Hot answers tagged

66

Learning about different numeral system develops the critical thinking and understanding. Arabic numerals are so ubiquitous that most of us take them for granted. Seeing other numeral systems and analyzing them creates a lot of opportunities for thinking about why did we pick one over the other and that there was a pick at some time, not a given (somebody ...


42

Common knowledge Roman numerals are part of the common knowledge in Western cultures for representing numbers. That's why it's valuable for children growing up in these societies to learn them. It's the same as the reason we teach children Arabic numerals. If you don't know how to read Roman numerals, you'll be effectively illiterate—or "innumerate"—...


37

As I said in the question this has attracted quite a bit of attention. And after a lot of nonsense, I did finally get an answer from a British maths teacher. Although measurements and conversions are taught, schools are also supposed to pass on the direct equivalences between these and Roman numerals. i.e. to teach that C and M are the basis for centi-, ...


31

It is easy to explain the most immediate disadvantage of allowing "aids" during exams: many students misjudge the situation, thinking that having books and/or papers means they can study less. In particular, they often misjudge information access time. But many students benefit from some form or degree of open-access exams, because they can relax a little ...


26

I disagree with one of the other answers when saying that "math is not about memory". Doing math is not only about memory, but remembering your definitions and theorems can be crucial to doing problems. The argument that a mathematician can just look of these things on books disregards the fact that when doing the problem, you need to collect all the aspects ...


26

One other little defense of roman numerals: a lot of students see the "place value" notation we have for numbers as inevitable, since they've used it from before they can remember. But of course it took hundreds of years to invent. Try multiplying CXI by X, for example -- imagining that you're a Roman who can't just translate these into Arabic numerals, ...


25

You forget, that school is not only about knowledge, but also about thinking. Learning Roman numerals and how they work teaches child, that the same thing may be expressed in different ways. And that we may define new system with a new set of rules and now we have to use these different rules to work with this system - hell, the whole maths is just about ...


24

Here's a few useful strategies: 1) Once you've written the exam, time how long it takes you just to write down the answers. That gives you a baseline on how much time someone (you!) who already knows all the questions would take to answer the exam. This is particularly useful for exams that are writing-heavy (like proofs and "explain this" questions). 2) ...


23

My background is in high school teaching, so my experience may not directly transfer, since the types of exams are different. However, I have found a very useful rule of thumb to be this: After writing the exam, I sit for it myself, i.e. I sit down to write down full answers in one sitting. Most students will take six to eight times as long as I did.


17

I allow notes on tests, because math is less about memory than about understanding, and I don't want students to focus on the memory part. I don't allow notes on quizzes, because they are on just one problem type, and I want students to be ready to think it through. You may find this blog post helpful: http://exzuberant.blogspot.com/2012/07/monkey-and-...


16

Aside from your own answer, I also am a firm believer in providing our children with a good educational background. Knowledge in itself is value, even if you cannot always use it for any practical reason, and even if it stands pretty much on its own. In the case of the roman numerals, you cannot do much with them, they do not lead on to other insights, and ...


15

All the answers so far are very general, so here's a very specific, practical answer. Students entering a second-semester calculus course need to be very good at taking derivatives. This includes memorizing the following parts of the differentiation algorithm: The power rule (including the meanings of fractional and negative exponents) The product rule ...


14

Many of the disadvantages of allowing aids can be, in principle, resolved by requiring that the only aids the students have are handwritten by themselves and setting a length limit. (I've seen somewhere between one index card [for non Americans: a piece of paper around 10 x 15 cm squared] and 4 pages of A4 [for Americans: 4 pages of letter paper].) ...


14

The situation you describe is pretty dire. At most US insitutions, an uncurved 61 is a D or F. If your mean is a D or F, and the median is below that (I think that's what you mean by leftward skew?) then most of the class is likely to fail. I think the first thing you should ask yourself is whether the tests were fairly evaluating the goals you set for your ...


