Questions tagged [exams]

This tag is intended for questions about exams as viewed from the point of view of an instructor.

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80
votes
15answers
14k views

Should I design my exams to have time-pressure or not?

Is it better to design an exam with fewer questions and relaxed timing or with more questions and a resulting time-pressure? One the one hand, it seems that students who really know the stuff will ...
38
votes
12answers
6k views

Formula sheets and books during tests and exams

Some teachers make memorizing formulas, definitions and others things obligatory, and forbid "aids" in any form during tests and exams. Other allow for writing down more complicated expressions, ...
37
votes
6answers
9k views

How can I estimate the length of an exam?

Background: I am fairly new at teaching, and in every subject I have taught, I have had difficulty estimating the length and difficulty of an exam. I need to write an exam for a university senior-...
34
votes
15answers
8k views

Should I change my take-home exam policy because of one suspected cheater?

This is just the third semester I've been teaching, but I've been tutoring for many years. At the moment I'm teaching to community college students a "Business Calculus" course whose curriculum is ...
29
votes
7answers
13k views

What are the comparative advantages of open-book versus closed-book exams?

I would like to know the advantages and disadvantages of open-book exams as compared to closed-book exams, particularly in standard undergraduate courses like calculus or linear algebra. My practice ...
27
votes
9answers
4k views

When handing back exams, what should we tell our students about the distribution of exam scores?

I've seen a variety of approaches to the day we hand back our exams. Show every score listed in order, so every student knows exactly how they compare to others Show an aggregated histogram, for ...
23
votes
6answers
2k views

What are some good rules for handling student questions during exams?

For example, I gave an exam earlier today with a problem that ended in the sentence Use the chain rule to find $(f\circ g)'(3)$. During the exam, one of the students asked me what the circle ...
22
votes
4answers
1k views

Non-answerable questions on exam: What to do?

What is a good strategy when you realize (e.g. while grading the exam) that a question on an exam was incomplete/wrong? More concretely: If it is decided that additional points should be given: How ...
21
votes
2answers
606 views

Exam philosophy

I'm curious if anyone knows of any books, studies, or other resources on the philosophy of creating and grading mathematics exams. After working as a graduate TA for 4 years and dealing with a wide ...
20
votes
2answers
667 views

Handing out $2 calculators for tests?

In a store last weekend, I saw a simple solar-powered calculator for $2. It had four functions plus a square root key. I'm considering the possibility of buying 50 such calculators and handing them ...
19
votes
4answers
2k views

Students' Messy Sheets: The Big Problem of Exams and Homeworks

Students' messy exam and homework sheets (which are messy because of a bad handwriting or an irregular logical argument in proofs) cause many serious problems. e.g. Reading their arguments takes ...
19
votes
8answers
2k views

How can I learn to write better questions to test for conceptual understanding?

I'm worried that I'm bad at realizing when a question I've written requires little or no conceptual understanding to answer. Like, when I'm writing a question for a homework assignment or exam, I'll ...
17
votes
12answers
10k views

Adding irrelevant humorous questions to a quiz exam

Sometimes, when preparing some calculus exams I try to have a "funny question" such as: T/F I love mathematics T/F Calculus 2 is easier than Calculus 1, ... So my questions are: Do you think ...
17
votes
5answers
1k views

How to award points for sense-making at the end of a problem?

Here is a statistics question I asked on a recent exam: How high should the doorway be to allow 97% of men to fit through it? I got a very large number of answers like "3 inches" or "0.0001 feet". ...
17
votes
4answers
2k views

What to do when students are not keeping their eyes on their own test?

At my university, exams take place in a lecture hall, but it is usually pretty packed. Along with alternating versions of tests, it is pretty easy for a student to look to the next row or their ...
16
votes
4answers
2k views

Requiring students to know all the proofs on an oral exam

I'm asking this question as a student, wondering what various pros/cons to the given formula for oral exams could be. Let me give some context first. I am a first year mathematics student at a ...
16
votes
4answers
5k views

Worldwide collection of final examinations in mathematics

I am interested in comparing mathematics (and also physics) final examinations from all around the world for the highest secondary school qualification in the particular country. Especially I am ...
14
votes
5answers
2k views

How to deal with answers containing completely off-topic/random/very wrong arguments?

