Mathematics education consists in the practice of teaching and learning mathematics, along with the associated research. Research in mathematics education concerns the tools, methods and approaches that facilitate the practice of mathematics or the study of this practice.

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What is the best way to solve this high school exercise?

Can you share with me how would you best solve this exersise to a high school student? Show that $f(x)=x^2-6x+2$ , $x\in(-\infty,3]$ is $1-1$ and find its inverse.
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0answers
141 views

Why to Use the Same Sign for Minus and Negative?

Using the same symbol for two different concepts may cause confusion. So if one decides to do so, they should justify this choice by showing its advantages over other choices. What about the minus ...
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1answer
196 views

Is the computer changing the way we teach and learn math in schools?

Back in school, what I got taught during school was labeled 'math', but it was actually 'rote arithmetics.' This seems to also be the case of many other people. Some came to hate it and never came ...
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1answer
210 views

What are the big ideas needed to develop conceptual understanding of fractions?

In order to be able to perform arithmetic on fractions, students need to understand what fractions are and how they operate. Just teaching rules (e.g. "to add fractions you must have common ...
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3answers
132 views

Derivative in interesting way

I am supposed to give a 15-20 minutes math lecture, where I am expecting around 20-30 people. The lecture is about derivative. Since this would be my first "class", I would appreciate any suggestions ...
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1answer
345 views

What is the use of Euler Totient or Phi Function?

What is most motivating way of introducing this function? Does it in itself have any real life applications that have an impact. I can only think of a^phi(n)=1 (mod n) which is powerful result but ...
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2answers
2k views

Number of Lines Passing Through a Given Point in the Plane

How can one prove that infinite number of lines pass through a given point in plane, using Euclid's axioms (or Hilbert's, if necessary)?
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5answers
289 views

Why $\sqrt {-1}\cdot \sqrt{-1}=-1$ rather than $\sqrt {-1}\cdot \sqrt{-1}=1$. Pre-definition reason!

It is for years that I teach complex numbers following a historical route. I start with the famous problem of Cardano: Find two numbers whose sum is equal to 10 and whose product is equal to ...
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1answer
114 views

interactive training in mathematics olympiad competition for 8th Grade: Ages 13–14.

I'll enjoy your kindness to ask this question, despite that it seems it'snt the right destination. Please show me an url, for training in mathematics olympiad competition for 6th Grade: Ages 11–12. ...
2
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2answers
87 views

What are some good games for teaching maths to children?

I am due to teach maths to a ten-year-old. I'd like to try out some games such as Nim and Conway's Soldiers. I've found this list on Wikipedia but Googling for more just gives me a load of Flash ...
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0answers
275 views

Is there an elementary introduction to higher order functions?

I am teaching a pre-calculus course (using the textbook by Michael Sullivan if it helps), and I realized that higher order functions seem to show up in with some frequency in pre-calculus and ...
3
votes
4answers
465 views

How to explain Fractional and Negative Exponents

My classmates doesn't understand Fractional and Negative exponents, since I was the top of my class, so they all came to me... Is there any way to explain it clearly to them?
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2answers
87 views

An Integral With an Odd Function That Isn't Contrived

When ever I teach calculus, single or multivariable, there is always the point in the text when the author covers odd functions and then gives an example of an integral to evaluates to $0$ because the ...
4
votes
1answer
823 views

What is the use of the Chinese Remainder Theorem

What is the most tangible way to introduce the Chinese Remainder Theorem? What are the practical and really interesting examples of this theorem. I am looking for examples which have a real impact on ...
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2answers
579 views

What's an induction problem that will be hard to answer with “backwards reasoning?”

I'm currently the teaching assistant for a course that serves as an introduction to rigorous proofs, and I've noticed some of my students have a tendency to try and use a sort of "backwards reasoning" ...
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1answer
420 views

Best applications-oriented introductory calculus textbooks?

Note: I've edited this question on October 9th, after establishing a bounty on it. What are the best introductory calculus textbooks that explain why calculus is important in a broad intellectual ...
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2answers
149 views

Trying to teach supremum and infimum.

