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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Is ripping off exercises plagiarism? [closed]

Just a quick question. I teach some undergraduate mathematics. I like to produce notes that contain exercises. Sometimes I make my own exercises, sometimes I take exercises from various sources and ...
4
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3answers
3k views

What is the most effective way of teaching mathematics to my 7 year old kid?

I want to help my kid excel in Math. I can see she has some trouble with additions,subtraction, multiplication and division. Will it help if I let her memorize the multiplication table? or use ...
10
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3answers
429 views

Statements in Euclidean geometry that appear to be true but aren't

I'm teaching a geometry course this semester, involving mainly Euclidean geometry and introducing non-Euclidean geometry. In discussing the importance of deductive proof, I'd like to present some ...
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3answers
151 views

Proofs for Undergraduates

I am teaching a course in proof technique to undergraduate students. One of the things they can do for their project is read an involved proof and explain it, for example Gödel's Incompleteness ...
5
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4answers
347 views

Counterexamples to “Naive Induction”

I was teaching a nine-year-old friend about prime numbers. When I asked him if he thought there were finitely or infinitely many primes, he answered confidently that there must be an infinite number. ...
6
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1answer
106 views

Integral using multiple methods

I'm teaching a Calculus II class and we are covering integration techniques. We've covered $u$-substitution, integration by parts, trig integrals, trigonometric substitutions, partial fractions and ...
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8answers
2k views

Why are epsilon-delta proofs difficult?

What conceptual difficulties do students learning epsilon-delta proofs have, or, why are the proofs difficult? Motivation I have to teach people and never found the epsilonistics particularly ...
8
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6answers
444 views

What are the technical reasons that we must define vectors as “arrows” and carefully distinguish them from a point?

I thought I'd bring this question to math.SE, as it could spark some interesting discussion. When I first learned vectors - a long time ago and in high school - the textbook and teachers would always ...
3
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2answers
137 views

Undergraduate approach to a problem about convex functions

I am preparing some sheets of exercises that I'll assign to my undergraduate students in biology (sophomore class, or first academic year in italian universities). This is the problem: Exercise. Let ...
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3answers
3k views

Getting Students to Not Fear Confusion

I'm a fifth year grad student, and I've taught several classes for freshmen and sophomores. This summer, as an "advanced" (whatever that means) grad student I got to teach an upper level class: Intro ...
10
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3answers
538 views

Why this proof $0=1$ is wrong?(breakfast joke)

We have $$e^{2\pi i n}=1$$ So we have $$e^{2\pi in+1}=e$$ which implies $$(e^{2\pi in+1})^{2\pi in+1}=e^{2\pi in+1}=e$$ Thus we have $$e^{-4\pi^{2}n^{2}+4\pi in+1}=e$$ This implies ...
2
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1answer
346 views

Compact and Locally Compact Spaces

I would like to consult with anyone who is reading this post on how do you explain the distinction between compact spaces and locally compact spaces to students who had just completed topology course ...
8
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7answers
983 views

What are the practical uses of $e$?

How can $e$ be used for practical mathematics? This is for a presentation on (among other numbers) $e$, aimed at people between the ages of 10 and 15. To clarify what I want: Not wanted: ...
12
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7answers
2k views

Why we need to know how to solve a quadratic?

Five years ago I was tutoring orphans in a local hospital. One of them asked me the following question when I tried to ask him to solve a quadratic: Why do I need how to solve a quadratic? I am ...
27
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6answers
2k views

How to tell $i$ from $-i$?

Suppose now we are trying to explain to students who do not know complex numbers, how do we distinguish $i$ and $-i$ to them? They will object that they both squared to $-1$ and thus they are ...
2
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5answers
4k views

Real life applications of general vector spaces

Students familiar with Euclidean space find the introduction of general vectors spaces pretty boring and abstract particularly when describing vector spaces such as set of polynomials or set of ...
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6answers
619 views

Is the Mean Value Theorem interesting to engineers, scientists, and others?