13

Since you remark that your question is "deliberately non-specific," here is a (necessarily) incomplete response: First are two links to documents about assessment that might be of interest, and then two grading schemes that I have encountered in mathematics courses. Documents: As far as the philosophy of creating examinations, early work on this was done ...


11

I’m a high school maths teacher and I use a way to test where crib sheets are allowed; yet pupils are rewarded for not using it. At the start of the test, the pupils use black ink and are not allowed to use the test aids (such as crib sheet and calculator). When they want to, they indicate to me that they want to use their aids, at which point they must ...


11

I think there is no general solution, but here are some ideas which could help estimating the time: Do you have access to old exams in the same subject or in something related? Look at them (inform yourself if the students were allowed to bring notes, books, etc.) and compare to what you want to do. Maybe you can also ask colleagues from a different ...


11

Not an answer, but perhaps a clue. Richard Feynman in one of his books (I think the title began "Surely You're Joking...", or it might have began "What Do You Care..."; hopefully someone else will recall the correct and full title) had a couple of stories regarding foreign high-level education (Brazil? physics undergraduate or graduate?)) as well as ...


10

Here is a small list of alternatives to an exam. Lets assume you are not constrainted by your university to some specific kind of progress. First lets collect some criteria we want: Everyone understood the topic should pass the course. Good motivated should should pass with a good grade. Students who, e.g., only learned some definition by heart, should fail....


10

My experience, even with grad students, strongly indicates that students do not realize that "passing the course" (or even "getting an A") is irrelevant, insofar as we want to demand something like perfect recollection of all details from all prior math courses. Apart from gaming-the-system issues, kids just can't fathom this, as it is quite contrary to ...


10

Fairness suggests that the grade a student gets shouldn't depend on the semester they happen to take a course in. So the first question I'd ask is what sorts of grades have students typically gotten in this course. If they haven't typically been averaging 61% at this point, then you need to know what's changed: are these actually a weaker crop of students, ...


10

I haven't tried this, but here are some comments and suggestions. Although one might expect students to be able to do basic arithmetic (and thus not need calculators at all), if your exam involves numbers with many significant figures or with square roots, it would make sense to let them use a basic calculator (since you are teaching freshman calculus and ...


9

I'd like to expand on points that Thomas made. Learning math is like learning a language, and a certain amount of memorization (note: not necessarily drilling!) is a necessary component of that. To use a language, you need to have immediate mental access to the basic vocabulary and grammar. (In math, that means not only the definitions, but the ...


9

In the example you mention of computing truth tables rather than use algebraic manipulations to answer questions about boolean expressions/sets, it's actually a wonderful situation where the students chooses the long and tedious way, not noticing a much more convenient method works much more nicely. In such cases, I let the student waste time getting the ...


9

A useful rule of thumb I got when I started up here (which has turned out surprisingly accurate) is "Solve the exam yourself, multiply by four." In any case, when possible I schedule twice that (some time is lost until everybody is seated, exams are handed out, etc.; and there is always some straggler arriving half an hour late...). But we don't have ...


9

One possible reference (mentioned here specifically for its introduction) is: van den Heuvel-Panhuizen, M., & Becker, J. (2003). Towards a didactic model for assessment design in mathematics education. In Second international handbook of mathematics education (pp. 689-716). Springer Netherlands. Springer Link. (Side-note: The second author, Jerry ...


9

If you use LaTeX to prepare your documents, there are many packages that automatically randomize the order of choices in multiple-choice questions. One recently updated package is esami. (This documentation is dated July 27, 2016.) Its official description is: The package allows to write various type of exercises (multiple choiche questions with ...


8

I believe there is a serious issue of talking past each other here. As MattF. hints at, I'm sure the parent has his reasons, which you should ask him about. You can't know if he is right or not without knowing what he thinks, and even less convince him he is wrong (if he in fact is). As you tell it, you have explained your reasons, but it seems they weren't ...


8

I would not give exam points for corrections. I would worry that the tutor might do too much of the work, and the student might still not understand. What I do is tell the students they must correct their problem, and do three others like it. They must do this for each problem they got wrong. Then they can do a test retake (alternate version, and get full ...


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