My Little Town 20120718: Mathematics Made Hard and Easy

(8 pm. – promoted by ek hornbeck)

Those of you that read this regular series know that I am from Hackett, Arkansas, just a mile or so from the Oklahoma border, and just about 10 miles south of the Arkansas River.  It was a rural sort of place that did not particularly appreciate education, and just zoom onto my previous posts to understand a bit about it.

When I was in school I had the good fortune to have a great many excellent teachers.  I even keep up with some of my high school teachers, and I was graduated in 1973.  Sr. Cabrini correspond on Facebook, and Sr. Pierre calls me from time to time.  They were both excellent and I glad to call them my friends.

On the other hand, I have had some really horrible ones.  One who has to be near the top of the list was Bill Holder, a mathematics teacher that I had at Westark Community College in Fort Smith.  That is now part of the University of Arkansas system, The University of Arkansas at Fort Smith.

Mathematics was not my strong suit.  I actually had to apply myself very diligently to make good grades in maths.  Algebra was not that hard, but I hated memorizing the formulae in trigonometry.  The made the calculus more difficult than it should have been for me, but I had an excellent professor in Fayetteville for Calculus III that made everything come together.  Although I did not have to do so, I went ahead and took differential equations my first year in graduate school and made a good mark in that.

But I struggled early on in maths.  Mr. Holder did not help.  Although I had done well in algebra in high school, I had Mr. Holder for college algebra and could muster only a C.  Now, I probably could and should have tried harder, so not of the blame goes to him, but a good part of it does.

The man could not teach.  His pedagogical skills were some of the worst that I have ever seen.  I am sure that he knew his material, but he just could not get it across into the students’ heads.  Part of it was that he had some difficulty in answering questions.  He could work the problems that he selected for examples, but if a student had a question about why he made a particular manipulation he much more often then not would answer in a very cryptic manner that only someone already fluent in maths could understand.

Now, on a personal level I liked Mr. Holder.  He truly was a nice guy and was polite and even jovial with the students, and he did not seem to show favoritism for or against any student in the classroom or during office hours.  He gave lots of partial credit (a good thing for me!) and obviously took a lot of time when he graded papers.  In retrospect, I understand a bit of why he was ineffective as a teacher, particularly as a maths teacher, and I shall reveal it when I contrast his teaching methods with a really good maths teacher (the one that I had for Calculus III).

He was obviously frustrated with his lack of effectiveness, and it was easy to pick up on that, even for a 16 year old kid (I was graduated from high school early for a couple of reasons, but that is a story for another day).  The way that he would try to get feedback was telling.

After he tried to answer a question, he would follow up with a phrase like, “Do you see?”  That is not bad in and of itself, but that was pretty much the only feedback tool that he ever used, other than tests.  He did not grade homework but did encourage us to to do the problems in the book and he would then work some of them in class so we could self critique our own work.  That is not very effective, for reasons to be shown later.  I can sort of understand why, though, because you and I all know that there is all kinds of collusion when homework is graded.

One of his most annoying traits was asking those “Do you see?” questions.  He had several and once, when he seemed to be pretty sure that he had not gotten his point across to a student he said, “Do you get the idea?  Do you understand?  Do you see?”.  Sheesh!

The only work that we did that counted were the hour long tests that he gave every week or two, and the final examination.  I had always done fairly well on the homework, but there were some key concepts that I just did not understand.  It was not so much that I did not understand the axioms and theorems, but rather struggled with the technique of problem solving itself.  I just was not very good at developing strategies to solve problems.

As I said, I struggled through and finally got a C for the semester.  The next semester I took college trigonometry and did better, but Mr. Coe was a better instructor than Mr. Holder.  I still hated memorizing the formulae.  I am poor at rote; I much prefer to learn a system that makes things make sense, because when things make sense it is easy to build on basic concepts and understand rather than memorize material.   As an aside, back in 1976 there was a swine flu scare (the outbreak lasted only a couple of months and was confined to Fort Dix, the Army base) and the government rushed to prepare vaccine for it.  It was released in October and there was an effort at Westark to vaccinate as many people as possible.  Mr. Holder had a shot an within a couple of minutes he hit the ground.  He had a reaction to the vaccine and passed out because of it.  He was OK after a while and did not injure himself when he fell.

Later on, when I arrived at The University of Arkansas I still struggled.  Calculus I was an unmitigated disaster for me, and I failed it.  I worked closely with my instructor (I had a real faculty member, not a TA), and he really tried to help me.  I almost dropped the class, and he told me that I had a fighting chance to pass and my more recent work was much better than at the beginning of the semester.  As I recall, he told me that if I performed at the level that I had been performing (this was close to the drop date) that concerning my earlier performance, “All is forgiven.”  I took him at his word and was doing well enough not to drop the class.  The final examination is what sunk me, because I foolishly did not go back and teach myself the material from early in the semester.

By that time I was taking some rather advanced chemistry courses, and they used the calculus.  Fayetteville had two tracks to get a bachelor’s degree in chemistry, the easy route that led to a B.A., and a harder one that required the calculus to get a B.S., and I chose to get a B.S.  Of course I had to retake Calculus I since it was a requirement for the B.S., but I began to learn the calculus not so much from the actual class, but in chemistry classes that applied the calculus to areas that I already had an understanding of and knew what kinds of answers were being sought.  That helped me develop strategies to solve the problems.

Calculus II was also a struggle, but I passed it just by sheer perseverance.  I knew that I could not stand another failing grade, and I worked extra hard to keep up.  I never excelled, but I did OK.

During this time I was taking yet more advanced chemistry courses, and was learning more strategies for solving problems.  Then everything changed.

