# Tag Info

78

The time-pressure not only sorts students by knowledge and speed, but also by who is susceptible to math anxiety. Mathematics Educator Jo Boaler comments in a popular media piece (which includes a few links to more formal research) that: research ... has shown that timed tests are the direct cause of the early onset of math anxiety. Her comments are ...

72

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 ...

45

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-, ...

27

I'm no native English speaker, but you can tackle that question from the mathematical point of view as well. The best verb depends on how you view the nature of definite and indefinite integrals. Operators/Functionals Indefinite integrals are operators mapping functions to a set of functions or function (as representative of the equivalence class). ...

27

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

A common approach in elementary school math is the use of "mad minutes" wherein a child attempts to madly complete as many arithmetic problems as they can. This is an extreme example of a timed assessment. In this description of some research, the authors suggest that when students have math anxiety, some of the mental resources they have available ...

25

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) ...

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

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.

18

This is not really a math problem, it's a social problem. Some schools, such as West Point and Cal Tech, have their own honor code systems for this sort of thing. From what I understand, they work very well. However, most schools do not have any such system. Social scientists and psychologists have studied what factors promote or prevent cheating. Cheating ...

17

While I agree in large parts with the other answers posted already, I would like to say a little something in defence of time pressure. In my experience teaching at the university level, many students fall into the trap of feeling like they understand a concept that they really ought to think about more. I fall into this trap myself sometimes: everything ...

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

Agreeing with comments and other posts: If you want more conceptual answers, give them less details in the set-up. Using your velocity problem, here are a couple of examples of making it more conceptual: Suppose that a truck's distance from you in meters at a time $t$ seconds after the big bang is given by the function $p(t)$. What does $p'(19)$ tell you (...

14

I would like to bring up something for consideration that's really come from the discussion in the comments on Benjamin Dickman's answer. There is a problem with the dichotomy presented in the question: my choice boils down to this: should I drop questions from my exam, even though this means fewer topics on the exam, in order that more students will not ...

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 ...

14

I would avoid the verb solve as I reserve this for things like equations, inequalities and problems. An integral is equal to a number or a function, so verbs like find, evaluate etc are more appropriate. I'd use compute only for numerical integration methods. evaluate and find are the two verbs that are used in textbooks and exams that I've come across. I ...

14

Cornell's Good Questions Project has a great question bank for conceptual questions.

13

Disclaimer: I'm not an educator, so my basis for this answer is quite limited anecdotal evidence. If you apply time-pressure to mathematics, you switch in some sense from testing what the student can do, to testing what the student can do easily. I would think that most of the time you want to test the former. The difference between "not knowing" and "...

12

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

For multiple choice questions it is much better to ask in a slightly different way, namely Are the following numbers even? yes no 1.) O O 17 2.) O O 22 3.) O O 33 4.) O O 42 5.) O O 57 6.) O O 61 7.) O O 49 8.) O O 99 9.) O O 13 10.) O O 30 The advantage is, that you explicitly open the ...

11

I think the given example is highly appropriate. You cannot cover every possible combination of ideas in class. Students display understanding of a concept (rather than "recipe following") by showing the ability to adapt at least a little bit to novel conditions. I think the problem you gave is a great homework problem. I personally like homework to be a ...

10

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 ...

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

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 usually phrase it as "Determine $\int x^2\ dx$" or "Determine $\int_1^3 x^2\ dx$". This way 1) it doesn't tip them off to what type of answer they should arrive at, and 2) it allows them to read the symbol $\int$ as either "integral" or (better in my opinion) "antiderivative". For completeness, in some problems I write "Set-up, but do not evaluate, the ...

10

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 ...

10

I would frame this issue a little differently than you have. I think it's unreasonable, at least in the context of courses which aren't well into a math major, to ask students to do something they have not been taught to do. That is, the problems on an assessment should be the same as problems they've seen already. The catch is that "the same" is actually ...

9

Long ago, I read some fascinating research that I have not been able to find online. The title (or part of it) was in French, though the article was in English. It started with something like y'a'til. It discussed the disparate impact of standardized testing on women and men. A large calculus course at a university with relatively high cutoffs of SAT ...

9

To start off, I'm a mere highschool student. There are a lot of things wrong with how education is done nowadays, but I'll keep focus on this issue at hand. Time is quite a big deal. For the last three years I've been competing in higher level mathematics with students around the state of Florida, and I've come to realize that time isn't a very good test ...

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