tall dark and mysterious » Those Who Can’t, Queen of Sciences.

So what is the point of introductory college math classes anyway

Moebius Strippe — Thu, 15 Dec 2005 00:00:00 +0000

For the past few months, I’ve been tutoring a college student in statistics. This tutee, unlike the other one I took on this summer, is good-natured, engaged, reasonably comfortable with basic mathematics, and in general an absolute pleasure to work with. But I figure there’s a reason that TD&M gets more hits in an hour than there are holds on every copy of Pollyanna in BC’s public libraries put together, and why mess with a winning formula? So enough about that student.”Let’s talk instead about the purpose of these statistics requirements for business and social science majors.”I taught such a course last year. My objective going into the course – and objective that made its way onto the syllabus – was for my students to emerge with a decent ability to assess and interpret quantitative data. Every lesson plan was subordinated to this purpose. I taught the standard intro-stats notation and terminology, but only as a means to an end. Each and every one of the ten quizzes and three tests that my students wrote contained at least one question that required that they answer in plain English. It was not enough that they be able to give me the bounds of confidence interval; to receive full credit, they needed to tell me what it meant. It was not enough for a student to tell me that a sample proportion fell inside the critical region and that we should therefore reject the null hypothesis; they needed to tell me what that meant in terms of a manufacturer’s or politician’s claim.”The class, for the most part, went rather well. Marks weren’t great; but I was confident that a good mark in my statistics class indicated a genuine understanding of statistics, and not just an ability to pluck out numbers that, when plugged into a meaningless equation, will yield the numerical answer that will be marked correct.”The statistics class that my tutee just completed was quite different. It covered the exact same topics as my class – sampling, measures of central tendency, distribution, probability, estimations of means and proportions, hypothesis testing – but this professor’s teaching and testing style was very different from mine. He gave a lot of assignments, and was fond of breaking questions down into multiple parts that lead a student to the answer. I’m not entirely opposed to some amount of that – hell, I think that such questions are probably the best way, at least initially, to deal with students who freeze when confronted with a problem that they can’t solve immediately – but this prof’s multi-part questions were ill-conceived, to say the least. In particular:” * Every question on a certain topic followed exactly the same template. No two topics shared same template. My tutee quickly figured out that an eight-part question in which the first part asked for a sample proportion and the second asked for the claim of the population proportion, was a hypothesis test that called for use of formulas 8.3 and 8.4. She also figured out that you could plug the first, second, third, and fourth numbers given in the question, respectively, into 8.3; 8.4 used the result of 8.3, along with the fifth number given in the question.” * Even if I had devoted my best efforts to the task, I could not have written questions more leading than this guy’s. For instance:” The distribution of student weights is unknown. 42 students are weighed a) b) c) Which of the following applies: o We can use Formula 7.3 because the distribution of student weights is normal. o We can use Formula 7.3 because the sample size is at least 30. o We cannot use Formula 7.3 because the distribution is not normal and the sample size is less than 30.” * The man was a certifiable jargon/notation fetishist. Tell me, how the hell else do you explain a question of the form “What is the sign (less than, greater than, or not equal to) that appears in the statement of the alternative hypothesis HA?” Or – and this is my bias talking, because I can never for the life of me remember which label goes with which – the query “would this be a Type I or a Type II error?” with no followup.”None of the questions had an “explain in plain English” portion. My tutee, whose term mark was among the highest in her class, could tell me that in Question #4 of Section 9, we reject the null hypothesis because x-bar fell in the critical region, but she could not tell me that what this meant was that the lightbulb manufacturer’s claim was bullshit. She solved the problems on her tests and assignments by