Mathematics Educators Stack Exchange
Mathematics Educators Stack Exchange

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1500 questions
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Is Linear Algebra Done Right too much for a beginner?

I have asked in Mathematics stackexchange, but I think asking here is more appropriate. I am self studying the book Linear Algebra Done Right by Axler. That's how I started using the great Stack Exchange in Mathematics! I do not have a background in…
JOHN
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Are students majoring in pure mathematics expected to know classical results in mathematics very well by their graduation?

For example, I am confident that very few students majoring in pure mathematics can write a complete proof to the Abel–Ruffini theorem (there is no algebraic solution to general polynomial equations of degree five or higher with arbitrary…
Zuriel
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Teaching methods to make a weak student good at math? (particularly student from social science background)

I am currently teaching a high-school student, 1st grade Social Science. He is weak in mathematics. My initial strategy was to explain basic concept but with high repetitions, so that he can have a strong foundation. Initially, I gave "Solving 1…
Arief
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Flipped introductory real analysis resources?

I am going to teach a flipped real analysis class next term, using Abbott's book. Does anyone know of resources for such a class? I have found the article: "Flipping the Analysis Classroom" by Christine Ann Shannon but would welcome student-friendly…
David Steinberg
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Don't these word problems seem designed to be confusing?

I'm a fairly new private math tutor, and I'm good at math (I have a BS from Caltech with lots of graduate level math), but becoming good at teaching math is something else, which I strive to improve at every day. I've starting working with my…
composerMike
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Motivation for polynomial long division

In the U.S. students in grades $\{9,10,11\}$ often learn long division of two polynomials, e.g.: $$ \frac{x^4 + 6x^2 + 2}{x^2 + 5} = x^2 + 1 - \frac{3}{x^2 + 5} \;. $$ I believe it is fair to say that almost never is any motivation provided: Why…
Joseph O'Rourke
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Integral calculus from the modern viewpoint

This is a soft question. What is the purpose of teaching techniques of integration at the college level? More specifically, in the sense of putting integration into practice, what value does teaching these techniques serve in a world which…
Chickenmancer
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Good real-life examples of transformations of function graphs

I am a graduate student teaching college algebra at a larger state school, and currently I'm covering transformations of graphs of function, i.e.: Given the graph of a function $y =f(x)$, what do the following graphs look like, compared to the…
Oiler
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Small 'new things' to confront talented high-schoolers with

Something my students* often struggle with is how to react on being confronted by 'new things', including functions, notation or definitions for which they are given sufficient definition but with which they are unfamiliar. I would like to get them…
dbmag9
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Can or should students do research in standard major math courses

The following is an expectation for our "course-based research initiative". I'll include the complete wording so you can best understand my question. Designing a Research Proposal/Project Embark on a research proposal/project by being able…
James S. Cook
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Subtraction using Addition (Austrian Method), is it useful to learn this method instead of the usual "borrow" method?

I came across this method to perform subtraction using addition and not using the "borrow" concept, apparently because it is harder to learn it that way. Video - https://www.youtube.com/watch?v=PKOd6S4-iXk This method is referred to as "Austrian…
user13107
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implication vs equivalence when solving equations

I remember we were taught in high school (Eastern Europe) the difference between implication ($\Rightarrow$) and equivalence ($\Leftrightarrow$) and were instructed, when solving equations to be mindful to always proceed with equivalances, not…
Marcus Junius Brutus
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How to show $(x - a)$ is a factor of a polynomial $p(x)$ if and only if $p(a) = 0$ (without division)

I am a graduate teaching assistant at a larger state university teaching a college algebra class. Today we begin our decent into polynomials and one of the facts we will soon get to is the connection between roots of a polynomial and linear factors.…
Oiler
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Interesting but very easy epsilon-delta problems?

I am teaching a real analysis class. Students in the class have inconsistent high school algebra skills. They now have a complete but tenuous understanding of $\varepsilon$-$\delta$ limits. I want to give them problems on which to consolidate their…
benblumsmith
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How much prior math should I review in teaching a graduate-level course?

I am scheduled to teach a graduate-level course in engineering whose basis is in the solution of ODE’s and PDE’s, and thus is about halfway between a math course and an engineering course. We introduce methods for solving these equations…
aeismail
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