Mathematics Educators Stack Exchange
Mathematics Educators Stack Exchange

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1500 questions
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6 answers

What should be memorized in math and what should be reference table?

I can never figure out what should be a memorization concept and what should be in a reference table. For example, in calculus, you are expected to memorize all the derivatives and integrals but in real life, you can always just look them up. In…
Lenny
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Category theory without categories and without theory

In undergraduate courses, students are often taught that a function is injective if it never maps distinct inputs to the same output, and it is surjective if every member of the codomain is an output. But in an undergraduate course, or a…
Michael Hardy
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Common phrases having different meaning

When talking with students it frequently happens that they misunderstand what you meant. The common example is the amount of rigor that one would consider "a proof", but there are other things, like smooth meaning $C^2$ or $C^\infty$, ring meaning…
dtldarek
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The word "and" rather than "or"

I asked my students the following question. Q: Express $\cos(\pi+x)$ in terms of $\sin$ and $\cos$. A: $-\cos(x)$. Students: Yeah, but where is the $\sin$ part? If I got this in an exam then I'd think I was wrong...yada-yada-yada.... Their issue…
user1729
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Linear algebra for engineers

When studying linear algebra in mathematics (I mean, for the people studying mathematics) there are many ways of approaching it, depending of your needs, however supposedly every mathematician should have about the same basic concepts, which I think…
Ana Galois
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5 answers

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 is correct. One common approach is to give $P$…
Willie Wong
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Teaching LU Factorization in a sophomore-level Linear Algebra course

I teach this course from David Lay's Linear Algebra and Its Applications, which on the whole is a great textbook and explains things well. It does not explain the steps of LU factorization well, so I started exploring online to see some other…
Sue VanHattum
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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 consist of easy questions, made up by the instructor,…
WetlabStudent
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How can we help students learn to effectively take notes?

All students seem to accept that they should take notes during a lecture. However, they don't think about why they are doing this. Most students think that the reason to take notes is to have a reference for later, but we know that the real reason…
Chris Cunningham
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Computing eigenvalues by hand without determinants

I'm teaching a linear algebra class and I'm considering presenting eigenvectors and eigenvalues without using determinants, as in Axler's book Linear Algebra Done Right. (See also Axler's paper "Down with determinants!".) However, I need students to…
littleO
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What is a good math "curriculum" for a mathematically precocious 4-year old?

I am parent to a 4-year-old son who is mathematically precocious. An example of what I mean (since I'm sure guys like Gauss were proving theorems at 4): He multiplies and divides small numbers easily, like knowing that if there are 3 kids and 12…
Akdinv
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Encourage students to strive for understanding despite looming exams

I am teaching an exercice section for a group of students who have (rather difficult and long) exams every two weeks. The students are focussed on the exams and barely willing to take the time to understand something because they are so nervous…
user11235
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3 answers

How to balance short-term learning outcomes with long-term goals and ethical considerations

Most discussions about teaching often assume that the learning outcome is the important variable (compare evaluations, discussions about clickers, discussions about syllabi, etc.). However, I find that there are teaching methods that I would not…
user11235
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Is there a critical class size for student participation (students perspective)?

I recently asked a question on the use of clickers and one comment I got was: I have a very low-tech clicker technology I use in all my classes. When a student doesn't understand something I say, they raise their hand and ask a question. But in my…
Johan Wikström
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Why are so many online sources "wrong" about directional derivatives?

I noticed many seemingly reputable online sources have "incorrect" description of directional derivatives for real-valued functions in several variables. Here, by "incorrect" I mean it disagree with the definitions in the textbooks I'm familiar…
user13395
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