I'm helping out my former calculus teacher as a volunteer calculus advisor, and I have under my supervision 5 students. They've already had an exam and... well, they failed. I read their exams and I ...
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6answers
2k views

Cool mathematics I can show to calculus students.

I am a TA for theoretical linear algebra and calculus course this semester. This is an advanced course for strong freshmen. Every discussion section I am trying to show my students (give them as a ...
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5answers
415 views

How to explain infinty to a $3^{rd}$ grader?

In my country in $3^{rd}$ grade in math kids learn the four basic arithmetic operation (addition, subtraction, multiplication and divison) up to $10 000$. My sister this year goes to $3^{rd}$ grade ...
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1answer
347 views

Workshop on Pascal's Triangle for Middle School Students

We're going to hold a three-hour math workshop for some middle school students. It'll about the Pascal's triangle. Well, we can ask the students to find patterns in the triangle, or try to prove some ...
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6answers
418 views

“$n$ is even iff $n^2$ is even” and other simple statements to teach proof-writing

I am supposed to teach undergraduate students who do not major in mathematics and I would like to give them a short introduction to mathematical reasoning and to the concept of proof. I am looking for ...
2
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0answers
130 views

Variation on the Sobolev space $H^1_0$

Let $\Omega\subset\mathbb{R}^n$ be a bounded open set, let $$ C^1_0(\overline\Omega) = \{u\in C^1(\Omega)\cap C(\overline\Omega):u|_{\partial\Omega}=0\}, $$ and let $C^1_c(\Omega)$ be the space of ...
86
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23answers
7k views

Why is there no “remainder” in multiplication

With division, you can have a remainder (such as $5/2=2$ remainder $1$). Now my six year old son has asked me "Why is there no remainder with multiplication"? The obvious answer is "because it ...
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2answers
162 views

Can abstract nonsense be helpful here?

Here a question for those among you, who teach Homotopics/Algebraic Topology at university. I encountered some questions that were in my view quite easier to solve in category hTop instead of Top ...
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1answer
57 views

Proofs as games?

A long time ago (but I can't remember when), I was introduced to the (pedagogical) concept of writing a proof as giving a winning strategy for a game. Basically, given a statement $\forall x\exists y ...
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11answers
2k views

Puzzles or short exercises illustrating mathematical problem solving to freshman students

At high school, the solution method to almost all mathematical exercises is to apply some technique or algorithm you have learned before. At the university, the situation is fundamentally different. ...
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5answers
135 views

Motivation for Studying Combinatorics (Middle School Version!)

I'm going to teach very elementary combinatorics (limited to basic enumeration) during two weeks to middle school students. At the beginning, I want to demonstrate the importance of counting in real ...
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1answer
42 views

Identify the derivative of a distribution

When someone wants to identify the derivative of a distribution $T\in \mathcal{D}'(\mathbb{R})$, we usually write, for $\varphi\in\mathcal{D}(\mathbb{R})$ , $$<T',\varphi> = -<T,\varphi'> ...
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4answers
385 views

A Handwaving Proof of a Specific Existence and Uniqueness Theorem

My problem is as follows: Given the second order homogeneous linear differential equation with constant coefficients $$a\frac{d^2y}{dx^2}+b\frac{dy}{dx}+c\,y(x)=0,$$ is there a good heuristic ...
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3answers
156 views

abstract algebra example book

It's very exciting when you can use the theory to solve "lower level" problems. For example, I'm looking forward to understanding why the quintic equation is not solvable. In the undergraduate ...
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0answers
34 views

The role of a uniqueness theorem for IVPs in a lower-division ODEs class

Please tell me your thoughts about this, and if you agree or disagree. I'll describe my current viewpoint, which is subject to change. Note that I've never taught a lower-division ODEs course. It ...
4
votes
2answers
189 views

What is the most motivating way to introduce modular arithmetic?