I am trying to decide whether to include whether to include the Mean Value Theorem in a calculus course I will be teaching. I am sort of leaning away from it, in light of the interesting discussion ...
13
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5answers
908 views

Best books in the genre “______ for Mathematicians”

I once heard someone (perhaps from someone famous -- anyone have a citation?) say that there ought to be a series of books called "__ for Mathematicians," each one of which would explain a different ...
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0answers
87 views

References on the equivalence of different definitions of integrability

While writing a chapter of a book about mathematical analysis, I decided to compare some definitions of integrability that are usually taught to sophomore students, in Italy. I briefly collect four ...
3
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1answer
368 views

How did the teaching of mathematics change since the 19th century?

Background: 1) In the book Gems of Geometry, chapter 9 Relativity, the author wrote: "The General Theory concerns gravitation and the mathematics behind it is considered rather difficult ( post- ...
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4answers
195 views

Examples of logs with other bases than 10

From a teaching perspective, sometimes it can be difficult to explain how logarithms work in Mathematics. I came to the point where I tried to explain binary and hexadecimal to someone who did not ...
3
votes
1answer
193 views

What is a motivating way to introduce vectors?

What is a good way to introduce vectors on a linear algebra course so that students are motivated from the start? I need an opening which will have a real impact. Are there any motivating examples?
1
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1answer
86 views

Polynomials and exponentials: showing that $n^k \le c\cdot a^n$

If $k$ is any real and $a>1$, prove that there exists a $c>0$ such that for any integer $n\ge 1,$ $$ n^k \le c\cdot a^n $$ To forestall any complaints about the imperative nature of this ...
13
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7answers
1k views

Teaching abstract maths concepts to young children.

I am interested in opinions and, if possible, references for published research, about the pros and cons of teaching abstract maths concepts to young children. My younger brother (five years old) ...
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1answer
228 views

An elementary (?) minimization problem

This morning, in Italy, there was the national exam of mathematics for students of high schools. One of the exercises asked to solve Heron's problem: given a straight line and two points lying on the ...
5
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5answers
663 views

Purpose of Linear Algebra

How much emphasizes should be on proof on a first course in Linear Algebra? I sometimes feel that they (proofs) crowd out a coherent vision for linear algebra. However I also think a central theme of ...
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1answer
2k views

Tips and examples for a poster presentation in pure mathematics

I will be presenting a poster in a few weeks but have no experience with them. I've seen and given plenty of talks, read and written papers, but I have never made or even seen a poster in pure ...
36
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24answers
5k views

“Negative” versus “Minus”

As a math educator, do you think it is appropriate to insist that students say "negative $0.8$" and not "minus $0.8$" to denote $-0.8$? The so called "textbook answer" regarding this question reads: ...
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1answer
467 views

Purpose of Inverse matrix

What use is the inverse matrix? I would not use it to solve linear systems but there must be some concrete or real life applications where it is used.
6
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2answers
254 views

Teaching permutations, How to?

I posed this question to my niece while teaching her permutations: Given four balls of different colours, and four place holders to put those balls, in how many ways can you arrange these four ...
5
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1answer
173 views

Forum for students - your experiences, recommendations, suggestions

Have you ever used online discussion forum or something similar for students of your course? (Or, if you are a student, have you attended a class, where something like this was used?) If yes, I'd ...
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3answers
249 views

Linear Algebra Journal

Is there any journal which has significant material on the teaching of linear algebra. I am investigating the most effective way to teach a course on Linear Algebra. What are the most important things ...
-2
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1answer
311 views

Mat-1.1020 L2 course material generated by students? [closed]

Mat-1.1020 L2 course is a course usually taken by theoretical-physicist-dept students in Aalto University, here official site. It is a mass course that a massive amount of students fail every year. It ...
27
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17answers
5k views

Examples of mathematical induction

What are the best examples of mathematical induction available at the secondary-school level---totally elementary---that do not involve expressions of the form $\bullet+\cdots\cdots\cdots+\bullet$ ...
5
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1answer
520 views

Who came up with the arrow notation $x \rightarrow y$?

