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deep archives <-- back to 02/15/23 Stories from the University of Minnesota 1981 - 1985 As I quit college after three years and never made a career of math, the stories on this page are my consolation. I might be an underachiever, but I test well. At the time, my test scores and other accomplishments at the U of M meant nothing to me. Forty years later, they are among my [microscopically] little mementos. My little "victories" at college aren't going to mean anything to anyone; but this collection of stories at least reveals quite a bit about what goes on in universities, where grades rarely mean much. Academics in fits and starts During my three years at the U of M, I had the experience of both of earning and not earning my grades. I was a math education major, which is many giant steps down from the true (electronic, chemical, etc) engineering programs. My nine semesters of math at the U of M: Calculus I Calculus II Calculus III Calculus IV Linear Algebra (not what is sounds like) Differential Equations Abstract Algebra (groups, rings, fields..) Euclidean and Non-Euclidean Geometries Foundations of _________ My three semesters of Physics at the U of M: Quantum Physics Physics I (mechanics) Physics II (fluids, thermodynamics, electromagnetism) (Actually, they were quarters -- not semesters, but "quarter" just doesn't read right to me.) Six stories: 1. Typicality at the U Third semester calculus: I attended the first class of the semester. I sat at the back of the lecture hall watching the professor copy material from our textbook (which he had lying on the table and kept consulting every few seconds) onto the blackboard. Word for word, symbol for symbol. He simply transcribed the book onto the blackboard. I observed every_single_student (yes I checked every student and found zero exceptions) in that lecture hall furiously transcribe what they saw on the blackboard into their notebooks. That is, they were simply transcribing what was in their textbooks into their notebooks.. .. even though they could see as plainly as I did from where the professor was getting his material. These are college students. If students are informed of what will be in a test, rather than required to gain a genuine understanding of the material, then the testing loses its meaning. I did not attend any more of those classes that semester. I mastered the material in the book and got my A. Semesters I, II and IV of calculus were not notably different from the above semester III story. In each case, no additional material was presented in class. The textbook was the sole source. In each of those four calculus classes, it mattered not whether you actually understood the theorems and had mastery in applying them to a variety of problems. All that mattered was that you memorized formulas and plugged in numbers. The problems on the tests never varied from the basic simple example problems in the textbooks. In other words, there was no distinction made between real mathematicians and those who can perform simple algebra and mere formulaic calculus by rote and through mnemonic device and have no competence beyond that. As long as you didn't make silly computational errors you would get your A. 2. Linear Algebra (not what is sounds like) This class was my biggest surprise. I had thought I would struggle in a math class that did not lend itself to graphing, i.e. visual representation. And such was the case with this advanced class for math majors, which involved abstract concepts pertaining to transpositions, rotations of sets, etc. But I found myself sitting at the back of the classroom, chair tilted back on two legs, head resting against the cement wall.. bored with the lectures, as I was mastering the material straight from the book, finding it to be not the slightest bit challenging. I had stumbled into my niche. I even showed the professor (Dr. Kinderlerer) how to solve a problem in the book that he had not been able to crack! He had told the students to ignore that problem, since neither he nor his associates in the math department had managed to fathom it. It really was not a difficult problem -- not at all, simply a very nifty problem. As I walked away from his desk, he was still staring blankly at what I'd written down, not comprehending it even with my verbal explanations. (A couple semesters later he encountered me in the lobby of the math building and let me know he considered me a math genius, which I'm not. Jo Ann Castle and Liberace are geniuses.) There were two tests -- midterm and final. Dr. Kinderlerer wrote our scores for the midterm test on the blackboard. There was my 100 at the top. The next highest score was 40. The lowest score was 11. These were math education majors. This was advanced material, even for university mathematics; but 40 percent correct for the second highest score in a class of thirty math majors? This was not normal sixty years ago. I also scored 100 on the final, but did not get to see how the others had fared as we received our scores after classes had ended for the semester. I don't doubt that the students who scored between 20 and 40 percent on those tests received A's and B's. It is what I witnessed in subsequent classes. See next story. 3. Differential Equations I was distracted and disinterested throughout the semester. (Her name was Laura.) I hardly opened the textbook or attended class. I never got a great handle on the material and deserved merely a passing grade. There were one or two tests. I did what I could with them. I stopped in at the professor's (Dr. Appel's) office after the final to find out what my grade was. He happened to have just finished establishing the curve and had that paper on his desk, which he showed to me. My lackluster score placed me in the B range. 