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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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
135 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
4k 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
567 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
101 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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0answers
60 views

If most of the mathematics needs a context to be not subject of interpretation, what part of mathematics doesn't need a context at all, if any?

In the past, I have asked this question here: Is mathematics the only language that is not subject of interpretation? And one of the answer started with: First, mathematics notation is subject ...
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2k 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
838 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 ...
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5answers
181 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
123 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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7answers
710 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
384 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
126 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
117 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 ...
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7answers
311 views

Is there a name for this type of logical fallacy?

Consider a statement of the form: $A$ implies $B$, where $A$ and $B$ are true, but $B$ is not implied by $A$. Example: As $3$ is odd, $3$ is prime. In this case, it is true that $3$ is odd, and ...
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1answer
84 views

Homogeneity Versus Heterogeneity in Student Groups

There is an overwhelming amount of research regarding homogeneous and heterogeneous grouping in education. The former refers to the practice of grouping "like" students together (regarding age, ...
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2answers
105 views

Software for visualizing partial derivatives?

I'm whipping up a set of notes, and I want to include a diagram or two showing some partial derivatives. Specifically, a diagram would include: a 3D surface of the form z=f(x,y), a plane of the form ...
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0answers
69 views

What's the acceptance of rational trigonometry in current mathematics courses?

I've been reading about Wildberger's rational trigonometry and I'm willing to learn it. I'm wondering if it's usage is accepted in undergraduate mathematics courses. It seems there's a redefinition on ...
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11answers
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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: $$ ...
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1answer
969 views

Is there a way of intuitively grasping the magnitude of Graham's number?

I have heard it stated before that Graham's number is so vast that it is completely beyond comprehension. It is way larger than the number of atoms in the universe, so cannot be related to real ...
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3answers
135 views

Operations on negative integers

I was trying to teach my younger sister some math, and it drifted on to integers, and operations on negative integers. So questions like: a) $-3+2 = ?$ b) $2- (-3)= ?$ c)$-3 -2 = ?$ had to be ...
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1answer
183 views

Examples of Metaphors in Statistics and Probability?

I have a couple of questions about teaching of Probability and Statistics for high school students: 1. Can I find metaphors for the teaching of basic concepts of Probability and Statistics? (Please, ...
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1answer
95 views

Graphical Demonstration of Linear Transformations on $\mathbb{R}^2$

I'm looking for some applet, program, software, demonstration etc. to use it in a class while teaching linear transformation in $\mathbb{R}^2$, so that the students can graphically understand the ...
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1answer
154 views

Learning Complex Analysis: Integrals vs. Power Series - ordering the development of results.

Over the last few months, I have been visiting elementary complex analysis. My exposure to complex analysis is pretty much limited to the material in three books: Ahlfors, Bak/Newman, and ...
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2answers
134 views

What is an effective means to make divisibility tests a mathematical 'habit', particularly for algebra?

Divisibility tests are a useful problem-solving technique for particularly dealing with larger numbers (thousands etc) and algebraic problems. However, I have always found that many students will just ...
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2answers
142 views

Request for reference and technical support

I am going to write my master thesis in order to become a teacher of mathematics (with second subject business management). Supported by the ERASMUS program I have the opportunity to do this in ...
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3answers
80 views

First-grader problem in arithmetic

I found this problem in a text book on arithmetic for first graders (7 y.o.) of the former USSR* . The problem comes from the section that covers single-digit addition and subtraction. Here is the ...
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0answers
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The Psychology of Math and Logic [closed]

I frequently hear comments from people to the effect that "Studies have shown that students who take (intro) logic courses don't show any signs of improvement in logical/rational/critical thinking." ...
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4answers
322 views

What is an effective means to get senior high school students to write their complete working out as part of their answer.

In Australia and in the International Baccalaureate (2 systems I have worked in), for better or worse, mathematics is assessed by criteria. This increases the importance of students to express their ...
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2answers
384 views

How to teach a High school student that complex numbers cannot be totally ordered?

I once again need your precious knowledge! I am not sure which is the best pedagogic way to teach a High school student about why complex numbers cannot be totally ordered. When I was in High school ...
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2answers
346 views

Is “problem solving” a subject to be taught?