pattern-matching on the rigid templates, and on following the leading questions. When I worked with her two nights before her exam, she stated matter-of-factly that she expected to forget everything from the course the next day.”If this what one of the top students in this statistics class has taken from the course, then I think it’s a pretty safe bet that this statistics class is not preparing students to assess and interpret quantitative data.”But I can’t hold this professor responsible, because he seems to be doing a good job under the circumstances: he’s got a jam-packed curriclum to follow, and is responsible for delivering a bevy of content at the expense of skills. Even though this prof he gives plenty of practice problems that prepare for the very predictable tests, and even though he gives excellent notes, and even though he is available for plenty of extra help despite all that, my student – who has been sick half the term and who, by her own admission, has been slacking off lately – is one of the top students. I’m certainly not going to second-guess what I presume was a conclusion that his students could not handle a more rigorous course, one that aims to train students to assess and interpret non-canned quantitative data.”I can’t blame him for concluding that there’s no way he can deliver such a course successfully, so he might as well not have his students hate him by the end of the term. And if that means that there’s no guarantee that an A student will understand what it means for a poll to be accurate within three percentage points nineteen times out of twenty, then so be it.”And there’s a big problem with that. If there’s one math class in which the question “what’s the point of this?” should never ever come up, surely it is introductory statistics. But I can’t for the life of me see how anyone could justify teaching a statistics course like the one I tutored.”I wish I could design such a course, because having taught it once, I know exactly what I’d do differently if I were granted full control over the format. In two words: less content. Oddly, calling for less content in a math class tends to invite charges of “dumbing down”, and we can’t have that! – nevermind that the textbooks of yore contained vastly less content than the ones of today – but emphasized mastery and application.”Here’s what I’d trim out of a single-semester intro stats class:” * Most of the probability section. I love probability – so much that I spent far too much time on it last term – but it’s easy to underestimate just how much difficulty students have with it. I’d get rid of everything that isn’t necessary for binomial probability applications, and leave those in only because of the normal approximation to them. (Height of stupidity: spending three weeks on permutations and combinations, and then glossing over connection between probabilty and statistics. Yes, I did that last year.)” * The Student’s-t distribution. There’s more than enough you can do with normally-distributed sample sizes, and if we’re going to wave our hands over the Central Limit Theorem anyway, why confuse matters with the rule that samples of size thirty use Table A5 while samples of size 29 use Table A7? This time would be better spent elsewhere.” * Though not on the “estimating the standard deviation” section. Estimating means is simpler and more relevant, and students still struggle with it.”The leftover time – and really, there isn’t much when you cover the rest of the course at a reasonable pace – can be used with hands-on activities, which are so natural for a statistics course. It can be used to have students design the sorts of questions that usually appear on tests: the data they encounter when they see the latest polls, or when they weigh precisely a bag of apples, provides suitable fodder for a variety of such problems. It can be used to discuss why one researcher would rather risk Type I errors, and another Type II errors. It can be used by emphasizing, over and over and over again, the implications of the material everywhere.”I don’t think that such a course would be at all dumbed-down from the one that my tutee took this year; to the contrary, it would require students to think far more deeply about the material. But such a course would be faithful to what I assume are the reasons for teaching introductory statistics. And if I were to teach it, I’d feel a lot more better about the answers I give to what’s the point of this stuff than I would if I were instead responsible for delivering the more content-heavy statistics class class that nearly every business and social science department requires its students to take.

