Reflections of a Life-Long Teacher
Important Concepts for Teachers and
Flipping a Statistics Class Worked Well
Determining Who Passes a Standardized Tests
The Perils of Teaching the Tough Stuff
Is My Poor Memory a Learning Disability?
Academics vs. Educators
Suggested Education Axioms and Postulates
Difficult Concepts to Teach
The Normal Curve is Special
Nurses Taking My Statistics Class
Two B's or an A and a C, That is the Question
The Cost of a Misdirected Education
What to Teach, That is the Question
The Path Not Taken
1. Much of behavior is learned.
1. Thinking on the margin example1
1Kevin J. Clancy, chairman and CEO of Copernicus, a global marketing consulting research firm reports
1 Making more sense of MCAS scores, by Kevin J. Clancy, Boston Globe, April 24, 2000, page A19
I followed many of the suggestions made by the consultant/coauthor of our free Test-Prep Mathematics book but her feelings that I should 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 non-symmetrical 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 few really tall people and a few really short people. A few people have really aggressive alpha personalities and others have milk-toast docile personalities. A few are academically gifted while a few are mentally challenged. A few are oversexed in relation to the middle and few could care less. Most people are in the middle. Personal traits may not perfectly normal but they are close enough to help us understand our dynamic world.
Human characteristics become more variable as a society becomes richer and also the length of time increases between major sacrifices asked of 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?
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 calculation learning obstacle was removed. Many students were familiar with the text as they had used the free Quick Notes Financial Accounting and/or the free Economics Interactive Class Notes with Links when teaching my other courses. These books were also concise two-page outlines per chapter followed by practice problems and complete solutions.
Methodology: Class one began with a 30 minute overview of material covered on the first on a disk take-home or in-the-lab computer exam. 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 lab learn to use Excel to calculate measures of central tendency. Lectures for a few nights were short previews as labs sessions with me and a few students helping with procedures. The class before the computerized test using Excel was a comprehensive 30 minute or so review where 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. The test was on a disk and also on the lab server. This procedure was followed for tests on probability, on hypothesis testing and on correlation plus regression.
1) Being an honor system take-home 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.
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 for them 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 and 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 doesn't 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 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 twenty-five got almost everything correct and got a 4 points on almost every problem. A very few indeed got everything correct.
A friend of mine was earning a nursing degree from a well-respected liberal arts college and fearing the possibility a very poor grade; she signed up to take statistics at one of my 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. I questioned why a nursing student who was poor at mathematics was required to take statistics.
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. Thinking that statistics really wasn't that important to being a nurse I asked why it was required. Apparently they had the same question and were told that 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, forget it. Same for business students. Knowing how much many of my students dislike statistics; I thought the requirement should be removed. Make it an elective.
I found myself discussing this requirement with a woman possessing a doctorate degree in nursing and she insisted statistic 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 non-quantitative 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? To feel good about themselves by making nursing a more difficult degree? I did it so you can do it! To get people with degrees that do not already have Statistics to take it and increase school revenue? Limiting it to students who like mathematics would mean statistics classes would be economically inefficient? The feeling of control? All of the Above?
The state of Florida just reversed a three year old law that required every student receiving a high school diploma pass Algebra II. Algebra Two! Are politicians crazy? Less than twenty-five percent of almost any population can comprehend algebra. To increase critical thinking skills? God determines such skills and all studies show they cannot be significantly increased!
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 7th decile when a primeval scream "I CAN'T DO IT' shattered the classroom. I calmed the student down but he was right. The circuits weren't there. Not his fault.
For another student understood that 4x = 16 means if four x's add to 16, x = 4. Some students then can't determine the value of x when 5x =25. About 25% just can't do it.
Once 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 ditto. I said I was sorry, that it was a mistake and then asked what is the answer? What is 1/4 as a percentage? He said I'll have to work it out. I said just look at it and guess the answer. 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 Test-Prep Mathematics he still didn't intuitively know that 25% is one-quarter!
An important town official dropped my evening college accounting class because he just couldn't do debits and credit. He took it the next term from a teacher that didn't teach debits and credits in our introductory accounting class. I taught said accounting class for forty plus years and didn't learn the second teacher was correct. Debits and credits were not appropriate for a class of open enrollment business students. Some can't do it. My class was a waste of a student's time. Kind of like Algebra for average student.
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 well-rounded 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!
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 self-confidence to make someone a little better at anything is one of the biggest mistake of our generation.
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 out loud was my biggest worry and spelling a close second. I couldn’t pronounce many of the words when reading to my group forth grade group and hated the awkward seconds it took for a group member 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 and 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 has 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 the competition did little and earned better grades. Hard work didn't 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. But it was not to be!
My Keene State College 1990 Economics 101 class was given data showing that average college graduates make 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 really high earners make 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 top-quarter. They became even more unsettled. Finally I gave them the lowest income statistic of all, the bottom quarter for median income of those with just a bachelor's degree. No professional degree and doctors in this group. From the back of the room I heard "you mean they are ripping us off. No I said: its 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 . But like any unwelcome news, parents, teachers,
and politicians will be the last to react properly. The collateral damage
has been immense. We've lost an entire generation of young American black males.
Now white males are committing suicide in ever increasing numbers. Many
live at home and do little but play video games. This will continue unless some responsible people in the mass/social media
helps make an educational system that improves the well-being of all
students . Here is the collateral damage of our love affair with college.
Educating the Class of 2034
|What to Teach, That is the Question|
Academics are scholarly. Pure knowledge is of prime importance, especially in their area of expertise. They tend to be prejudice toward their expertise thinking everyone should have substantial knowledge.
Academics who work in education usually begin by teaching. With strong belief in their subject area, academics often get involved with curriculum development, academic standards and become department heads.
students, 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.
|Quick Notes Statistics began as class handouts for a day class I was teaching to traditional Franklin Pierce College. 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, 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; they did not have the mathematically ability to comprehend difficult mathematical concepts. She later became very interested in the stock market and traded on the Internet where hopefully she used decision theory based upon E(x) and new about stock market bubbles.|
Two-person golf teams A and B play an 18n golf match play contest in which the team having the least strokes to complete a hole wins the hole. Ties are ignored. When falling two behind a press is created for a second over the remaining holes. After 12 holes Team B is two-up and Team A presses. After 16 holes team B is down three on the first match. How does the press stand. That is who is leading? It is amazing how many golfers do not know the answers. Even successful people at a exclusive private club! Lawyers! Business Owners! If two down becomes three down the margin or press 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