One thing that changed was me.  I got much more serious about doing well in college and also decided that I wanted to go to graduate school.  I knew that I had to do well to have a chance, and I wanted to be able to be graduated with a B.S. in the spring of 1980.  (I know, I wasted a lot of time betwixt 1973 and 1977, but the former Mrs. Translator and I were married in the summer of 1977 and I got more serious then as well.  I was barely 20 years old.)  To do that, I had to take Calculus III in a summer session.  I actually chose to do that because that was the only course that I took that session so that I could focus on it.

I had the outstanding fortune of getting a session that was taught by Professor Kesee.  Oddly, he retired before the fall semester started, so I was one of his last students.  Dr. Kesee knew how to teach.  One thing that he did, and told us in advance that he would, was to begin each class with what he called a “quizzie”.  Generally one of his quizzies was four or five problems and we had about ten or 15 minutes to finish.  Then he would lecture and work problems the rest of the time.  He was excellent at answering questions, and oddly there were not that many because he was very effective during his lectures.  We later learnt why.

The quizzies were really pretty hard.  (One wag in my class said, “If these are his quizzies, I would hate to see his testes!”)  He graded the quizzies and handed them back to us every day.  I was often disappointed with my performance, but over time got better at them.  I did not always catch it, but sometimes the same problem would be repeated up to several times, sometimes using different numbers, sometimes not.  He gave regular tests, and always graded them and returned them within a day or two.  I was surprised that I was doing so well on the tests, and made As on them sometimes, often made Bs, and rarely a C.

Then the last day before finals came.  Everyone was dreading the final, or at least I was, but I was encouraged that I had done well on most of the tests.  I still worried about my often poor performance on the quizzies, though.  That last day before the final he was giving us hints on how to do well on the final, and then said this:

You know all of those quizzies that I gave you every day?  You thought that they were going to count towards your grade, but I lied to you.  I used them to see if I had been able to get the concepts across to you, and when you had trouble with a particular problem, I used that to show me that I needed to go back and get the point across.  That is why the same problem would show up several times.  The quizzies were my tool to measure my effectiveness as your instructor.

Now that was a teacher!  He went to a LOT of trouble to grade each and every one of those quizzies when he knew that he was not going to use them for the final grade.  Not only that, for the first time since high school I really did understand maths!  I ended up with a B, which was really good for me in that area, but I was at the point that I had confidence in my knowledge, if not outright mastery, of the calculus.  I felt competent for the first time in a long time in that area, and that gave me confidence that I could learn more maths.

I was indeed graduated in the spring of 1980, and applied for graduate school in chemistry immediately.  By that time I was fairly well known in the chemistry department, and one of the professors told me that it was very unlikely that I would be accepted because I already had a B.S. from that institution and what he termed “academic incest” was sort to taboo.  He encouraged me to apply to other graduate programs, but I did not.  The former Mrs. Translator and I were comfortable in Fayetteville (in my opinion the most livable town in Arkansas) and neither of us wanted to move too far from family.  We could get in my 1967 Camaro and be with family (all of our parents were living then) in an hour and a half.  For those of you who know the route betwixt Fayetteville and Fort Smith (US Highway 71, a very deadly highway, you will agree that this is a very fast transit time.

I took a summer job at Mity Mite Motors in Fort Smith, a lawnmower dealer and small engine repair shop after I was graduated in 1980.  One day the telephone there rang and whoever answered it handed it to me.  It was Professor Davis, the chair of the graduate student recruiting committee.  Sure enough, I had been accepted for graduate school in Fayetteville!  He said that the academic incest issue was moot since I had attended Westark for several semesters.  I later learnt that they did not have as many applicants as they would have liked, but what the heck.  I got into the school that I wanted and had a very successful graduate school experience.

Many of you may wonder why a Ph.D. in a hard science (mine is in Organic Chemistry, and that is a tale for another time) uses words like “betwixt”, “learnt”, “burnt”, and the like.  That is a tribute to my roots growing up in Hackett.  They may be a bit obsolete, but I promise you that I use them purposely.  Grammatically, they are not quite incorrect just yet, but have fallen into disuse.  I know that preferred usage now is “between”, “learned”, and “burned”, but I use these words purposely, not out of ignorance.  If you read my writings closely you will soon see that I am pretty much a stickler for proper grammar and syntax and in particular proper spelling.  You may also notice that I rarely use contractions when I write (in more informal speech I often do use contractions).  That is just a quirk of mine.  Even when I send text messages I spell out entire words.  My friend remarked to me a couple of months ago that she was impressed that I do not use the contractions so common to texting.  As far as I have been able to tell, I was only the second resident from Hackett to earn a Ph.D..  Ironically, the other was Bill Dummitt, a few years older than I who also got a Ph.D. in chemistry, but I do not know his discipline.

Here is a little more backstory.  Bill and I, along with several students at Hackett, would meet with Mr. Brockman after school to study chemistry.  I was only in the fifth or sixth grade, and Bill was in high school.  Please read the tribute to Mr. Brockman; he was very influential in my choice to go into science and I would like to think that for a long time that I did him proud.

I know that this is not exactly about childhood memories, but what the heck.  This is still about actual experiences that I had during younger days, so I think that it fits with the spirit of the series.  Please add experiences that you had back when.  I know that I like to read them and from comments others like to read them as well.

One final thing:  a couple of weeks ago a wrote a piece about the kitten that The Girl and I got for The Little Girl.  Here is a picture of him that I took yesterday.  He is growing well and The Girl and I gave him his first round of vaccines Thursday past.  He has sneezed a little the past couple of days, but because of all of the rain and the consequent rise in mold spores, so have I.

Here is one that I took today with The Little Girl Holding him.  They played together for a long time today.

Warmest regards,

Doc, aka Dr. David W. Smith

Crossposted at

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