On teaching college students what they should already know

Moebius Strippe — Tue, 31 May 2005 00:00:00 +0000

Rudbeckia Hirta succinctly explains that if you can’t do algebra, then you can’t take calculus:” Due to reasons beyond my understanding, high school math and college math are completely unaligned. The K-12 system sends us students whose knowledge is a mile wide and an inch deep: we get students who are shaky at algebra, frightened of fractions, and unsure of how to find the areas of basic plane figures (and completely unable to accept the idea that it is a reasonable request to ask them to solve non-standard problems where the method of solution is not immediately obvious), but they have been exposed to matrix arithmetic, computations from polynomial calculus and other supposedly “advanced” procedures. You would think that the “college prep” track would prepare students for college, but it doesn’t. Recently I read somewhere (maybe in Focus?) that there is more calculus taught in high schools than there is at colleges.”See also: mathematics by pattern matching, word problems, et al. So much of this problem can be traced to the fact that students do not understand that an equation is a relationship among quantities. Each equation they see is a concept unto itself, to be memorized and applied to the word problem on the test that looks like the word problem that I did on the blackboard and that used a similar equation. If the word problem on the test doesn’t look like any of the problems I did in class, then that question is “totally unfair”. Most students will leave the question blank, or solve a completely different problem (one with a ready-made equation) in the space provided.”This New York Times op-ed is about teaching freshman English to illiterate college students, but I’m sure that anyone teaching freshman math to innumerate college students can find plenty to relate to. I’m not sure I’m willing to buy into, wholesale, the author’s belief that content should be ignored in favour of form, but I can’t argue with success:” On the first day of my freshman writing class I give the students this assignment: You will be divided into groups and by the end of the semester each group will be expected to have created its own language, complete with a syntax, a lexicon, a text, rules for translating the text and strategies for teaching your language to fellow students.” 14 weeks later – and this happens every time – each group has produced a language of incredible sophistication and precision.” How is this near miracle accomplished? The short answer is that over the semester the students come to understand a single proposition: A sentence is a structure of logical relationships. In its bare form, this proposition is hardly edifying, which is why I immediately supplement it with a simple exercise. “Here,” I say, “are five words randomly chosen; turn them into a sentence.” (The first time I did this the words were coffee, should, book, garbage and quickly.) In no time at all I am presented with 20 sentences, all perfectly coherent and all quite different. Then comes the hard part. “What is it,” I ask, “that you did? What did it take to turn a random list of words into a sentence?” A lot of fumbling and stumbling and false starts follow, but finally someone says, “I put the words into a relationship with one another.”"An equation is a relationship among quantities. How many times have I tried, and failed, to get this idea across? Imagine getting students to realize it for themselves! Unfortunately, many students lack the intuitive ideas about math needed to know, even subconsciously and with the help of leading questions, that equations are anything other than a jumble of letters, numbers, and symbols. (Even though I spent twenty minutes showing how we could use the definition of a circle and the Pythagorean Theorem to derive the equation of a circle in the Cartesian plane, nearly all of my students were angry that I wouldn’t provide the formula on the test. I mentioned, incorrectly, that they could derive the formula themselves, on the test, if they needed to; of course, I was wrong.) But I would gladly sacrifice 80% of the poorly-learned content in a first-year