What the best way to introduce congruences in a number theory course? I am looking for something which will have an impact. What are the really interesting applications of congruent mathematics?
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1answer
74 views

Rates of Change Question with Mixed Units

I have come across the following question in a past exam paper of a module that I will be teaching this semester. The volume $V$ of m$^3$ of earth removed from a pit after $t$ hours is given by ...
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1answer
547 views

About game theory for high school students

I am a mathematician with a background in analysis who is teaching at a local high school in his spare time. There is some room for extra curricular math subjects and I want to use it for game ...
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1answer
57 views

Where are the resources on the prime number theorem?

I am looking for resources which explain the prime number theorem to 18 year old students. I am not seeking a proof of the result but something which will have an impact and motivate a student to ...
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votes
4answers
431 views

How to Make an Introductory Class in Set Theory and Logic Exciting

I am teaching a "proof techniques" class for sophomore math majors. We start out defining sets and what you can do with them (intersection, union, cartesian product, etc.). We then move on to ...
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votes
2answers
350 views

Did Euler have a trick? [closed]

Did Euler have a trick for discovering things? Some sort of general method he could apply to mathematical objects he came across to see if they yielded any new truths? Did he just ask the right ...
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8answers
510 views

Ceiling and floor functions

What are some real life application of ceiling and floor functions? Googling this shows some trivial applications.
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2answers
165 views

Is it a problem being unable to understand a mathematical definition without examples?

I was reading a book on coding theory, there was a definition fot the Hamming's Distance and also one example. Understanding purely from the definition was hard but the example helped to give meaning ...
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2answers
13k views

Why are prime numbers important in real life? [duplicate]

What practical use are prime numbers? Why do we emphasise the teaching of prime numbers?
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4answers
787 views

How to convince a high school student that differentials don't work like fractions in general?

It all started when I tried to convince a 10th grader that if $f$ is a function defined on $\mathbb{R}^n$ the differential is defined by: $\large \displaystyle df = ...
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1answer
116 views

A way to teach Archimedean property

A student asked me how to understand the Archimedean property, I tried to re-read with him what he has already done in class (well, actually copy from the blackboard in class). However I think I'm not ...
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6answers
8k views

Teaching a 4 year old maths

Im 18 years old and getting to grips with advanced mathematics (pre-university) and I have a younger brother of 4 years old (quite an age gap). I want to get him interested in learning (and away from ...
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2answers
3k views

What is a standard precalculus syllabus?

I'm about to start teaching a calculus I class next week and I was wondering what I can expect from my students. I'm a Brit teaching in the US so I am unfamiliar with the system. I am hoping that ...
4
votes
5answers
202 views

Collecting different answers to a simple problem

I am collecting different answers to the problem below for possible publication in a pedagogical note I am writing. Please post freely (avoiding repetitions), and let your imagination go wild with ...
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4answers
157 views

Resources to help an 8yo struggling with math

Friends of mine asked me for suggestion for one of their children (age 8) who had bad scores at the local Star test (the family is based in California). Both parents work, so they have also limited ...
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9answers
1k views

Should a high school introductory calculus class teach $\varepsilon$-$\delta$ proofs?

It seems to me that most high school students are comfortable with the intuitive notion of a limit ("as $x$ gets arbitrarily close to $c$, $f(x)$ gets arbitrarily close to $L$") and gain little ...
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4answers
2k views

Self-teaching myself math from pre-calc and beyond.

Going to be starting grade 12 (pre-calculus) shortly and looking to get ahead. I would like to try some more rigorous stuff on my own and have a couple questions. Ideally I would like to be prepared ...
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1answer
139 views

The Value of a series

What is the value of the following series $\sum_{n=1}^\infty\sum_{m=1}^\infty\sum_{k=1}^\infty \frac{1}{mnk(m+n+k+1)}$
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2answers
138 views

How to construct a cube

My friend has asked me this question. I have no idea how to answer, but I think the question is interesting enough to be noted here: Consider 3 pieces of wire (not necessary of equal length). Is it ...