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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130
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15answers
8k views

Identification of a quadrilateral as a trapezoid, rectangle, or square

Yesterday I was tutoring a student, and the following question arose (number 76): My student believed the answer to be J: square. I reasoned with her that the information given only allows us to ...
0
votes
2answers
50 views

books about relation between Mathematics and reality and life? [on hold]

Which books I should read to understand better Mathematics? Intuition books to understand better Maths. The books show clearly the relation between Mathematics and reality and life.
2
votes
8answers
427 views

Ceiling and floor functions

What are some real life application of ceiling and floor functions? Googling this shows some trivial applications.
9
votes
4answers
515 views

Non-traditional math concepts for early education

I am currently working on source material for a math-related software project with my mother, who has a PhD in Elementary Education and specializes in math education. While she has quite a strong ...
54
votes
21answers
5k views

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 ...
29
votes
18answers
29k views

How do I explain 2 to the power of zero equals 1 to a child

My daughter is stuck on the concept that $$2^0 = 1,$$ having the intuitive expectation that it be equal to zero. I have tried explaining it, but I guess not well enough. How would you explain the ...
2
votes
0answers
32 views

how to teach steady state in queueing - if at all? [closed]

I am teaching an undergraduate course in Operations Research to business students (they are not: maths students). I want to check, if and how teaching the steady state makes any sense. As in the ...
47
votes
16answers
15k views

Why is negative times negative = positive?

Someone recently asked me why a negative * a negative is positive, and why a negative * a positive is negative, etc. I went ahead and gave them a proof by contradiction like so: Assume $(-x) * (-y) ...
12
votes
1answer
295 views

Algebraic structures associated to flexagons?

Flexagons strike me as objects that would admit investigation in a first course in modern algebra. I'm surprised to be unable to find a reference discussing flexagons using modern algebra language. ...
3
votes
2answers
614 views

What's the most effective ways of teaching kids - times tables?

I'd like to help a $6$ year old who already has a pretty good grasp of $2$, $5$, and $10$ times tables.
0
votes
1answer
15 views

Algorithm for finding Complex Eigenvectors?

I'm wondering if there's a fairly easy algorithm by which one can, by hand, find eigenvectors corresponding to complex eigenvalues for small matrices. Of course, one can always row reduce, but it can ...
6
votes
2answers
382 views

How to explain lagrange multipliers to a lay audience?

So I will be giving a seminar to a scientifically mature lay audience (think bio/social science undergrad level). I have been told that I should count on less than half the audience to have experience ...
1
vote
2answers
113 views

Why study Lowest Common Multiple - LCM

What is the most motivating way to introduce LCM of two integers on a first elementary number theory course? I am looking for real life examples of LCM which have an impact. I want to be able to ...
10
votes
15answers
12k views

What concepts were most difficult for you to understand in Calculus? [closed]

I'm developing some instructional material for a Calculus 1 class and I wanted to know from experience for yourself, tutoring others, and/or helping people on this site where is the most difficulty in ...
15
votes
9answers
2k views

Motivating infinite series

What are some good ways to motivate the material on infinite series that appears at the end of a typical American Calculus II course? My students in this course are generally from biochemistry, ...
8
votes
4answers
833 views

What are or where can I find style guidelines for writing math?

I am a scientist writing my first manuscript with a substantial amount of mathematical methodological documentation. I am using LaTeX, but this is not my question. I would like to find a list of ...
5
votes
1answer
56 views

Best program for creating educational math animations?

I'm looking for recommendations on what program to use for creating mathematical animations. These animations will be used in creating educational videos for high school math -- Trigonometry first, ...
106
votes
44answers
12k views

What's your favorite proof accessible to a general audience? [closed]

What math statement with proof do you find most beautiful and elegant, where such is accessible to a general audience, meaning you could state, prove, and explain it to a general audience in ...
11
votes
1answer
143 views

Has the age at which we teach Mathematics changed over the last two centuries?

My experience of learning Advanced Trigonometry and Calculus is that it was done to 17 and 18 year olds (School Curriculum in Australia). I assumed that it was similar in the UK, US and Europe. In ...
17
votes
1answer
554 views

Which universities teach true infinitesimal calculus?

My colleague and I are currently teaching "true infinitesimal calculus" (TIC), in the sense of calculus with infinitesimals, to a class of about 120 freshmen at our university, based on the book by ...
10
votes
2answers
481 views

How to introduce type theory to newcomer

I want to introduce (dependent) type theory to some friends having background in mathematical logic and set theory. To make this introduction easy I would like to give an informal presentation that ...
-1
votes
0answers
49 views

Why do some mathematics professors teach more/less courses than others? [migrated]

Not sure if this belongs on the Academia site, but since I'm a math major and the question is based solely on my observation of mathematics professors, I figured this site would be best. At my ...
7
votes
3answers
156 views

Algebraic number theory topics for undergrads

What are some interesting topics or problems in algebraic number theory which could be presented to students in a first undergraduate algebra course (which covers some elementary number theory, ...
1
vote
5answers
143 views

Why do counits go that way?

Imagine you want to motivate for an audience the definition of an adjunction in terms of unit and counit. So you can say: Often two functors $\mathcal{C} \begin{array}{c} \stackrel{\large ...
56
votes
16answers
8k views

Interesting “real life” applications of serious theorems

As a student one sometimes encounters exercises which ask you to solve a rather funny "real life problem", e.g. I recall an exercise on the Krein-Milman theorem which was something like: "You have a ...
4
votes
2answers
284 views

Teaching the Concept of Infinity to Children.