4. Physics I (mechanics), Physics II (fluids, thermodynamics, electromagnetism) Since physics was my minor (math education was my major), it was important to me to master all the material in the physics book. And so, during Physics I (calculus-level mechanics), I worked every problem in the book, not just the assigned ones. I made sure I understood the physical and mathematical basis for absolutely everything. Of course I got my A. And of course, so did the incompetents. The simplistic testing made no distinction. Physics II was the same semester as differential equations (number 3 above) -- a particularly "distracted" time for me. I didn't attend the class, as it conflicted with my courtyard time with Laura. (It was obsession.) I hardly opened the book. I faked my way through the one test, which of course was the "final". I couldn't have gotten more than twenty percent correct answers. I got a B in the class. Are you getting a sense of the two paradigms which yield the same results? When the tests are extremely easy, everyone ends up with an A or a B. When the tests are a bit challenging, the curve simply changes to accomodate the lower scores, such as 20 to 50 percent correct. Nearly everyone still gets an A or B. To skip #5, which is on the previous page, Click --> to story #6 further down the page. ---------------------------------------------- 5. The exception Here is the cherished exception regarding academic standards at the U of M. When I mentioned to a peer that I was taking an advanced math class (topics such as groups, rings, fields, cosets, mod-transforms..) from Dr. Gershenson, she said, "Get out of that class!!" She then told me that she had gotten him for one of her (basic) math classes and that she, along with most of the other students, had abandoned the class after learning from him that there would be no curve. Rather, he would be holding them to a pre-set standard, and they saw "F" written on the wall. (I had once done a math-study session with her. Her approach to math was 100 percent rote and mnemonic device -- zero percent comprehension. It was horrifying.) I ignored her advice. I was smitten with Dr. Gershenson. This was by far the most difficult class I ever took. Dr. Gershenson filled the blackboards in that classroom with hierglyphics a few times every session. The ten of us who stuck around for the class (twenty-five had abandoned it) filled our notebooks during those sessions. I even began bringing a voice-recorder to review things he'd said. There were pop-quizzes, which I did fair-to-poor on. There was a take-home final, which we had one week to complete. It consisted of seven problems. I was unable to fathom what two of the problems were even about. I simply couldn't understand the questions. So I went to see Dr. Gershenson. On the door to his office there was a sign saying that he was a student career advisor, which kind of struck me as significant. I didn't dare ask Dr. Gershenson to explain both of the mysteriously worded questions, so I picked just one of them. I told him that I didn't understand the question on problem four. What happened next was one of the most amazing experiences of my life. Dr. Gershenson looked at me in the most penetrating, caring manner I'd ever been looked at. He looked like he wanted to reach inside me and turn dials to get me to understand. He deeply wanted me to succeed. He asked me a question. I answered it. He asked me another question, which I answered.. then the lights went on in my head. Suddenly I understood the question. He was so emotional that his eyes were moist. After I left his office, I understood why he was a student career advisor. I'd never felt such warmth coming from a person. I ended up solving 5 1/2 of the seven problems on the test, placing me in a tie for highest score. And I swear I could have solved 6 1/2 if only I'd also asked Dr. Gershenson to illuminate the other mysteriously worded problem. Also, in truth (in my mind), I had the highest score, as I was the only one to solve problem number seven, a full two-page solution involving intermediate results; that is, I had to develop a new theorem which I then used to prove the theorem in question. It was a problem Dr. Gershenson had expected no-one to solve! My two-page solution, along with my commentary explaining and justifying my operations, looked just like something out of an advanced math text book. I could hardly believe it was generated by me. It was by far the most satisfying experience of my college days. It's what a university experience is supposed to be. And of what practical value was that math to a prospective high school math teacher? I would just say it produced some math maturity, along with inadvertent cross-training -- a handy thing for a math teacher. And Dr. Gershenson awarded no A to anyone in that class. At least one other person besides myself received a B. Those pop-quizzes were brutal. ---------------------------------------------- 6. 