Reflections of a Lifelong Teacher 

Index  
Important Concepts for Teachers and
Parents Flipping a Statistics Class Worked Well Determining Who Passes a Standardized Test Is My Poor Memory a Learning Disability? Suggested Education Axioms and Postulates The Perils of Teaching the Tough Stuff Academics vs. Educators 
Difficult Concepts to Teach The Normal Curve is Special Nurses Taking My Statistics Class The Cost of a Misdirected Education Two B's or an A and a C, Which is Better? What to Teach, That is the Question The Path Not Taken A Sad Ending to My 35Year Career 
1. Much of behavior is learned. 
1. Thinking on the margin example^{1}

Determining
Who Passes ^{1}Kevin J. Clancy, chair and CEO of Copernicus, a global marketing consulting research firm "...developed a statistical model to predict MCAS (Massachusetts Comprehensive Assessment System) scores..." at different schools based on these socioeconomic characteristics “ ... percentage of families that receive aid to dependent children; have two parents; are below the poverty line; are white; and hold a college bachelor’s degree or higher. What we learned is that how well children perform on MCAS scores has almost everything to do with parental socioeconomic backgrounds and less to do with teachers, curricula, or what children learned in the classroom.” ^{1} Making more sense of MCAS scores, by Kevin J. Clancy, Boston Globe, April 24, 2000, page A19 This is old but have not seen data to the contrary. Please

