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72

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 ...


42

Your student should get full marks. In fact, I would say that even a more complicated example, like $$\int 2x\cos(x^2) dx = \sin(x^2) + C$$ should be awarded full points as long as the student justifies this by differentiating $\sin(x^2)$. In fact, this solution demonstrates deeper understanding of the meaning of these symbols than the variable ...


35

I think there's room for differences of opinion on this, and the answer might depend on the ages of the students or who the specific students are. When I was a student I enjoyed questions like this, but I'll explain why I don't include "funny" questions now that I'm the one making exams. It comes down to cost and benefit. I think the actual benefits are ...


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 ...


29

It's not just one student. As mentioned in comments, this is just the tip of the iceberg. Various studies gauge the percent of college students who cheat at somewhere between 75% and 98%. I would recommend that you have in-class, proctored exams. That's the only way to ensure that one's math course is not, essentially, a fraud. You may even want to check ...


28

No, I think this is a really silly idea. Let's assume that students are trying to get a 100% score. What is the correct answer to "I love mathematics - true/false"? Is the "I" there the teacher? The student? If it is the student what is demonstrably the correct answer? How can the teacher marking the exam possibly know if the student loves mathematics or ...


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 ...


25

Do NOT give exam questions that are intentionally more challenging than homework or in-class problems. I would recommend precisely the opposite. The point of the exam is really a spot-check that students know the basics and aren't just faking their way all through the class. If there is a time-limit, then that is already a lot more pressure/high-stakes ...


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) ...


24

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 are used ...


24

Not a good idea in my opinion. I am on the Autism spectrum and as such I am a very very literal person and I am often derailed by trying to understand a poorly-defined question. Neurotypical people can look at a poorly defined question and naturally understand that some of the interpretations are absurd and most will naturally understand the meaning. I have ...


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.


21

There is a middle ground: closed-book, with some notes. The disadvantage to open-book exams is that students will waste time looking for answers in the book. I know this from experience. As I personally have a very bad memory, I wanted to keep that aspect out of it. But I saw many students wasting time during exams, flipping through the book. (Have you not ...


21

Let's start by saying that I strongly advice against such a dual-exam. Even if you and everyone involved in the planning think it is fair, students might think differently. In this way, you open up the floodgates for grade complaining. They might not succeed, but even the fact that some might try will cost you a lot of time and possibly reputation. Now, in ...


18

I agree with the other post that you should give full credit unless there were clear directions saying what would and wouldn't be acceptable approaches. I think it would be very, very hard to convey to students why using the integral of tan, which they happen to know, is off limits, while using other integrals they know is allowed, other than as a detailed ...


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-...


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 ...


17

First, make sure they know that: The purpose of exams is to test students' knowledge and understanding. The burden of proof is on their side, that is, blank/unreadable sheets work against them. The teachers might choose to decipher some of the messy work, but this choice is intrinsically unreliable, erratic and may produce unfair results. The teachers ...


17

There's no abstract reason that an imperfect proof by contradiction should categorically fail to get credit. A proof should generally get partial credit based on how much knowledge of the relevant material it demonstrates. An incomplete proof by contradiction could correctly get the main idea but omit some of the technical material needed to make the ...


16

I feel that this will be handled on a case by case basis, but there are some guidelines that can help. If a question is difficult due to bad wording or poor setup: Throw out the question and grade the exam as if it weren't part of your total. Give bonus points to students who got it right or partially so. If a question is wrong: Give full credit for the ...


15

There are a few reasonable approaches, and they vary mostly in (a) intrusiveness towards the students and (b) effectiveness Walk intently in the direction of the student, cough, and stare at them for a minute. From the perspective of the "potentially cheating student", this is quite effective. There's no way they'll pull any funny business while you're ...


15

In some cases (e.g., during an open-book exam), you can opt for no-questions policy. However, I think that case-by-case is the best option. Each time a student asks a question, what I ask myself is (with some stretch, you could call this a “general rule”), $$\text{Would the answer give the student unfair advantage?}$$ Such an approach might mean that ...


15

Making a course easier to pass is not the same as making a good course. There is a certain corpus of knowledge with which practitioners are expected to have instant recall (a.k.a: "automaticity"). If one were to be looking up all of these basic facts constantly, one would not be able to accomplish anything practical. These basic topics are the ones mostly ...


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 (...


15

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 ...


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

Since dtldarek's answer addresses well the issues of fairness to students, I'll mention another consideration. When writing exam questions, I try to make sure each question has a certain intent, that it probes the student's knowledge of a certain concept/definition/technique (or some combination). When a student asks a question during the exam, I have these ...


14

If you are worried about fairness, I'd offer the answer to any students' questions to the whole class, whether announced to the class verbally, or written down on the board.


14

Get a sheet signed by each student who took the exam, use that to check nothing is amiss. I collect exams (and keep them during the whole grading process) into large, sturdy envelopes. So no sheet can wander away. I separate exams by question, each question to be graded separately (some by TAs). Students are required to turn in all questions, with a sheet ...


13

Other people have given other good reasons to have old exams be public, but I want to emphasize the one Andrew Stacey points out in comments: old exams often are public, and pretending they're not only confuses yourself and punishes students with less access. If students get to take their exams home (as they can at most schools, though I know there are ...


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