Mathematics Educators Stack Exchange
Mathematics Educators Stack Exchange

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Teaching logic through "high school algebra"?

I am going to be teaching a discrete math class in the fall. One of the major goals of the course is a solid understanding of the basics of logic: the precise meanings of "and", "or", "not", "implies", "if and only if", "there exists", and "for…
Steven Gubkin
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Quizzes (with questions known in advance) instead of homework in a graduate mathematics class. Good Idea or Bad Idea? Pros and Cons?

I'm teaching a graduate course in mathematics next semester. I'm planning to have a midterm and a final exam. But I'm thinking about having weekly (or once-every-two-weeks) in-class quizzes instead of homework assignments. My plan (for each week) is…
MichaelGaudreau
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Is higher-math pedagogy responding properly to Wolfram Alpha's existence?

Is the current state of math teaching in undergrad college courses struggling with the availability of easy cheap access to Wolfram Alpha? The homework problem below, one of 40 assigned from one community college lecture, took my son and me each…
Rob Perkins
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In what curricula are "rectangles" defined so as to exclude squares?

Most contemporary curricula define the word "rectangle" inclusively, so that all squares are automatically rectangles. Are there curricula in which this convention is not followed? That is, are there curricula in which "rectangle" is defined so as…
BCLC
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Pedagogical advice/articles for graduate student teaching assistants

Are there any good pedagogical resources or articles that you would recommend to math graduate student teaching assistants (TAs)? Is there any sweeping advice that you would give a TA to improve their effectiveness in discussion? I'm asking this…
Mike Pierce
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How to design a fair oral exam for >10 students?

Oral exams take place at two different points in during their study: As final examination to end their study (i.e., when the students have finished all necessary courses, they have an oral exam about 2-3 courses in a field, e.g., an oral exam…
Markus Klein
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Writing Fractions "Correctly"

I very often see students writing, for example, $1/3x$ when they mean $\frac 13x$. I used to tell them not to write $1/3x$ beause it looks like $\frac{1}{3x}$ until I realized that, according to PEMDAS, it really does mean $\frac 13x$. I feel that…
Steven Alexis Gregory
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How to teach abstract algebra for the first time?

I am a Ph.D student in computer science. I am TAing one course this semester, which requires the basics of abstract algebra like rings, fields, ideals, and basic theorems about them. I have done two courses in the mathematics department related to…
ddd
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Without a constraint of time, is self-study with math textbooks better than college courses?

This question is about mathematics only. My forethought is that courses are usually based on textbooks, but they have less content than the textbooks. There are less problem sets, and chapters are skipped. Is it true that you can learn more by…
Minh Khôi
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What are some fun/nonstandard examples of arithmetic/geometric series?

I am teaching those topics (arithmetic/geometric series) just now, and want some not so standard (fun) examples, which can be used essentially at high school/beginning calculus level. I'm considering some, and will post them as answers, but first…
kjetil b halvorsen
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Can we explain to undergraduates how points make a line?

Many of my students arrive in college believing that lines are (in some way) made out of points. They also believe that points have no length. They want to know how a bunch of zero length points make a line of length 1? Edit I did ask this question…
Jim H
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Is Calculus Necessary?

That title is a quote from Fred Roberts: Fred Roberts. "Is Calculus Necessary?" Proceedings of the Fourth International Congress on Mathematical Education. 1980. p.52ff. "Calculus is not necessary. That will be my premise in this…
Joseph O'Rourke
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Why don't textbooks explain proofs' discovery?

This question concerns only proven statements. I don't know if research papers do, but most math textbooks don't. Counterarguments: Space? 1.1. The increased length from explaining the discovery is justified; if proofs' discoveries aren't explained…
user155
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First year undergraduate text that teaches calculus using probability as a primary motivating example?

There has long been debate about whether a first year undergraduate course in discrete mathematics would be better for students than the traditional calculus sequence. The purpose of this question is not to further that debate, but to inquire…
Jon Bannon
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Problem "seeing" the perimeter of a figure

I was helping a home-schooled student with her homework when we came upon several images of figures that we were supposed to find the perimeter of. In several of the figures, some of the lengths were not given; yet, with some thought, the perimeter…
Steven Alexis Gregory
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