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.

learn more… | top users | synonyms (1)

2
votes
4answers
296 views

How would you create a math class that centers on the cultural experiences of African American and Latino students [closed]

I need to write a paper on "Ethnocentric Mathematics" and I have no idea what kind of effective teaching strategies are available. We read an article from this scholar named Tate who explained that in ...
5
votes
6answers
351 views

What is the point of quadratic residues?

What is the most motivating way to introduce quadratic residues? Are there any real life examples of quadratic residues? Why is the Law of Quadratic Reciprocity considered as one of the most ...
11
votes
2answers
137 views

Is the maximal path through a math book necessarily linear?

I'm studying with two main math books (Munkres and D&F) these couple of months. My method so far is just going through the book page by page constructing everything in it (independently if I can) ...
11
votes
3answers
153 views

Applications of functions of the form $f(x)^{g(x)}$

Early on in my calculus education, I learned how to take the derivative of $x^x$ by re-writing it in the form $e^{x\ln x}$. More generally, this technique is helpful in finding the derivative of ...
5
votes
2answers
160 views

Is it better to teach or to grade?

As a graduate student at my university, I have the option many times of deciding what type of work I do for support. The two basic options are to teach either a calculus or college algebra course, or ...
3
votes
1answer
60 views

Topic for teaching assessment

I'm in the position to have a teaching assessment with a tutoring agency next week. This assessment will include me teaching the assessor a topic of my choice in 15 minutes, demonstrating the Socratic ...
2
votes
0answers
66 views

(Actual) applications of basic differential and integral methods

If this isn't the place, I apologize: At the end of my calculus class, we asked the students (among other things) what some applications of calculus methods are. Disappointingly, many focused on the ...
4
votes
0answers
507 views

Soft question : First year student and confused

I hope I won't tire the fellow mathematicians with this question but I am very, very confused... I am a first year undergraduate student of Mathematics. I can't say I am a prodigy, maybe having an ...
5
votes
5answers
162 views

$\mathrm{card} ( \mathbb{Q})=\mathrm{card}( \mathbb{Q^c})$: Overcoming Wrong Intuition

This is a widespread intuitive argument, asserting that $\mathrm{card} ( \mathbb{Q})=\mathrm{card}( \mathbb{Q^c})$: Between any two rational numbers there's an irrational one and vice versa. So ...
10
votes
4answers
317 views

Is studying mathematics chronologically a good idea or not and why?

In high school nowadays most mathematics you learn is fairly 'old'. You have your geometry, all of which (taught in high school) was known to the Greeks more than 2 thousand years ago. You have ...
1
vote
0answers
90 views

How would you explain the pdf of the normal distribution to high school students (11th/12th graders)

I will be teaching the normal distribution in January and I need to know how to effectively explain the concepts that does not in any way confuse students or make them feel that the material is ...
4
votes
2answers
205 views

What is a good example to show high school students why a proof for induction is a reasonable kind of proof?

I teach average-level high school students who have not had much beyond Algebra 1. I want to show them why induction makes sense. I want the sort of problem where it is intuitive that a statement is ...
2
votes
1answer
131 views

Explaining probability theory versus statistics

I'm not sure whether this question was asked before, but it's hard to search because of lots and lots non-descriptive titles like "statistics and probability". The context: There is an anecdote I ...
24
votes
9answers
642 views

What are the applications of continued fractions?

What is the most motivating way to introduce continued fractions? Are there any real life applications of continued fractions?
3
votes
0answers
69 views

Math for kids with Cuisenaire rods

I work with kids and i am searching some cool stuff to do with Cuisenaire rods. Thinking about an application i thought that i can show to my students what will be the sum of first $N\in\mathbb{N}$ ...
1
vote
0answers
127 views

Software/Applet to Draw Tree Diagrams (for Enumeration Problems)

I need a software/applet/flash file which easily draws tree diagrams for simple enumeration problems: I want to give number of the vertices in each layer, and it draws the diagram which shows all the ...
4
votes
4answers
242 views

Showing How Prime Factorization Helps Solving Problems

I need some problems conceivable by middle school students, which are not easy to solve unless the prime factorization of some number is known. An example: It's not easy to know wheter $n$ can be ...
3
votes
2answers
82 views

Motivated and unmotivated mathematics courses [closed]

The standard calculus course does not acquaint the student with the reasons why calculus has been and continues to be important in the intellectual development of humankind. Rather, it attempts to ...
3
votes
1answer
164 views

What are the benefits or losses of learning real analysis through a constructivist approach instead of a standard apporach?

Recently I've found some courses on real analysis that use the constructivist approach and I got curious on some aspects: What are the benefits of learning through this approach? Is it ok to learn ...
1
vote
0answers
106 views

Question about limits

I am quite new on SE. I see a lot of question about integrals, series, limits. I am wondering if there is a limit to teachers (or textbooks) imagination in these areas.
13
votes
10answers
439 views

$2\times2$ matrices are not big enough

Olga Tausky-Todd had once said that "If an assertion about matrices is false, there is usually a 2x2 matrix that reveals this." There are, however, assertions about matrices that are true for ...
2
votes
0answers
46 views

Resources for Teaching High School Statistics

I am a student teacher looking for resources to teach high school Probability & Statistics (untracked). The second semester will be inferential statistics and will include these following topics: ...
4
votes
1answer
96 views

Planning a mockup maths class for high school related to river reactivation

I have to plan a mockup maths lesson where the "main topic" should be river reactivation. The given suggestion is to focus on computing cross-sectional areas of rivers using basic geometry and for ...
2
votes
0answers
134 views