It often happens that students answer (partly) a questions in an exam (lets assume this part is okay), but then add something completely off-topic or something very wrong in their answer (see examples ...
14
votes
3answers
610 views

Cute Word Problems

I'm wondering about the use of word problems on exams which are "cute": they have a slightly funny story, or some sort of pop culture reference, or tie into a running theme of some kind. (As an ...
13
votes
6answers
3k views

Is it a bad idea to offer variants of a final exam based on the type of allowed calculators?

Background/rant: I am in charge of teaching our single quarter course on vector calculus (don't ask me why the department head thinks the area can be covered in half a semester). The two biggest ...
13
votes
4answers
264 views

It is good to have old exams (with solutions) published?

What are the arguments in publishing or not publishing old exams? If yes, should they contain also a solution? Would you publish them directly after that particular exam or publish your old one's just ...
13
votes
4answers
1k views

What are effective alternatives to a written math exam to evaluate knowledge?

Some students do not do well under pressure or testing situations and cannot demonstrate their knowledge of a math subject with a written exam. On the other hand, I think that students that do not ...
13
votes
4answers
896 views

As a TA, how to reduce imprecise notations/statements in students' exams

I'm not a course instructor, just a TA of the first quarter calculus course who lead discussion sections and grade exams. When grading the midterm, I found large number of students showed some ...
13
votes
3answers
257 views

How to keep track of your old exercises in a heavy proof based course?

In a typical course (proof-based, for the context of this question) I have about 50 exercises that I might want to use when I teach the course again. Each exercise might be used in the same way as ...
12
votes
5answers
693 views

Descriptive Thinking vs. Formal Writing

Sometimes I come across some exam answers which describe a proof sketch or a counterexample very well but are not written formally. Such proofs show that particular student understand the general ...
12
votes
4answers
9k views

What should you do if you lose your student's exam?

Several times, I have come close to losing a student's Calculus exam. These exams are usually common exams, with everyone grading 100's of stacks. I've had exams go in wrong piles or get squished in ...
12
votes
2answers
228 views

How do you incorporate the results from a final exam into evidence of learning in a valid and justifiable way (i.e. grade determination)?

How do you incorporate the results from a final exam into evidence of learning in a valid and justifiable way (i.e. grade determination)? This question is open to all education levels. What is your ...
12
votes
2answers
378 views

How to test knowledge on the real numbers in a written exam?

In German universities, the first-year students typically start their analysis courses with introducing the real numbers. Most commonly, the incompleteness of $\mathbb{Q}$ is discussed using the ...
12
votes
4answers
380 views

How can I encourage my students to team work?

I have a motto, "My class is not an Olympic swimming pool! It is a museum full of the masterwork paintings! Relax and enjoy all of this mathematical beauty which I am drawing on the blackboard!" By ...
12
votes
2answers
328 views

Resources on how to mark a maths exam

I am looking for some resources which tells someone how to mark a (1st year undergraduate level) maths exam paper. Ideally it would cover the basic stuff, like making an error at the top doesn't ...
11
votes
8answers
800 views

Intergration by differentiating will get you $0$ marks - but how to explain why?

When integrating and differentiating, sometimes one direction is easy and the other is harder. A nice example is $\frac{d}{dx}\tan x=\sec^2x$, where differentiating is easy but integration (without ...
11
votes
7answers
574 views

Why don’t all professors let students use notes, books, etc. on exams?