college math course if I could instead effect a solid understanding of what equations really meant – and how to get one from a sentence or two of information. I wonder if Fish’s lesson could be adapted to the first-year math classroom.”At Critical Mass, where I found the NYT piece, Erin O’Connor isn’t optimistic even about applying it to the English classroom:” [M]ost university composition courses are taught by graduate students who are a) not necessarily good writers themselves, and b) often more interested in using the composition classroom to practice teaching the content they hope to teach as non-composition teaching English professors, and you’ve got a situation in which the Fish vision, regardless of its merits, is pure pipedream.”Ditto. No one teaches precalculus if they can avoid it; at Island U, it got passed from temps to new faculty to the department head, who teaches the courses that no one else will teach. Everyone says that the precalculus course needs to be completely revamped, but given the option, they’d rather take a less thankless teaching assignment than put forth the effort to revamp it. And around and around we go.”Gather ye round and swoon over my (ex) department head.”" Righteous Indignation, Those Who Can’t.”The second semester of the year has ended, this time for real: this brat wrote her final exam last week. Finally. Department Head handled the whole affair, from arranging the exam date to grading the paper, and MLIHASIM got the C that she needed. So, good on her, I guess. Not content, however, to leave the course with her honour even vaguely intact, she penned a valedictory email to Department Head, thanking him for supervising and grading her exam, which she’s sure was a huge burden for him, but what could she do? – if it were up to her, she pointed out, she wouldn’t have had to write that exam at all. She informed him that for the most part she “enjoyed having [me] as a teacher”, and that I was “good at explaining the basics”, but that my “tests and exam were significantly harder than the homework” and in fact contained some “questions that we never did in class.”* Since she hadn’t done math in years and years, she had a tutor “show [her] how to do all of the homework problems” and yet she still found the exam “very hard”. Oh, and she talked to some other students and they agreed with her, and would Department Head “please keep this sort of thing in mind” the next time he hires faculty? If this sounds familiar, it is: she aired precisely this grievance (minus the hiring advice) every single goddamned time we met outside of class, not to mention several times over email.”Department Head forwarded me this note. He also, God bless him, forwarded me his reply, which was basically all,” Dear MLIHASIM,” I’m glad you enjoyed Moebius Stripper as an instructor. As for your other remarks, I’m afraid that your expectations of a college-level math course are incompatible with reality. MS’ exam was no harder than the ones I give when I teach this class with the same text (and hence with similar homework). Math is not about memorization; in fact, mastering it requires that you be able to apply the concepts you learned to new problems. That you did not learn to do this in spite of the effort you put into this course indicates that a C was an appropriate, if not generous, mark for you to achieve. MS taught this course exactly as it should be taught, and exactly as I would teach it – though I don’t think I am as patient as she is! Speaking of which, your hiring advice is rather moot, as I’m the one who will be teaching this course – as well as the follow-up – next semester. Say – I guess that means I’ll have you in my class! See you next term and have a good summer, and I look forward to seeing you in the fall.”Dealing with students who think that they should be allowed to dictate the terms under which they learn (or fail to learn) the subject is frustrating. I can’t imagine how much more frustrating it would be if those students had the support of my boss.”* However, some of the exam questions were actually identical to questions on the review sheet – which MLIHASIM had actually told me she wasn’t going to do, because it too was too hard.