I followed most of the suggestions made by the consultant/coauthor Pam Cohen for our free TestPrep Mathematics book. Her suggestion we not use a normal curve as the model in the statistics section was not one of them. She felt the data was often not normally distributed and nonsymmetrical data would be better. I felt the normal curve is one of the most important concepts to be taught and many students leaving school do not comprehend this importance. Life is about balance.
There are a few very tall people and a few very short people. Most are people are in the middle. A few people have aggressive alpha personalities and others have milktoast docile personalities. A few have academic gifts while a few people have low mental ability. A few are oversexed in relation to the middle and few could care less about sex. Most people are in the middle. Personal traits may not perfectly normal but they are close enough to help us understand our dynamic world. It is very possible human characteristics become more variable as a society becomes wealthier and also the length of time increases between major sacrifices are asked of her citizens. The positive extremes get more positive and the negative extremes get more negative. Some Normal distributions become skewed and a very few become bimodal. Do weight, bullying, income and satisfaction with government fall into this model? Others? 
Flipping a Statistics Class Worked Well Teaching Statistics to Open Evening College Students by Walter
Introduction: After years of traditional teaching to open enrollment college and junior college students, I switched to my now free then inexpensive programmed textbooks Quick Notes Statistics and Excel Statistics Lab Manual. With all the problems and their data sets written in Excel, many of the calculationlearning obstacles were removed. Many students were familiar with the text, as they had used other books from the Quick Notes series. Quick books are concise one and twopage outlines per chapter followed by practice problems and complete solutions.
Methodology: Class 1 began with a 30minute overview of material covered on the first test. It was on a o be takehome or used in our computer lab. We then adjourned to the lab with some of the better students leaving to study the lectures on their own and do required work at their leisure while the others joined me in the Excel lab to calculate measures of central tendency. Lectures for a few nights were very short previews. Labs sessions with me and a few students helping with procedures took up most of the class. The class before the computerized test using Excel I conducted a comprehensive 30minute review at which I again saw the better students and after the review, a few students were off to the lab to finish their computerized lab set due before the test. Tests for probability, hypothesis testing and correlation/regression followed the same procedures.
Result: 1) Being an honor system takehome or in lab computer exam resulted in the same grade distribution as for a traditional in class test where students did calculations. A large note card/cheat sheet was allowed.
2) Using computers, more material was easily covered with less work and anxiety.
3) Only the better students learned more, much more.
Students for open enrollment college classes had for 35 years divided into four groups.
Group one learned central tendency but got lost on probability. They completed the course requirements but never really learned much. They passed with low grades because of my easy grading procedures.
Group two calculated some probability functions. Hypothesis testing was poor as they ran into trouble deciding which Excel menu procedure to use for each of the eight different problems on the take home/lab exam. I had warned them that over 35 years grades always went down with each tests but many were still disappointed. Some of these adults worked really hard but having to choose between finite and normal distributions, large and small samples and then between one sample and two samples eventually led to mistakes.
Group
three often got the statistic correct but then had difficulty
determining to accept or reject the no change null hypothesis. All the
studying in the world does not help because they had never really understood
what hypothesis testing was all about. Group four had one final hurdle to explain what the answer meant. They had correctly accepted or rejected the null hypothesis but what did it mean? They needed to write in the analysis section that the new procedure was faster or had less defects or that the new diet was better/worse or else it was back to group three and a B grade. Less than six from a class of twentyfive got almost everything correct, They got 4 points on almost every problem. A very few indeed got everything correct. I used this system for about six classes before retiring in 2002. All had the same result.
Base on this experience, I believe the computer will help the better students more than the average students. What computers do for average students has been limited but using computers to assist teachers managing an Individualized Curriculum approach to education is promising. 
Nurses Taking My Statistic Class A friend of mine was earning a nursing degree from a wellrespected liberal arts college and fearing the possibility of a very poor grade; she signed up to take statistics at one of the easier evening campuses that I managed for Franklin Pierce College. I agreed with her logic but the campus she planned to attend had a very demanding teacher and a low grade was possible so I suggested a campus change. She did and was pleased with the result. She got a C grade.
Why a nursing student who was poor at mathematics was required to take statistics is beyond me! I often asked nurses who were visiting Franklin Pierce College why they were taking my evening statistics class. Many said their home school required statistics and evenings were convenient and sometimes easier. Thinking that statistics really was not that important to being a nurse, I asked why it was required. Apparently, they had the same question and learned it was required for undergraduates because it was needed for a nursing master's degree dissertation. Well why not require it for graduate students and not as undergraduates?
Statistics is a good for those who are mathematically inclined but it is useless for those who were not so inclined. Take it, be miserable, finish and forget it. This also applies to business students. Knowing how much many of my students disliked statistics; I wanted the requirement removed. Make it an elective.
I found myself discussing this requirement with a woman possessing a doctorate degree in nursing and she insisted statistics was necessary for a master's degree and taking it as an undergraduate got it out of the way. We agreed to disagree but just before parting, I asked her for the topic of her doctorate dissertation. Hearing the title I said, "that doesn't require statistics" and she replied, "I chose to do a nonquantitative dissertation." Asked about her master's dissertation she said none had been required!
Why do academics set academic requirements that can only be reasonably accomplished and applied by the top students? To push wages up by limiting supply. Does it make them feel good about themselves by making nursing a more difficult degree? I did it so you can do it! To optimize revenue per student as limiting statistics to students who like mathematics would mean statistics classes would be economically inefficient? Do they want to create a feeling of control? All of the Above? Please email antonw@ix.netcom.com with thoughts and suggestions. Return to 
Is My Poor Memory a Learning Disability? I found elementary school academically difficult. Good grades in arithmetic, average grades in science and history, and poor grades in reading, spelling, and language. Reading aloud was my biggest worry and spelling a close second. I could not pronounce many of the words when reading to my fourth grade group and hated the awkward seconds it took for a group member to help. As for spelling, forget it. I always missed the first word and sat down. I wonder if just sitting while the game continued affected me. Thankfully, my 4th grade national reading comprehension scores were about two years above grade so I realized I might have been dumb, (as in verbally challenged), but I wasn't stupid.
A few years ago while trying to remember who sang the 1960's song "Down Town" I thought about the picture of the singer on my record album that I had played many times and Patella Clarks name popped into my head. I tried thinking of a picture when trying to remember another name and again it worked. Retired in my late fifties I had discovered a memory trick.
Memory had made my early school life difficult. Could memory training have helped? Hard work and a liking for history had gotten me B's and C's while my competition did little work and earned better grades. Hard work did not help in French 1. I had no chance. If there was any way to get a C grade and take French 2 and sit next to Patricia, the most beautiful girl in the world, I would have found a way. However, it was not to be!