Note: This question has been cross-posted to MathOverflow: see here. I am witnessing a new curriculum change in my country (Iran). It includes the change of all the mathematics textbooks at all ...
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0answers
80 views

How to get interest in the mathematics of tax

In a similar vein to my previous thread, I will also be teaching about the mathematics behind taxation - to a lot of people, this is very mundane - but that is not true of everyone. The practicality ...
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2answers
92 views

What is an effective and practical means to teach about natural logarithms and log laws to high school students?

My students are quite practically minded, and I have found that teaching them concepts in a practical manner to be very helpful (maths 'experiments'; modelling on the smartboard etc). I am looking ...
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2answers
662 views

Relearning from the basics to Calculus and beyond.

Assume someone has very limited knowledge of math. (low level high school, 5-6 years ago) How would they learn from the basics of algebra, geometry and trigonometry to a solid foundation for calculus ...
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26answers
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How to teach mathematical induction?

Some students are not convinced that a proof by mathematical induction is a proof. I have given the analogy of dominoes toppling but still some remain unconvinced. Is there very convincing way of ...
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1answer
66 views

I'm gonna give probability regularization classes

There's this group of high-school level kids that failed probability and they want me to teach them so they can pass that subject, i agreed to be their teacher for this 2 weeks, however i'm not ...
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1answer
93 views

Would this be an effective way to study and comprehend text's?

This is probably a grey area question but I am going to test the waters anyway. What I am thinking of doing would be to basically record myself doing examples from textbooks and making lessons for ...
251
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29answers
36k views

My sister absolutely refuses to learn math [closed]

My 13-year-old sister has a problem which, given the way math is currently taught, I doubt is anything but all too common. She has a low grade in her math course and only ever attempts to memorize ...
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20answers
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Is there a great mathematical example for a 12-year-old?

I've just been working with my 12-year-old daughter on Cantor's diagonal argument, and countable and uncountable sets. Why? Because the maths department at her school is outrageously good, and set ...
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12answers
2k views

explaining the derivative of $x^x$

You set the following exercise to your calculus class: Q1. Differentiate $y(x) = x^x$. A student submits the following solution: Let $g(a)=a^x$ and $f(x)=x$. Then $y(x) = g(f(x))$, so by ...
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0answers
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What is good chalk for lecturing?

This question might be odd, but after watching one of Gilbert Strang's lectures I find I am jealous of his great, smoothly flowing chalk that never seems to get dulled down. Anyone know what it is, or ...
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3answers
613 views

Importance of Neatness / Organization / Speed in Math?

Pretty simple question here but it does relate to math. I ask this as my writing is quite messy, possibly a cause of silly mistakes. How important is neatness in math? Does having messy writing put ...
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3answers
208 views

Statistics Workshop for High School Students

We are going to hold an introductory workshop about the statistics. The participants will be students who have just finished their 8th or 9th grade. The workshop consists of 10 two-hour sessions. The ...
5
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1answer
219 views

Determine if a conic is degenerate with the determinant.

There is a natural bijection between conics (written as homogeneous quadratic) and 3x3 matrices: $$C=aX^2+2bXY+cY^2+2dXZ+2eYZ+fZ^2\Leftrightarrow \left(\begin{array}{ccc} a&b&d\\ ...
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1answer
96 views

A zero for a homogeneous polynomial is a zero for the associated inhomogeneous polynomial

I am trying to prove a simple statement from Reid, Undergraduate Algebraic Geometry, pg 16. Let $F(U,V)$ be a nonzero homogeneous polynomial of degree $d$: ...
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4answers
311 views

the role of logic in math and education

My question is somewhat related to this discussion: Is Mathematics one big tautology? I have a computer science background and I have always approached math from the logic point of view ...
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6answers
779 views

Why is the definition of “limit” difficult to understand at first?

Tomorrow I teach my students about limits of sequences. I have heard that the definition of limit is often difficult for students to understand, and I want to make it easier. But first I need to ...
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3answers
187 views

learning/teaching approach to rigorous math with the goal of improving

I will state this now: yes, this is a subjective question. But I feel the answers people give may benefit students. I want to get better at doing non trivial proofs. Real analysis is standard ...
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0answers
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Optimal partition for a riemann integral

I am a statistician tasked with teaching an elementary calculus course. I am about to teach Riemann sums. The breakpoints for the rectangles (the partition) that make up the Riemann sum need not be ...
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1answer
53 views

Chi square independence test

How to work out chi square independence in the following table? Below is the observed and expected data concerning 7 themes displayed in a newspaper over a period of 3 months. I understand how to ...