when coming up with new solutions. Implicit in our ability to think differently is our ability to come up with new and original thoughts and this is related to our world view.

Aside from the superficial aspects of world view like politics or opionions, our world view is something inculcated in us since we were born. It is the cultural aspects of our world view, the cultural mythology, the cultural interpretation of relgion, and the cultural history of how to solve problems that affects our ability to understand and solve problems in the present day. It is only when we are aware of our world view that we can broaden it.

Learning a different language implicitly teaches us the world view of a different peoples, different languages have different words for same thing, sometimes they have words for things or events that we don't have, or sometimes may not have a word for a thing or an event common in our native culture. Watching television shows from other parts of the world also help us broaden our world view (if you can understand the language or they have subtitles). Reading the history or mythology of different peoples can help understand their world view.

Our goal is to broaden our world view in hopes of broadening the amount of new thoughts we can have, thereby helping us come up with different solutions to old problems or new solutions to unsolved ones.

John G.

How to Learn Math and Do Proofs

Welcome

2005-01-04T10:59:00.000-08:00

Hello everyone, welcome to my new blog. I decided to get rid of the forum and change to a blog. Very few people were posting in my forum and I realized I was using more like a blog and less like a forum. I will take all of the posts from the forum and post them here.

If you want to comment please click on the comment link below.

John G.

How to Learn Math and Do Proofs

More Ideas

2005-01-04T03:53:00.000-08:00

Another exercise we can perform is to take a well established physical theory or mathematical idea and slightly change some of its basic axioms. We should explore what effect this change will have on the theory, what happens to our well established results, or what effect it will have on other physical phenomena. This is a good way to tune our intution to what consitutes plausible changes in our theories.

In addition used book stores are a great repositry of physics and mathematics books at cheaper prices.

John G.

Creativity vs. Rigor

2005-01-01T23:58:00.000-08:00

To be successful in nearly any scientific field you need both a creative and a detailed rigorous mind.

When we are first learning a subject it would beneficial to approach the subject in a detailed and rigorous manner. The reason is that when we are first learning a subject we are prone to understanding and applying the concepts in an erroneous fashion, hence our first priority should be detail and rigor.

Now once we understand the concepts and know how to apply them, in order to advance our respective fields, our main priority should shift to creativity. This is actually more difficult than being detailed and rigorous, for true genius lies not in perfection but in originality, and it is very difficult to have a truly original idea in modern times. There are some methods to "increase" one's creativity but since creativity is subjective they are bound by one's own thinking.

John G.

Know Thyself

2004-12-27T09:00:00.000-08:00

Knowing oneself is very important, not only in mathematics but in life. Knowing one's character is very important, for you will see your strengths and weaknesses.

In mathematics or physics your weaknesses usually expose themselves as lack of mastery, lack of attention to detail, lack of consistency, pushing a problem through even though you know you missed or passed over a critical detail, etc. Sometimes one's weakness only shows up under certain conditions like a quiz or a test.

If you can identify your weakness try to turn it into strength by constantly training yourself in activities that involve your weakness somehow, push yourself to overcome your weakness everyday until you gradually turn it into strength. If its test taking take a test everyday and time yourself until you not only get all the questions correct but you feel comfortable with test taking.

One's weaknesses have the tendency to show up in the most inopportune time, and if one doesn't do something to deal with them they may become a barrier to one's progress.

John G.

The Movie Hero

2004-12-11T21:36:00.000-08:00

If you haven't seen the movie "Hero" here is a little summary:

"In a distant war torn land, a ruthless emperor is rising to power with an iron fist and his massive armies. To control everything, he will stop at nothing. International action star Jet Li is a fearless warrior with no name on a mission of revenge for the massacre of his people"

There is one scene in the movie when "Jet Li" is about to fight an opponent. Before they fight both "Jet Li" and his opponent visualize the entire fight, they close their eyes and go through every move and every countermove their opponent will make.

This is the type of visualization we should strive for when solving problems, we should be able to visualize the solution from start to finish in our minds.

There are other things we can learn from the movie, training techniques at first we imitate our teacher, then we practice perfectly, then we can employ the techinques in actual problem solving situations.

John G.

Supplements for your brain!!

2004-12-06T20:42:00.000-08:00

Last Friday (Dec 3,2004), on ABC (I think it was 20/20) there was an interview with Victor Conte. Conte is the CEO of Balco, the company that supposedly gave steroids to famous world-class athletes like Marion Jones, Barry Bonds, Jason Giambi, and others. What is interesting is that during the interview he revealed that by using his chemical enhancement program coupled with a rigorous training regimen he took average athletes and made them into the best athletes in the world.

I do not endorse what Balco did, it was wrong not only because using steroids gives you an unfair advantage, but also because using steroids is bad for your body in the long run.

20/20 showed how nearly all of the athletes mentioned above broke world records after they had worked with Conte. Conte revealed some details of his chemical enhancement program; calendars indicating what substances to take on a day to day basis and revealing details of the substances used and why. What was most impressive was that he had "project world record" where he took an average sprinter and made him into the fastest sprinter in the world.

Many would say that using steroids is akin to using a cheat sheet on a test, but this is not a valid analogy. Steroids enhance your body's ability to perform; you do not have to rely on machinery outside of your body. Using a cheat sheet is more analogous to attaching a motor to move your legs faster. Using Steroids is unfair to those honest athletes who don't want to use them.

Though many of these athletes had preexisting talent and ability many of them where simply average in their sport. Not only that, they where most likely competing against others who had more ability and also used steroids. So steroids alone don't guarantee you will be the best, you need a well-designed training regimen as well.

I asked myself could something similar be applied to standardized tests??? Could one design a program to take an average person with average "abilities" and make them score in the 99th percentile on the SAT or GRE, without cheating?? This will basically guarantee your entrance into any university you want. It would be beneficial to research safe and legal substances that increase our ability to think and perform coupled with a training regimen. We can plan our day to day activities to increase our ability to solve problems and decrease the time spent on solving problems.

We can learn much from Balco, that sometimes what seems impossible is possible.

John G.