The Cost of a Misdirected Education My Keene State College 1990 Economics 101 class was given data showing that average college graduates earned much more than high school graduates. They had seen it before. That is why most of them were in college. Then I showed them median income of college graduates. They were disappointed with the lower number. I explained how some highincome earners made the mean higher than the median. Then I showed them data indicating the bottom quarter of college graduates earned about the same income as high school's topquarter. They became even more unsettled. Finally, I gave them the lowest income statistic of all, the bottom quarter for those with just a bachelor's degree. There were no professional degree and higher in this group. This was the true measure of the earnings of an academically poor college graduate. From the back of the room, I heard “you mean they are ripping us off". No, I said, ”they are selling something many incorrectly feel is best for everyone.”
It took about twenty years but I pleased to report that because of the Great Recession, mass media coverage of the decreasing economic return from a college education is no longer sporadic. However, like any unwelcome news, parents, teachers, and politicians will be the last to react properly.
The collateral damage from an overly academic public education system for all students has been substantial. We have lost an entire generation of young black American males who didn't finish high school and have few life skills . Now many unsuccessful middle class white males live with their parents and do little but play video games. This group is committing suicide at everincreasing rate. College debt is over $1,200, 000,000 000 and the over supply of graduates will keep their salaries low. Most nongraduates will default on debts. Social unrest is mounting.
Collateral damage will continue to grow unless responsible people allow an educational system that improves the wellbeing of all students. It is time to end our love affair with overly academic education. See Proposed Education Manifesto leads to Educating the Class of 2034

The Perils of Teaching Teaching mathematics is arguably the most difficult task faced by teachers. Teaching me English was extremely difficult. The following incidents happened to me while teaching an adult evening statistics class. I was stressing the importance of drawing and then labeling a normal curve to determine the seventh decile when a primeval scream "I CAN'T DO IT' shattered the classroom. I calmed the student down but he was right. The circuits were not there. This was not his fault. For another student understood that 4x = 16 means if four x's add to 16, x = 4. Some students then cannot determine the value of x when 5x =25. About 25% just cannot do it.
While working with a
class to work the kinks out of
TestPrep Mathematics An important town official dropped my evening college accounting class because he just could not do debits and credit. He took it the next term from a teacher that did not teach debits and credits in our introductory accounting class. I taught said accounting class for forty plus years and did not learn the second teacher was correct. Debits and credits were not appropriate for a class of open enrollment business students. Some cannot do it. My class was a waste of a student's time. This is similar to Algebra for average student.

Two B’s or an A and a C,
Many years ago I began asking my evening adult college students which was better, two B's or an A and a C. Almost all said 2 B's. Being wellrounded was their reason. Then I rephrased the question. You need a serious operation and must choose a doctor. Do you choose a doctor with average in bedside manner and average in operating ability or one with a C in bedside manner and an A in operating ability? I'll take the famous Dr. House every time. The IRS has questions about my tax return. I want the best tax accountant I can find and their auditing ability and personality mean nothing. NOTHING!
Here is how I learned this important lesson. Teaching mathematics is arguably the most difficult task faced by teachers. Teaching me English was difficult. The following incidents happened to me while teaching an adult evening statistics class. I was stressing the importance of drawing and then labeling a normal curve to determine the seventh decile when a primeval scream "I CAN'T DO IT' shattered the classroom. I calmed the student down but he was right. The circuits were not there. This was not his fault. For another student understood that 4x = 16 means if four x's add to 16, x = 4. Some students then cannot determine the value of x when 5x =25. About 25% just cannot do it.
While working with a class to work the kinks out of TestPrep Mathematics a student complained that I was trying to trick him when I had accidently put a change a fraction to a percentage problem in the change a fraction to a decimal section of a problem set.
He said let me do it. He had not learned enough about mathematics in 12 plus years of school and even given my great free book TestPrep Mathematics he still didn't intuitively know that 25% is onequarter! An important town official dropped my evening college accounting class because he just could not do debits and credit. He took it the next term from a teacher that did not teach debits and credits in our introductory accounting class. I taught said accounting class for forty plus years and did not learn the second teacher was correct. Debits and credits were not appropriate for a class of open enrollment business students. Some cannot do it. My class was a waste of a student's time. This is similar to Algebra for average student.
A young
lady in my statistics class heard this example and at the break she thanked me as she had been told
her poor math ability made her very average and being very good at English was
not good enough. She also said page two of the
Quick Notes Philosophy
at the front of her workbook I had provided made her feel much better.
Sacrificing selfconfidence to make someone a little better at anything is one
of the biggest mistake of our generation. Proposed Education Axioms and Postulates Will Stagnate Median Income Hurt Our Children?
Please

