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Moebius_strip
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Jacques, re scrambled exams, funny story about that: a former officemate of mine once gave 2 exam versions: same multiple choice questions but with the choices scrambled. Student X copied the answers off Student Y, who had a different version of the test. They handed in identical answers. Y got close to a perfect score; X got zero. A day later, X went to my officemate to plead for mercy. He'd been having a hard week, he explained; lost his job, broke up with his girlfriend, got sick - the whole nine yards. He hadn't had time to study. Please could my officemate allow for a retest? X spent fifteen minutes begging my officemate, but she wouldn't budge. She told him that his zero stood. At no point during this conversation did she accuse him of cheating, and at no time did he confess. Incidentally, this was the best- and most successfully handled case of cheating I'm aware of.
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Jacques, here were the last two times I accused a student of cheating: * In one class, I gave individualized assignments: everyone gets the same basic questions, but with the numbers changed. This way, students can collaborate but not copy off one another. This didn't stop a group of three students whom I knew to be close friends, who all handed in identical answers....quite a feat, as they didn't even have identical *questions*. All three students were given zeroes on the assignment in question, and protested but did not formally appeal. * At the beginning of the final exam, I told students to put all of their notes away, and verified that they had done so. Then I came around with the tests and formula sheets. Half an hour later, I lifted a student's formula sheet and found, underneath, several pages of his own notes. This time the dean got involved and issued a warning to the student but no punishment. Pretty clear-cut, I think, but neither got the severe punishment that I had been told as an undergrad was given to cheaters (expulsion, black mark on record).
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Re cheating, I think the takeaway point from these comments is that the TAs' supervisor should make a point of going over the school's policy with the TAs, and TAs should make sure they are well acquainted with said policy. I remember having to improvise the first time I caught cheaters, which leaves way too much room for error: my experience is that post-secondaries will not take action against cheating unless the case is airtight, which means that it's easy for an instructor unfamiliar with protocol to have their cheating accusation dismissed on a technicality.
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@Nick - good policy on changing grades, and one that I implement now as an instructor. Now that I'm teaching, I am realizing how inadequate my own supervision was when I was a TA. Despite your comment that no one hired profs for their managerial skills, I would have benefited from half the guidance you offer in this post. I was a grad student at UBC, where math TA's actually run their own classes (usually sections of first year calculus). I took a one hour "how to teach" seminar, was handed a textbook and a list of chapters to cover, and was let loose on 40 students. I chose what homework to assign, I designed my own tests, and did all my grading. At the end of the term all dozen or so sections of the course wrote a common exam that we instructor/TAs didn't get to see in advance. As you can imagine, a student's success in the course was heavily dependent on whose section they ended up in. (One fellow grad student decided to teach an overly theoretical course that had almost no connection to the introductory curriculum he was being paid to deliver; TA oversight was so nonexistent that the course coordinator didn't find out about this until a second grad student TA gave him an anonymous tip, two thirds of the way through the term.) @Mandos: Yes to your #3, and it embarrasses me anew every semester.
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Plenty of this is good for new instructors as well. I teach math, where there is less leeway in grading than there is in essay-based courses (though still plenty), and I would add this: "You are an authority figure, even if you don't feel like one yet. Stand your ground. Listen to your students and be kind, but don't be afraid to say no. If you accidentally added up a student's test mark incorrectly, or if you accidentally didn't give full marks to a correct solution, apologize and correct your mistake. But if you gave a mark of 2/5 on a question and the student thinks they should have gotten a 4/5, don't be afraid to tell them that it's not up to them to decide how much credit a wrong answer deserves."
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But you're teaching at the post-secondary level. What (or who) is driving these curricular changes? I can't speak for other post-secondaries - I teach at a polytechnic, to students who have very clear ideas of what they plan to do after graduation - but where I am, to a large extent, it's industry. Technological advances have led industry to use, and hence require, a broader set of skills. A deeper (or equally deep) set of skills would be nice too, but if we're going to stick with 4-year degree programs (or 2-year diploma programs), something has to give. Time will tell whether, on balance, my school and others have made the right choice. Interesting question about the connection between basic number sense and doing higher order math, and one on which I'm not sure I have much professional insight. But to extend Phil Koop's last comment - that graphing a function can be useful, but only if you have some notion of what to expect - I'd say that "knowing what to expect" is something that ought to be, and no longer is, developed from a young age. Better to train the younguns recognize that 3,4798x2,043 is about 7,000,000 before expecting them to figure out that the function y=ln(x)/x should look "approximately like so" before invoking their TI-84+'s.
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Excellent post. I teach math at the postsecondary level, and I can tell you that your observations about calculators impeding the development of number sense are dead on. Back when I taught financial math, I'd always ask some basic interest rate question: "Joe invests $100 at 2% interest per year, compounded monthly. How much does he have after five years?" Without fail, I'd have at least one student merrily report that Joe would have eleven billion dollars after five years. It didn't occur to them that this couldn't possibly be right. I never got the name of the bank that provided such attractive incentives for opening savings accounts, alas. It's only been ten years since I was an undergraduate math student, but I can see that the ubiquity of powerful calculators and software are allowing for curricula which, for better or for worse, include more and more sophisticated applications - in less depth - in the same number of teaching hours. A generation ago it was unthinkable for students to be allowed to bring in (or be given) formula sheets for exams. You had a handful of formulas that you'd have burned into your brain by the end of the semester, and use them as appropriate. Now, with computations so quick, the focus has shifted; I handed out an 8-page package of formulas for an exam I just gave. During class time, I had no choice but to present those formulas with minimal or no justification, so I couldn't expect students to be able to derive (or even remember) them themselves. (This was a class for engineers.) I allowed another group - statistics students - to bring in their own formula sheets. I didn't give any restrictions on length, and many students brought in entire notebooks in which pairs of formulas such as "a+b=c" and "a=c-b" were listed separately. To some students, each formula is a separate fact; the concepts unifying those facts escapes them. Alas, my department, by and large, has given up on banning graphing calculators. It's a losing battle. Often, my only restriction on calculator use is "you are not allowed to use any calculator that can talk to other calculators." This after my department head caught a student using the Integration App, for which I believe he'd paid $0.99.
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May 29, 2011