I read that the arrow notation $x \rightarrow y$ was invented in the 20th century. Who introduced it? Each map needs both an explicit domain and an explicit codomain (not just a domain, as in ...
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5answers
246 views

Issues with text problems

When I tutor, I often see people who kind of know the stuff they cover in school at the moment and succeed at straight problems like: Find the derivative of $f(x) = \frac 12 x^2$ But when it ...
5
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2answers
287 views

certain examples of fields of fractions

Rational numbers, rational functions, and Gaussian rationals are examples of fields of fractions. In each of those cases, one knows what the quotients are long before one hears of the idea of ...
2
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0answers
198 views

Motivating questions for some topics in undergraduate calculus

Being a grad student I'm going to teach a whole class for the first time the coming summer and I'm looking for some motivational problems which I could use to introduce different topics. In other ...
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3answers
183 views

“the product of the factors” versus “the factors of the product”

Could somebody please compare and contrast the meanings of the two phrases: "the product of the factors" and "the factors of the product." In terms of expressing possession. Thank you.
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1answer
120 views

“unexpected” isomorphism between finite posets?

The set of all divisors of a square-free number, partially ordered by divisibility, is trivially isomorphic to the set of all subsets of the set of prime factors, partially ordered by inclusion. Are ...
16
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14answers
2k views

Explaining Horizontal Shifting and Scaling

I always find myself wanting for a clear explanation (to a college algebra student) for the fact that horizontal transformations of graphs work in the opposite way that one might expect. For example, ...
2
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2answers
588 views

What is an effective way to teach children the Cartesian coordinates?

My nephew is preparing for a $4$-th grade state test. They need to learn topics like reflection about $x$ or $y$-axis of a point( say $(3,5)$ reflected about the $y$-axis). I tried to explain but ...
4
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5answers
595 views

High school math definition of a variable: the first step from the concrete into the abstract…

variable: A symbol used to represent one or more numbers. High school students are justifiably confused by the two distinct concepts: a variable as something that “varies” in an expression, such ...
1
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1answer
254 views

When my teacher gives me a question involving summation notation, do they expect us to calculate it by hand?

Assuming we don't have a calculator that can do summation notation. My class is not up to summation yet, but I'm asking a question involving this concept because I'm not all that experienced using it. ...
6
votes
5answers
418 views

trivial but non-trivial equivalence relations

Define a binary relation $R$ on a set $A$ by saying $xRy$ iff $x$ and $y$ have the same whatever. "Whatever" is of course some specified function on $A$. This is a "trivial" equivalence relation: ...
4
votes
1answer
505 views

Why don't they teach Fundamental Theorem of Algebra in High School? [closed]

I am currently in AP Calculus BC and one more year to go, I have heard about Fundamental Theorem of Algebra several times, and with the resources that is out there today I tried to search and study ...
2
votes
2answers
302 views

Opinions on foundational math materials to teach 8th grade, 9th grade kids at a Summer Camp

I have been asked to teach mathematics/physics to a few 8th grade/9th grade kids for a summer camp. I have been thinking about it and I realized that I could go about it in two ways: One of the ways ...
3
votes
1answer
561 views

learning maths for statistics

Apologies if I have posted this in the wrong place first off. My work has taken me into a unexpectantly large amount of statistics. In order to really understand what I am doing I need to understand ...
7
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1answer
343 views

Implicit use of the Implicit Function Theorem when finding tangent lines to polar curves.

Recently I found myself having to teach students how to find the slope of a tangent line to a curve in $\mathbb R^2$ given in polar coordinates by the equation $r = f(\theta)$. The students' calculus ...
8
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2answers
421 views

Infinite Series: Fibonacci/ $2^n$

I presented the following problem to some of my students recently (from Senior Mathematical Challenge- edited by Gardiner) In the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55... each term ...