I was recently out with the family and we left it up to the children where we ate lunch (11 and 9 years old). They couldn't agree and were going back and forth calling each other names. This ...
2
votes
0answers
79 views

Argument for the zero vector not being defined as an eigenvector

Two days ago, my lecturer of Advanced Numerical Methods gave a review on the topic about eigenvalues and eigenvectors. Just as the lecturer presented the definition of eigenvalues and eigenvectors, a ...
18
votes
16answers
4k 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, ...
1
vote
1answer
60 views

Understanding and teaching the concept of derivative

I need to prepare an introductory lecture about derivatives and the concept of differentiation to a class of people with a general mathematical background (who have also studied calculus a few years ...
2
votes
8answers
347 views

A pedagogical proof that 9's can be ignored when calculating digital roots

I was asked by an elementary school teacher for a proof that you can ignore all 9's when calculating the digital root of a number. For instance, when calculating the digital root of 7593329, you ...
1
vote
0answers
47 views

Ideas for math problem solving class for undergraduate students in university

In our university there is a huge gap between two group of students. a group of them came from Math Olympiad competitions and have a very strong background from high school but others, they have just ...
6
votes
1answer
123 views

Transitioning to Higher Level Mathematics

I am just finishing grade 12 pre-calculus at my school and have strong interest in math. The problem is, it seems some important elements of higher level math are not in my schools curriculum that are ...
3
votes
0answers
104 views

Examples of categories which appear naturally without objects

Regarding the morphisms-only-definition of a category (which is equivalent to the usual one dealing with objects and morphisms), I would like to ask: Which examples of categories in practice appear ...
55
votes
25answers
6k views

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 ...
2
votes
3answers
86 views

Teaching cardinality

I would like to give a class of 60 minutes to my undergraduate students about cardinality. I would like to begin with the definition of cardinality and end with one or two good application of this ...
4
votes
2answers
90 views

Is there a way to prove that the order of an element in a Group divides the order of the Group, WITHOUT USING LAGRANGE'S

This is a very easy fact we use in Group Theory, But somehow, I wondered that whether there may be another way (other than Lagrange's Theorem) to prove that the order of an element divides the order ...
19
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11answers
9k views

3D software like GeoGebra

Does it exist a free interactive geometry software, like GeoGebra, which works for 3D geometry? I would be able to draw spheres, great circles, and so on.
6
votes
1answer
4k views

What are good resources to self-teach mathematics?

I am teaching myself mathematics using textbooks and I'm currently studying the UK a-level syllabus (I think in the USA this is equivalent to pre-college algebra & calculus). Two resources I have ...
3
votes
4answers
130 views

Good way to convince a young kid that $0*0 = 0$?

My little brother (6 years old) asked me a question ("What is $0*0$?") and gave an answer to his own question which I found ridiculous so I refuted it but he still thinks he is right. He says that ...
0
votes
1answer
36 views

Find functions with ''smart'' tangents.

This is a didactic question. Given a differentiable function $y=f(x) \;, x,y \in \mathbb{R}$, I want to construct an exercise in which we have to find a straight line that passes through a point ...
3
votes
1answer
86 views

Two categories sharing the same objects and morphisms

Is there a natural example of two categories $\mathcal{C}$, $\mathcal{C}'$ which have the same class of objects and the same class of morphisms, including source and target maps, but different ...
11
votes
3answers
125 views

Can you recommend a book to learn to teach math to a child?

I am looking for a book which contains some ideas on introducing a child to mathematics. I am not particularly looking for a textbook to be used as part of the teaching (though feel free to mention ...
25
votes
13answers
701 views

Examples where it is easier to prove more than less

Especially (but not only) in the case of induction proofs, it happens that a stronger claim $B$ is easier to prove than the intended claim $A$ (e.g. since the induction hypothesis gives you more ...
525
votes
151answers
33k views

What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)

I'm a children's book writer and illustrator, and I want to to create a book for young readers that exposes the beauty of mathematics. I recently read Paul Lockhart's essay "The Mathematician's ...
1
vote
2answers
76 views

Abstract/formal interest of rings

I am about to introduce first year undergrads to the concept of rings, after spending some time looking at groups; and I would like to give them more than a practical motivation (the most usual rings ...
1
vote
0answers
64 views

Intuition behind the link between coding theory and group theory

I am trying to find an easy link between group theory and coding theory. The usual path that most of the texts follow is that they present introductory material on groups, fields, rings, etc., and ...
2
votes
2answers
58 views

Necessity of algebraic symbolism

We solve different problems algebraically .For example,if we add $20$ with a number and the sum is $42$.What is the value of the number.To solve we denote the number as $x$ and write like this ...
92
votes
11answers
6k views

Is there a domain “larger” than (i.e., a supserset of) the complex number domain?

I've been teaching my 10yo son some (for me, anyway) pretty advanced mathematics recently and he stumped me with a question. The background is this. In the domain of natural numbers, addition and ...
0
votes
1answer
106 views

How to explain this question to a 6 year old

My daughter who is in 1st grade is learning to grasp he meaning of multiplication and has not yet been introduced to division. she is appearing for Kangaroo Math Competition. Following question has ...
5
votes
3answers
99 views

Explaining that $1 \cdot 3 \cdot 5 \dotsm (2n+1) = 1 \cdot 3 \cdot 5 \dotsm (2n-1)(2n+1)$

I have a few students that are having trouble understanding that $$1 \cdot 3 \cdot 5 \dotsm (2n+1) = 1 \cdot 3 \cdot 5 \dotsm (2n-1)(2n+1),$$ specifically that $$\frac{1 \cdot 3 \cdot 5 \dotsm ...