4000X versus 1X My final semester at the U of M was a time of the greatest emotional depression of my life, which is perhaps one of the reasons that it was in fact my final semester. My math class that semester was Foundations of _________. I attended only the first session and never opened the book. Why I didn't drop the class I don't know. I was probably too depressed to even fill out the form and submit it. Then, on the day of the final (the one test in that class), I decided there was nothing to lose by going to class and taking the test. I got in my Volkswagen Bug and got on the freeway headed to the U of M. It's an eight minute drive down the freeway. While driving down the freeway, I opened the textbook lying on the seat next to me, glanced at the syllabus which I'd written on the inside cover, turned to the relevant pages, then absorbed a bunch of the material by way of glancing back and forth between the book and the traffic with which I was sharing the road. I arrived at class and took the test. Based solely on what I'd absorbed while driving down that short stretch of freeway, I solved most of the problems on the test. I got a B on the test and for the class. I couldn't have spent more than three minutes absorbing theorems from an entire semester's worth of foreign material -- and still solved most of the problems. (Four minutes of paying attention to traffic. One minute of flipping pages. Three minutes absorbing material.) (In retrospect, it was likely somewhere between 40 and 60 seconds spent absorbing material. I can still see it quite clearly.) Not as remarkable as it might seem. I'd played a hunch and focused on just a couple or three theorems. Those very accessible concepts, and especially one of them, was the key to most of the test. This is about the lightness of the test. The B that I had obtained in Dr Gershenson's class had required 4000 (more likely 12000) times as much time and effort as did the B just mentioned. And this latter case well-approximates the standards at the University of Minnesota -- breeding ground for student loan debt. -------------- I see I've omitted one of the math classes -- Euclidean and Non-Euclidean Geometries. With the notable exception of the famous identity e^(i*pi) + 1 = 0 (which I wrote with frosting on my math-teacher brother's retirement cake), the semester was unmemorable. I remember only that I scored 100 on Dr. Miller's embarrassingly simple final exam. (I say "embarrassing" because after five minutes I set my pencil down and then didn't know what to do with my eyes -- didn't know where to look. I could tell that Dr. Miller was looking at me. But there was just no point in reviewing my test paper. When it's done it's done.) All of us in that class were math education majors. Unmemorable? I must be losing it. By the time the first week was over, Laura and I were sitting next to each other. Clear evidence of how easy the class was. Postscript ---------- More scary(?) stuff: I've peered at great length into the works of geniuses and can confidently say I'm not one of them. They wouldn't be able to see me in their rear-view mirrors. So how is it that my score on the test for admission into the College of Education at the U of M caused the test administrator to literally almost fall over backward in her spring-loaded swivel chair (I really did think she was going over) and exclaim that she had "never seen a score like this". The test was the Miller Analogies Test. The College of Education administration considered it to be the ultimate intelligence test (it measures one's ability to analyze, independent of acquired knowledge) and thus adopted it as their admissions test. She didn't simply state that it was the highest score she'd ever seen -- rather that she'd never seen a score that was even like it. Doesn't seem to make sense. I thought teachers were supposed to be among the brightest of us, and it was soon-to-be teachers -- including math and science teachers of course -- that I was going up against on that test. If only it weren't for the reality as described four paragraphs ago, I would be especially proud of my Miller Analogies Test. At any rate.. the test administrator became instantly flustered and dispensed with the interview, which was supposed to constitute the other half of the admission requirement. I guess she didn't want to insult the "genius". I also guess that actual geniuses don't apply for admission into the College of Education. And actually, one doesn't need to be a genius to teach high school math. (That's part of the reason it appealed to me.) The geniuses prefer to be in authentic (electronic, computer, etc) engineering programs. I just looked up Miller Analogies Test and found it described as follows: "The Miller Analogies Test is a standardized test used both for graduate school admissions and entrance into high I.Q. societies." -- Wikipedia "The Miller Analogies Test assesses the analytical thinking ability of graduate school candidates -- an ability that is critical for success in both graduate school and professional life. The MAT helps graduate schools identify candidates whose knowledge and abilities go beyond mere memorizing and repeating information." -- pearsonassessments.com/graduate-admissions At the time of the testing in 1985, my severe depression precluded me from having any interest in asking what my actual score was. But upon writing this essay, I became interested in learning what my raw score was, so.. I contacted the U of M College of Education, who forwarded my request to the Office of the Registrar, who contacted the Department of Curriculum and Instruction, who forwarded the request to the Graduate Student Services & Progress office, who forwarded it to MAT Scoring Services (a.k.a. pearson.com -- the entity behind the MAT). None of the above entities have kept records going back to 1985. It matters less now anyway. The score would have lesser meaning in the context of today's testing procedures: While reading about the MAT, I learned that, these days, students are allowed to prep for the MAT by taking as many iterations of the test as they care to prior to taking the one that counts. When we took the test in 1985, we had no idea what the test would be. There was no possibility of skewing the results in one's favor by doing targeted prepping. This is yet another example of how meaningless testing can be in higher education. Postscript: Of all the tests for which one can do prepping, I'd say the MAT (and I.Q. tests in general) is the one that is the most impervious to skewing. <-- back to Gershenson pampered life <-- back to deep archives <-- back to |