Last semester I had a teacher who let us use any type of information in the exam, for example the course notes, books, solved exercises, etc. The only thing he did not let us use was something ...
11
votes
4answers
319 views

How to design multiple choice questions

I've seen the previously-asked questions about the effectiveness of multiple choice problems, but I want to know about design. What are best practices in multiple choice problem design? The "common" ...
11
votes
5answers
2k views

A Method to Grade a Multiple Statement or True and False Question

I am trying to come up a method to grade a multiple choice question. I prepared a test that consists of some questions and each question has 10 options for which 3 to 5 options are correct. When I ...
11
votes
5answers
4k views

Grading scale: how to handle multiple choice questions with different number of choices

Suppose you have been told to give a multiple choice exam, and to nullify the effects of random guessing by penalizing incorrect answers. Suppose there are $N$ available choices, of which exactly one ...
11
votes
2answers
230 views

How useful are quizzes in undergraduate math courses?

So I have given quizzes in two different ways (1) Quizzes will be a problem taken "verbatim" from an example in this weeks reading, prior to the topic being presented in class. and (2) Quizzes ...
10
votes
5answers
2k views

Advantages on repeating question in student's answer

I see a lot of students who repeat the whole question (i.e., before starting with anything which has some content, they write down all assumptions, claims, etc.) in their answers in homework or exams. ...
10
votes
5answers
952 views

Is there some standard method to measure the difficulty level of mathematics problems?

First off I apologize if this question comes out to be off-topic. I wasn't sure weather to post it on MSE or here. Lately I gave an exam named SSC-CGL. This exam is conducted every year in India for ...
10
votes
2answers
265 views

Placement tests for middle school math

Our district has changed its approach to placing students in grades 6 and 7 math classes. Students considered for placement above grade level must now take a test composed of problems drawn from the ...
9
votes
5answers
433 views

What is a fair way of constructing exams with tiered levels of difficulty?

I would like to construct an exam that has C-level, B-level, and A-level questions. I would like a student who answers all C-level questions correctly a passing grade, a student who answers all C and ...
9
votes
2answers
1k views

How does a take-home exam differ from a homework assignment?

I've taught several upper-level courses recently, and have considered giving take-home exams to reduce the time pressure in the classroom. However, their homework already consists of proving various ...
9
votes
3answers
2k views

Questions for Oral Examination in Mathematics

I am working on some research on implementation of oral assessment in mathematics classroom, and I was wondering are there any questions/problems/concepts in mathematics that can be only assessed ...
9
votes
2answers
354 views

How do I grade long calculations in a mathematics exam in a fair way?

I am currently grading a problem in an exam on analysis for mathematics students. One subtask is to calculate a certain integral (The resulting term has to be as simple as possible.). For this part I ...
9
votes
1answer
144 views

Experimental results about the variability of grades on a math exam

"[Myth] that exams are objectively graded. Daniel Stark and Edward Elliot sent two English essays to 200 high school teachers for grading. They got back 142 grades. For one paper, the grades ranged ...
9
votes
1answer
394 views

Are there examples of countries where the use of CAS systems or graphing calculators was deemphasized or discontinued?

In the last 30 years more and more countries introduced graphing calculators and then CAS systems to their high-school students. But are there already any examples of a trend in the opposite direction?...
8
votes
2answers
368 views

Should students be given partial scores when they gave an incomplete proof by contradiction?

In a quiz, there was a question asking students to show something doesn’t exist. A lot of them gave proofs by contradiction. Initially, I designed the marking scheme so that an incomplete proof by ...
8
votes
3answers
462 views

A student is cheating and I don't know how

I'm teaching a course at a community college called "Business Pre-Calculus", which is basically some varied rudimentary algebraic concepts integrated with some topics from basic economics and finance. ...
8
votes
5answers
247 views

Mathematics exam — How to keep brain functioning through a four-hour exam?

So my question isn't directly related to math, but I think you might be able to help me. I'm a 17 year old, last year at school. My class specializes in math/physics (that's our educational system in ...
8
votes
2answers
1k views

Take-Home Examination on Ordinary Differential Equations?

I am planning to give my students a take-home examination on ODE. The main topic that I would like to cover is Linear Differential Equations of Order Greater than One. For example, I will give my ...
8
votes
3answers
785 views

A4 paper of notes in an exam

What are the effects of allowing students take one paper, say of A4 size, full of whatever they want, into an exam? It might be called a cheat sheet or something similar. Students might write it by ...