Questions tagged [education]

For math questions related to the teaching and learning of mathematics. Note that Mathematics Educators Stack Exchange may be a better home for narrowly scoped questions on specific issues in mathematics education.

This tag is for questions that are primarily about mathematics, but are related to mathematics education. Also consider using the or the tag. On the other hand, questions that are primarily about teaching and learning mathematics would be a better fit for MathEducators.SE.

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Good Physical Demonstrations of Abstract Mathematics

I like to use physical demonstrations when teaching mathematics (putting physics in the service of mathematics, for once, instead of the other way around), and it'd be great to get some more ideas to use. I'm looking for nontrivial ideas in abstract…
Jamie Banks
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Can I think of Algebra like this?

This year in Algebra we first got introduced to the concept of equations with variables. Our teacher is doing a great job of teaching us how to do them, except for one thing: He isn't telling us what we are actually doing when simplifying/solving…
Nico A
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What are good "math habits" that have improved your mathematical practice?

I currently feel like I am not doing maths the best way I could; that is, I'm not making the most out of my time when I'm working on maths problems. The main thing I feel is that I'm not organizing my mind and my derivations as clear as I could,…
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Self-studying real analysis — Tao or Rudin?

The reference requests for analysis books have become so numerous as to blot out any usefulness they could conceivably have had. So here comes another one. Recently I've began to learn real analysis via Rudin. I would do all the exercises, and if I…
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How do you explain the concept of logarithm to a five year old?

Okay, I understand that it cannot be explained to a 5 year old. But how do you explain the logarithm to primary school students?
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A Case Against the "Math Gene"

I'm currently teaching a mathematics course for elementary educators (think of it as math methods, but with less focus on methods and more focus on content). In a student's essay, I encountered the phrase "one is either a 'math person' or not". That…
Austin Mohr
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How to convince a math teacher of this simple and obvious fact?

I have in my presence a mathematics teacher, who asserts that $$ \frac{a}{b} = \frac{c}{d} $$ Implies: $$ a = c, \space b=d $$ She has been shown in multiple ways why this is not true: $$ \frac{1}{2} = \frac{4}{8} $$ $$ \frac{0}{5} = \frac{0}{657}…
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Should an undergrad accept that some things don't make sense, or study the foundation of mathematics to resolve this?

I'm a second year math student. And I've the following problem. When I prepare myself for an exam, I can distinguish two phases. First I'm mainly interested in whatever is necessary to pass the exam. This means that I do not always read the theory…
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Easy math proofs or visual examples to make high school students enthusiastic about math

I'm a teacher in mathematics at a high school. Math has fascinated me for almost my entire life, so I would like to bring that enthusiasm to my students with beautiful yet easy to understand proofs or demonstrations. It's meant for students who are…
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What are some conceptualizations that work in mathematics but are not strictly true?

I'm having an argument with someone who thinks it's never justified to teach something that's not strictly correct. I disagree: often, the pedagogically most efficient way to make progress is to iteratively learn and unlearn along the way. I'm…
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What is your favorite application of the Pigeonhole Principle?

The pigeonhole principle states that if $n$ items are put into $m$ "pigeonholes" with $n > m$, then at least one pigeonhole must contain more than one item. I'd like to see your favorite application of the pigeonhole principle, to prove some…
Álvaro Lozano-Robledo
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Easy example why complex numbers are cool

I am looking for an example explainable to someone only knowing high school mathematics why complex numbers are necessary. The best example would be possible to explain rigourously and also be clearly important in a daily day sense. I.e. complex…
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Is Lagrange's theorem the most basic result in finite group theory?

Motivated by this question, can one prove that the order of an element in a finite group divides the order of the group without using Lagrange's theorem? (Or, equivalently, that the order of the group is an exponent for every element in the…
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How to effectively and efficiently learn mathematics

How do you effectively study mathematics? How does one read a maths book instead or just staring at it for hours? (Apologies in advance if the question is ill-posed or too subjective in its current form to meet the requirements of the FAQ; I'd…
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Are all mathematicians human calculators?

I asked my dad why he did not major in math he said "because he is not good at math". I think I like math, and I think I'm ok at it, but I'm not gifted or anything like that, I just like math. I think I'd like to major in math, but I see all these…
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