Dynamic Geometry Software for Straight-edge and Compass Constructions

Geogebra is a very good dynamic geometry software. It has so many default tools, e.g. parallel line, angle bisector, tangent to the circle, inscribed and circumscribed circles, etc. But I want the ...
2
votes
1answer
75 views

Fair Division: Making the Differences in Players' Valuations Believable

When teaching basic fair division algorithms, the students always propose some simple and (at the first glance) correct solutions for $n$ players, which unfortunately are not correct! The only way I ...
3
votes
4answers
238 views

Hilbert's Hotel and Infinities for Pre-university Students

Hilbert's paradox of the grand hotel is a fun and exciting ground to base a talk on the set theoretic concept of infinity for interested students - even in middle- and high school. However, it does ...
0
votes
1answer
94 views

Are Parabolas similar intuitively?

All parabolas are similar, but are they all similar in that it is just a question of 'zooming in and out' intuitively speaking? It seems that there should therefore be on all parabolas a curve from ...
3
votes
2answers
183 views

Good at abstractions bad with numbers

Ever since I had an interest in math I was aware that what I'm good at and what really pulled me was the abstract thinking. My intuition for even the simplest number related concepts (modulo ...
3
votes
0answers
80 views

A question on mathematical writing.

One of the problems I am grading this week is as follows: Given a simply connected bounded domain $\Omega$ on $\mathbb{R}^{2}$, prove that there exist a line that separates it into two parts of equal ...
0
votes
3answers
78 views

Mean Value Theorem Motivation

I am currently practicing presenting mathematics to various audiences and am considering the example of the mean value theorem. I was wondering how would I be able to motivate this theorem to a ...
2
votes
1answer
129 views

Motivations for Prime Factorizaton

I'm at the beginning of some middle school math sessions on divisors, gcd, lcm, and prime numbers. It's the first place in the curriculum that the students encounter the three latter concepts ...
8
votes
4answers
464 views

Is $\tan\theta\cos\theta=\sin\theta$ an identity?

A friend of mine, who is a high school teacher, called me today and asked the question above in the title. In an abstract setting, this boils down to asking whether an expression like "$f=g$" is ...
7
votes
2answers
777 views

Explaining Hypercomplex numbers to Children.

Imagine a highschool freshman walks up to you and asks you what hypercomplex numbers are. Explain to her, in a fair amount of detail, the different types of hypercomplex numbers in a way that any ...
2
votes
2answers
169 views

How important are tests in math study?

I'm currently trying to teach myself math through reading. I've made a schedule to keep my pace and to make sure I finish enough problems. Should I add to my routine a timed test now and then?
1
vote
0answers
242 views

What are some good ideas in teaching combinations and permutations

I am a student teacher trying to brainstorm some effective lesson plans for combinations and permutations for a high school statistics course. My master teacher has decided that he will introduce ...
1
vote
0answers
55 views

Why do we need primitive roots?

What is the most motivating way to introduce the order of a modulo n? Apart from simplifying powers of residues is there any other use of the order? Are there any examples which have a real impact on ...
1
vote
1answer
241 views

Parabola & Area Proving (Integral)

This is not a homework question. I am a new teacher (just graduated) and a student asked me this question. The points A(3,9) and B(-2,4) lie on the parabola y=x^2. The line y=x+6 joins A and B. The ...
30
votes
20answers
2k views

Good math bed-time stories for children?

What are some good references/books/articles from which to derive some good bed-time math stories to pique a child's interest in math? I am fascinated by math (used to hate it as a kid) and want my ...
2
votes
3answers
49 views

Commutativity or Distributivity - Which One to Use to DEFINE Multiplication of Negative Numbers?

It's easy to calculate $3 \times (-4)$, using the meaning of multiplication: $3 \times (-4)=(-4)+(-4)+(-4)=-12$. But it's not the case about $(-4)\times 3$! To DEFINE $(-4)\times 3$ we can choose ...
65
votes
22answers
6k views

Is math built on assumptions?

I just came across this statement when I was lecturing a student on math and strictly speaking I used: Assuming that the value of $x$ equals <something>, ... One of my students just rose ...
1
vote
2answers
103 views

A Good Example of an Argument That Cannot Be Reversed

My students are having a hard time with assuming what they must prove. A good example of what they are doing is when one wishes to show that $\lim_{x\to 3}(2x+1)=7$. They will assume that ...
6
votes
1answer
202 views

Are Base Ten Logarithms Relics?

Just interested in your thoughts regarding the contention that the pre-eminence of base ten logarithms is a relic from pre-calculator days. Firstly I understand that finding the (base-10) ...
3
votes
0answers
62 views

understanding maths by translating it to real world? Any learn to formulate Initiatives? [closed]

I am CSE graduate, I was very much interested in physics. I had several theories during my higher secondary school like i thought of vacuum as a special medium than nothingness and like gravity is ...
0
votes
0answers
146 views

Gauss' Summation Trick; Applications and Generalizations

I'm going to write an article about the summation trick attributed to Guass and its applications and generalizations. I'm sure you know what is the trick I mean: $1+2+\cdots+100=101+101+\cdots+101$ ...
1
vote
0answers
55 views

Evaluating elementary school math textbook

My daughter's elementary school is currently using Saxon curriculum, and I'd like to figure out what other sources, if any, should be age appropriate for elementary school children to enhance their ...
4
votes
3answers
211 views

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.
2
votes
0answers
127 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 ...
6
votes
1answer
176 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 ...
0
votes
1answer
113 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 ...
2
votes
3answers
114 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 ...