Academics are scholarly. Pure knowledge in their area of expertise is of prime importance. Educational academics often begin by teaching their specialty. Some become department heads and determine curriculum content and academic standards. Educators enjoy the classroom environment and seeing someone learn important economic and personally useful material. 
Educators enjoy the classroom environment and seeing someone learn important
economically important and personally useful material. Educators believe intelligence is normally distributed. They get discouraged when teaching a curriculum designed by academics because said curriculum is often beyond the grasp of academically average students. Textbook content is controlled by academics who are influenced by their prejudice toward the purely academic and publishers who are concerned with profit. 
What to Teach, That is the Question Quick Notes Statistics began as class handouts for a day class I was teaching to traditional Franklin Pierce College students. The math department chair noticed I was teaching the expected value of x and mentioned skipping it as being not important. Not interested in collateral damage, I said nothing but felt what was important should be determined by student needs. Since many were business majors, the E(x) was important. She like many mathematicians stressed the counting rules and other theoretical probability concepts. I didn't because the population at schools like Franklin Pierce consist of mostly of "Middle Prepared Students" who not do not need theoretical probability; most had average mathematically ability and had little use for difficult mathematical concepts. She later became very interested in the stock market where she used decision theory based upon E(x) to trade on the Internet 

Thinking on
the Margin^{1}
Twoperson golf teams A and B play an 18 hole golf contest in which the team having the least strokes to complete a hole wins the hole. Ties are ignored. When falling two holes behind a press is created. It is an additional match for the remaining holes. After 12 holes Team B leads by two, they are twoup. Team A presses. After 16 holes team B is down three on the first match. Which team leads the press? It is amazing how many golfers do not know the answers. Lawyers! Business Owners! If the first is two down then the additional match is one down.

Your knowledge mind will always try to capture and control the awareness path. This defeats the purpose, and letting go of control is the hardest thing we knowledge based people can do. Secondly, it is an interesting practice to read the Bible, Zen, or any books on consciousness and see if you can read it as “not knowledge”. See if you can read the sayings of Jesus and hear it as not a set of words to live by, but a pointing to getting out of your knowledge and into your awareness.
Tom Lane 7/11/06.

Looking back, I taught a few poor classes. I taught many subjects and the first time is always difficult. Once I had a major problem. One of the adult students who knew more about investments than I did made sure everyone in the room knew it. It was a long eight weeks. Another time I inadvertently talked down to a class. After a few classes, I knew something was wrong and asked the class. They pointed out my indiscretion but it was too late. It was another long eight weeks. My last class was my worst. I had worked hard to use the Internet in a 2002 statistics class. A student who possessed enough Geekability to help with her career advancement saved me. Another student in the class really annoyed me after the first test with his open desire for a higher grade. It continued after tests two and test three. I was so upset that I did not award many A grades. The student who had helped me was so upset with her grade that she quit school.
This was the first I was aware
one of my actions had caused a student to quit school. That is the
Cardinal Sin for adult learner teachers. When an adult learner quits
because of your teaching it is time to do something else. Thanks!