Book review: Essentials of Statistics, 2e, by Mario F. Triola

Moebius Strippe — Mon, 28 Feb 2005 00:00:00 +0000

[I've decided to make a habit of reviewing all of the textbooks I use. This one's cross-posted on amazon.com, which contains many reviews of math texts, very few of which seem to be written by people who know much about math or math texts. I've also reviewed the dreadful precalculus book, and a calculus text that I'm appreciating a lot more in retrospect.]“* * *”Triola’s book is, for the most part, an excellent choice for an intro stats course. As an instructor, I find it relatively easy to work with, and the included STATDISK gives students many opportunities to analyze large sets of data without having to enter hundreds of values into calculators or computers. It also contains a lot of examples taken from actual data sets; this is the text that will deflect that ubiquitous “what’s this useful for in real life” question from students. A few issues, though, dog the book. In order of importance:” 1. Chapter 3-6, on counting methods is either underdeveloped or overdeveloped, depending on perspective. The short section gives an everything-but-the-kitchen-sink survey of the topic – permutations and combinations and such are dealt with in one fell swoop and followed up with only a smattering of problems, giving students little oportunity to fully digest the most mathematically-intense part of the course. If you’re teaching this course to math majors, you’ll need additional time and material for this section (I recommend Sullivan and Mizrahi’s Finite Mathematics); if you’re teaching humanities/social science majors, who are more concerned with data collecting and analysis, I’d recommend skipping this chapter entirely.” 2. The book makes such frequent references to the TI-83+ calculator that one is inclined to wonder if Triola is receiving kickbacks from Texas Instruments. Contrary to what the book would have you believe, it’s not necessary to invest in this beast (retail price: >$100) in order to compute standard deviations and correlation coefficients; my students are managing just fine with their $15 calculators with statistical functions.” 3. In Chapter 4, there’s some mention of the principle that if, under certain assumptions, the probability of an *observed event* is very low, then the assumptions are probably incorrect. There’s some merit to that, to be sure (if all 1000 of my coin flips came up heads, it’s natural to question the original assumption that my coin was fair), but Triola would do well to apply the critical thinking procedures exalted in Chapter 1 to elaborate on this. For instance: it’s highly unlikely that Betty Terwilliger would have won the jackpot in the Lotto 6-49 if the contest wasn’t rigged (probability: 1/14000000 or thereabouts), and yet, she did. (Similar arguments can be – and have been – used to defend intelligent design and astrology.) It’s a subtle concept, one that deserves more attention than the cursory “this is the law, and it’s important” treatment that Triola gives it.”These flaws aside, Essentials is a sound survey of the subject, one that’s very nicely designed with its audience of humanities and social science majors in mind. The examples are timely, and the anecdotes are interesting and relevant. The book justifies the subject matter without getting bogged down in formality, which is an ideal balance for its intended audience. In the hands of a knowledgeable and experienced instructor with sufficient prep time, it provides very good support to a statistics course for non-majors, but it’s not self-contained.”Everything I Ever Needed To Know About Setting Math Tests, I Learned From My Five-Year-Old Self”" Those Who Can’t, When We Were Young, Know Thyself.”Every semester, I get complaints from students who take issue with my testing style, which requires them to avail themselves of cognitive functions more complex than those of memorization and pattern-matching. The standard complaint is a variation of “some of the questions on the test are different from the ones you gave on the homework, and that’s not fair.” I have a variety of explanations and analogies I use for this purpose; these days, I tend to explain that I want to see my students apply what they are learning in my class, and I point out that there are very few jobs in which one’s boss will assign only tasks that are identical to ones that he or she has outlined step-by-step before . None of those jobs, I tell them, require university educations. In fact, I point out to the students to whom this is relevant – many of my students are in my class so that they may have career options beyond the dull, low-paying jobs at which they worked for a decade or so.”But I’ve never used the most apt analogy available. My most compelling reason for testing beyond the exact material I presented in class has its roots in my early childhood.”When I was four and a half, five years old, my mother was pregnant with my brother. Five is an awkward age for this sort of thing – it’s old enough to see through the stork explanation, but too young to really understand the