Mathematics Educators Stack Exchange
Mathematics Educators Stack Exchange

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What do mathematicians call a proof?

In mathematics education, "proof" is widely used for many kinds of argumentation. For instance, one example could be called a proof, if it is paradigmatic in the following sense: The argument can immediately be transferred to the general case. (To…
Anschewski
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Requiring basic skills to pass a course without increasing their grading weight

As I grade my final exams, I sometimes find calculus 1 students who will pass with a C but lack critical skills like the chain rule. This can be for a number of reasons, for instance: They understand the concepts but cannot do the…
Chris Cunningham
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What is a number?

In a set theoretic point of view all mathematical objects are sets. We "call" some of them as numbers (e.g. sets in $\mathbb{N}$, $\mathbb{Q}$, $\mathbb{R}$, $\mathbb{C}$, $Ord$, $Card$) but what is rigorous definition of a number? In fact this…
user230
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The "water triangle" proportional reasoning task

(I previously asked this at The Mathematics Teaching Community, but I'm hoping it would attract further answers here.) The Wikipedia page on proportional reasoning mentions a "water triangle" task. It seems that the task was created in the 1970s,…
JRN
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What are some good mathematical applications to present in an abstract algebra course?

One of the main difficulties for a student learning abstract algebra is understanding the motivations behind concepts like groups, normal subgroups, rings , ideals etc. Also, many have difficulty understanding why algebra is important and how it has…
user774025
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Good examples of proof by contradiction?

In later courses on automata theory, many students just seem incapable of getting a proof that a language isn't regular right, be it using the pumping lemma (see also the many questions on the matter on http://math.stackexchange.com) or the (often…
vonbrand
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Explaining why volume of cone is a third of cylinder

I came across this video explaining to kids why the volume of a cone is a third of the cylinder of same cross-sectional radius and height. Essentially the explainer presents pre-created cylindrical and conical objects with equal dimensions, and says…
Bravo
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What to do when a majority of students have insufficient mastery of the prerequisite material?

I'm currently teaching a second-semester calculus course in which a significant percentage of my students (over half) either tested into the course just out of high school, took a much easier first semester at a nearby community college, or simply…
Alexander Gruber
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What does it take to find a good math book for self study?

I'm 20 and I never learned math properly in my highschool. I found my interest in math last year and I've been searching for books since then. I tried Khan academy but I have difficulty paying attention to videos. I prefer reading over video…
Abdul Kalam
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Best textbooks to introduce measure theory and Lebesgue integration?

What are the best textbooks to introduce measure theory and Lebesgue integration to undergraduate math majors? Many students in such a class will go on to graduate school and be required to take a similar course in their first year. As such, is it…
Gamma Function
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Does anyone teach logarithms via slide rules?

I just inherited two slide rules from my grandfather-in-law, one wood with smooth action despite nearly a century without use.1 (I used a K+E slide rule myself as an undergraduate in the 1970's.) It struck me that the conversion of…
Joseph O'Rourke
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Computational topology for engineers

Increasingly, I see computational topology being applied to problems involving sensor networks, robotics, data analysis, signal processing and various other areas. The topics I mention are interesting to many of my engineering students, but they…
J W
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What's a good policy for accepting late homework?

There are a lot of ways of handling late homework submissions, of which I've only tried a few. The general policy I've settled on is something like the following. Homework must be submitted at the beginning of class on the day it's due. Late…
Adam Bjorndahl
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Why is absolute value difficult?

My understanding is that students find absolute value to be challenging to learn or understand. Off the top of my head, I can come up with two possible reasons for this. Absolute value is a piecewise defined function. Piecewise defined functions…
Tommi
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Algebra 2 textbooks that incorrectly claim that all solutions of polynomial equations can be found

Over the years I have occasionally encountered a number of Algebra 2 textbooks that make an incorrect (or at very least extremely misleading) claim along the lines that "all solutions of a polynomial equation can be found using a combination of the…
mweiss
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