nuts and bolts of conception. My mother’s first-pass attempt to negotiate that murky territory between Satisfy Child’s Curiosity and They Don’t Need To Know Everything Quite Yet was, I presume, a pretty standard simplification of affairs. Bypassing the nitty-gritty of it all, Mom’s explanation segued right from foreplay into conception: Mommy and Daddy cuddled a lot, she told me, and then the baby got inside Mommy.”This made sense to me at first, and I, wanting a baby of my own, decided to apply my new knowledge. I don’t think I’ve ever greeted my father as affectionately upon his arrival home from work as I did that week during my mom’s third trimester, and both of my parents were quite touched by this display of love until they discovered my ulterior motive. The limitations of the cuddling story thus revealed, my mother sat me down beside her, and explained the whole damned thing to me, or close enough. I don’t remember exactly how she presented the story, but I do recall that it involved a penis and a vagina and a sperm and an egg and a uterus, and all sorts of other cool stuff I had never heard of before. I was fascinated. (I was also, I should mention, touched by how much my parents must have wanted babies if they were willing to go through all that to have us. Not just the pregnancy and labour part, but the rest of it, too.)”This was a real mouthful, especially for a child not quite five, so during the course of the story, my mother would periodically ask me questions to ensure that I was following:” So tell me, honey, where does the baby grow?” The u-ter-us.” Good, sweetie, that’s right!”#NAME?”My mother was wonderfully impressed with how well I was taking it all in, and she regaled her friends and relatives with stories of how her precocious not-quite-five-year-old daughter actually understood how babies were made.”This all exploded a few days later, when I approached my mother earnestly with a question. I’d been thinking about this a lot, I said, and I understood all the stuff about how the baby gets made, and how it gets fed, and where it comes out, but there’s something I just don’t get.”What is it, sweetie?”Mommy, I said, when it’s time for the baby to be born, how does it jump over the sperm and the egg?”A few years ago, when my mother told me this story, she reflected at length on how she’d really, truly believed that I understood the human reproductive process, and then – that question. I could repeat parts of the story back to her, but I had missed the point utterly.”I know now, however, exactly how my mother felt. I don’t have a five-year-old and a negative-point-seven-year-old, but I have four math classrooms full of first-year students. Many – nay, most – of them put long hours into their homework, and a majority are reasonably proficient at producing answers to homework problems, as long as their friends, their tutors, or their instructors have worked out identical examples before. Many of those same students have no true understanding of simple algebra. They can repeat things back to me, but they have no concept of the hows, the whys of it all. I’d be a negligent teacher if I allowed that group to excel without addressing the huge gaps in their knowledge.”And this is what accounts for my (firm! non-negotiable!) philosophy of giving tests containing questions that differ ever so slightly from the examples from class and from the homework. In testing my students thusly, I’m not trying to trick them; I’m merely trying to gauge how well they know the material, rather than simply how well they can memorize the limited set of problems I do in class. In one class, for instance, I discussed how one can produce a graph by seeing how the function differs from a simpler, more familiar function. I did several examples involving parabolas, absolute value, and square root functions, and I assigned some homework on the topic. On the test, instead of giving them a function and telling them to give me a graph, I gave them a graph and told them to find the function. This allowed me to distinguish between the students who merely sleepwalked through the assignment, and the students who actually thought about it.”This approach has made me unpopular with a vocal contingent of my students, many of whom see no tension between their bald admissions that they can’t add fractions, and their routine claims that they deserve A’s and B’s in my class. I will not bend on this issue, and on occasion I toy with the possibility of telling them the story from my childhood that gave rise to my dogmatism.”Yes, I’d say to them, you did the homework, and you can do questions that are identical to the ones I did in class. Questions like that test if you know that the baby grows in the uterus.”But getting you to repeat the homework questions that I showed you isn’t enough to convince me that you realize that the baby doesn’t jump over the sperm and the egg, and that’s at least as important.”At some point, my mother brought home Where Did I Come From, which I still think provides a marvellous, age-appropriate, and quite thorough explanation of above. I highly recommend it.

Teaching binary math to third-graders

Moebius Strippe — Sat, 12 Feb 2005 00:00:00 +0000

A few weeks ago, TangoMan from Gene Expression sent me this fascinating description of a teacher’s use of the Socratic method to teach binary math to schoolchildren. It’s too interesting to excerpt; read the whole thing.”I don’t teach math to little kids very often, but I’ll have to keep this in mind if I ever get back into math mentoring. One thing that came to mind in reading this page: this is the answer to the inane claim that the only alternative to teaching little kids boring drill-type math that will surely turn them off the subject forever, is to gloss over the boring routine stuff and give them calculators while they’re still at the age where they’re liable to chew on them. The kids in this link learned some real math, and had fun doing it.

Two thoughts on the statistics quiz

Moebius Strippe — Sat, 29 Jan 2005 00:00:00 +0000

Last week, Rudbeckia Hirta at Learning Curves posted a handful of definitions of the Pigeonhole Principle, as given by her students. Go read them if you haven’t already: they’re not only spectacularly incorrect, they’re also bizarre, incoherent, and could rival the output of The Random Sentence Generator. I was jealous. My students’ incorrect answers just make me cry, not laugh. I said as much in the comments, and RH replied, You would get equally comic answers if you were able to ask this sort of question. Maybe you could try, “What is a function?”"I have no qualms about designing quizzes with the singular purpose of acquiring fodder for entertaining blog posts, so The opportunity presented itself this week, when I decided to check if my students really knew what the standard deviation measured, and not just how to evaluate it. “What characteristic of a data set does the standard deviation measure? Explain in a sentence or two,” I instructed, and tingled with anticipation as I collected the papers.”I sat down to grade them later that day, and “I got nothin’ for you, folks. Apparently my students actually know what characteristic of a data set the standard deviation measures.”Hunh. I guess that’s okay, too.”* * *”One aspect of my job that never fails to surprise me: the strange and many ways in which my students don’t understand the subject. I’m still caught off guard by these, even after tutoring and teaching math for years. And I’m not referring to the sort of dear God, why can’t they add fractions already frustration that I experience on occasion and have chronicled in detail, but rather the very frequent oh, they’re confused by THAT. I didn’t even realize that that could be confusing realizations.”For instance: on the stats quiz, I asked students to write down the formula for the standard deviation, and also to specify what each of the variables represented. The question was, for the most part, quite well done: most got the formula right or close to right, and most were able to tell me that x-bar was the mean, the xi’s were the data values, and n was the number of values.” and then, half a dozen or so of them also went on to explain that the capital sigma meant to add stuff up, and that the symbol that looked like a checkmark with a horizontal tail meant to take the square root.”They don’t know the difference between variables and functions. I had no idea.

The rejected first draft of the course catalogue

Moebius Strippe — Thu, 25 Nov 2004 00:00:00 +0000

Rudbeckia Hirta breaks down the first-year math courses at her university. I think her descriptions are more useful than the standard “polynomial, rational, trigonometric, exponential, and logarithmic functions, their graphs, and applications”-type outlines, which give little idea of what students should expect from a psychological standpoint.

Sign of the times

Moebius Strippe — Mon, 22 Nov 2004 00:00:00 +0000

I’ve bemoaned my students’ inability to do simple mathematics many times on these pages; I’ll spare you a rerun. Suffice it to say that by and large, my younger students – all of whom are less than a decade my junior – have been weaned on calculators, and consequently, an appalling number of them can’t multiply integers or add fractions in their heads, or even on paper.”What has surprised me is the number of students who have expressed to me that they feel cheated by their education. I’ve had a good half dozen students tell me that they wish they had not been given calculators so early. “If I hadn’t been allowed to use a calculator at such a young age, I would be able to multiply simple fractions together and add double-digit numbers,” said one student in what has become a typical conversation. “It’s ridiculous – and students today are allowed using calculators while they’re learning to add!”"But then she continued, in all seriousness: “I think that students shouldn’t be allowed to use calculators in math class until at least grade four.”

Two quick stories about my classes

Moebius Strippe — Sat, 30 Oct 2004 00:00:00 +0000

1. Yesterday, a handful of students from my late morning class arrived in class bedecked in holiday garb – goblins, witches, and ghosts were the most popular. “Miss,” one student said, “are you dressing up as anything for Hallowe’en?”"”Yeah,” I replied, “I’m dressing up as a math teacher.”"Twenty-five students rolled their eyes at me.”"Come on,” I challenged, “what are you more scared of – goblins, or next week’s test?”"They concurred.”2. My university has an odd way of scheduling classes, and as a result, many of my students have only my class on Fridays. Consequently, many of my students have recently fallen ill to the Friday Flu, an illness that afflicts approximately five times as many students on Fridays as it does any on other day of the week.”Eight days ago, ten students – out of twenty-eight – showed up to my late afternoon precalculus class. Nearly all had been present for their test two days earlier, and over twenty were there the following Monday. I wagged my finger at the Monday crew, informing them that I’d given a full fifty-minute lesson the previous Friday, and that I had trouble believing that all of them had perfectly legitimate reasons for being away that day. They were appropriately sheepish, but as any math teacher knows, lessons tend to sink in better when they’re presented in more than one way.”We’re covering functions these days, and I presented them with some graphs of increasing and decreasing functions. Anticipating the frequent, “what does this have to do with real life?” query, I gave an example: “For instance, we can look at a graph that gives Friday attendance as a function of time.” I had the data from the past seven weeks: 34, 30, 27, 22, 20, 14, 10. “The larger the value for t,” I said, “the smaller the number of students at time t.”"Twenty-three students showed up yesterday.