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.
11
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12answers
773 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
2answers
431 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
votes
5answers
470 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 ...
0
votes
1answer
166 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
290 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: ...
2
votes
1answer
411 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
200 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 ...
2
votes
1answer
231 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
votes
1answer
261 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
votes
2answers
293 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 ...
17
votes
8answers
2k views
Why do introductory real analysis courses teach bottom up?
A big part of introductory real analysis courses is getting intuition for the $\epsilon-\delta$ proofs. For example, these types of proofs come up a lot when studying differentiation, continuity, and ...
6
votes
3answers
2k views
How to justify small angle approximation for cosine
Everyone knows the picture that explains instantly the small angle approximation to the sine function (as defined by the parametrisation of the unit circle): "what's the length of that arc?" "See how ...
5
votes
0answers
316 views
Connecting finite automata and regular languages in teaching/applications
I am considering giving a presentation to middle schoolers, aged about ten to fourteen, about finite automata and regular languages.
Average American students have no problem with uses of the ...
3
votes
8answers
2k views
Explain for students: Why does 0 mod n equals 0 (zero)?
I told my students that the mod operator basically gives the remainder of division, so upon seeing:
0 mod 10
Some students (apparently) reasoned that, "10 goes ...
10
votes
4answers
1k views
What is the best way to develop Mathematical intuition?
I want to develop my pure mathematics knowledge and would like to know what is the best way to develop mathematical intuition? I am going through exercises that ask for proofs and I don't have the ...
9
votes
4answers
306 views
A Book of Neat Theorems for Laymen
I'm looking for reading assignment ideas for my students. I'd like them to read up on results in mathematics in layman's terms. For example, the Monty Hall problem, or Borsuk Ulam as the "Ham ...
0
votes
1answer
155 views
Taxonomy for math exercises (K-12 highschool) [closed]
I would like to build an online collection of math exercises that can be indexed and cross-referenced. So I need a way to characterize an exercise somehow.
Example: $\sin^2x + x =0$
Does it ...
17
votes
5answers
613 views
Elementary problems with group theoretic solutions
I am helping a friend develop a course in abstract algebra that is designed for high school students who have no knowledge of abstract algebra or any real exposure to formally rigorous mathematics. To ...
8
votes
3answers
299 views
Motivation for solution to constructing a set of 1983 distinct integers such that no three are consecutive terms of an arithmetic progression
Problem:
Is it possible to choose $1983$ distinct positive integers, all less than or equal to $100,000$, no three of which are consecutive terms of an arithmetic progression? (Source: IMO 1983 Q5)
...
1
vote
0answers
253 views
How can I use an abacus to teach concepts to a toddler?
My 18-month old son got a $10\times10$ abacus as a Christmas present, and he enjoys it as a toy. I'm fine with him just playing with it, but I don't want to miss an opportunity to introduce ...
4
votes
3answers
148 views
diversity and teaching
I recently attended a discussion about interviewing for math jobs, and apparently a question that is coming up frequently is something like this:
"We have a culturally diverse student body. How does ...
5
votes
1answer
219 views
Elementary arguments concerning the stereographic projection
How does one give a proof that is
short; and
strictly within the bounds of secondary-school geometry
that the stereographic projection
is conformal; and
maps circles to circles?
8
votes
3answers
569 views
Motivation behind the definition of GCD and LCM
According to me, I can find the GCD of two integers (say $a$ and $b$) by finding all the common factors of them, and then finding the maximum of all these common factors. This also justifies the ...
22
votes
3answers
538 views
Why the emphasis on Projective Space in Algebraic Geometry?
I have no doubt this is a basic question. However, I am working through Miranda's book on Riemann surfaces and algebraic curves, and it has yet to be addressed.
Why does Miranda (and from what little ...
1
vote
4answers
183 views
Two questions related to probability theory and pedagogy
A housemate of mine and I disagree on the following question:
Let's say that we play a game of yahtzee. Of the five dice you throw, two dice obtain the value 1, two other dice obtain the value 2, ...
2
votes
1answer
97 views
weakly locally one-to-one?
Is there any standard name for this concept that is weaker than local one-to-one-ness?
In some open neighborhood of $x_0$ there is no point $x\ne x_0$ such that $f(x)=f(x_0)$.
Or, if you like: In ...
2
votes
1answer
234 views
what is teaching kids the rules and exceptions in multiplication called?
I recall reading a website quite some time ago about the rules and exceptions of multiplication with regards to teaching children. For instance: ...
2
votes
2answers
109 views
Advice for Calculus Tutoring
I am tutoring a friend in calculus. Right now, she is working on finding relative maxima and minima as well as Rolle's theorem. While she gets how to find relative maxima and minima she does not get ...
1
vote
0answers
129 views
Lesson plan for teachers
I teach mathematics at school level. Lesson plans are soul of any lesson that a teacher takes in a class. I want to create lesson plan on different mathematics topic as per the level of the syllabus ...
20
votes
6answers
953 views
Do online lecture recordings hurt or help math students at university? [closed]
Continuing with my series of soft questions on teaching practice:
My university uses a system whereby all lectures (given via computer slides or hand-writing on a sort of overhead projector called a ...
15
votes
2answers
582 views
“Best practice” innovative teaching in mathematics
Our department is currently revamping our first-year courses in mathematics, which are huge classes (about 500+ students) that are mostly students who will continue on to Engineering.
The existing ...
5
votes
3answers
257 views
Good lecture optimization problem involving $\ln x$ or $e^x$
I am teaching a Calc 1 of sorts, like a slightly easier version of Calc 1 with no trig. I want a good optimization/practical problem to do in lecture that involves $\ln x$ or $e^x$, to combine review ...
16
votes
7answers
562 views
Exciting games and material to motivate children to math
We are a group of people trying to motivate children, especially living in the countryside, to science and math. We have different activities with children such as doing scientific experiments and ...
7
votes
3answers
428 views
The Power of Taylor Series
I am teaching a Calculus class and we are finishing up power/Taylor series this week. The last section of the chapter is on applications, but the only ones listed there are approximating non-rational ...
4
votes
1answer
171 views
Algorithm for keeping a concrete version of Euclid's argument simple
(My actual question is at the very bottom of this posting.)
Suppose you're teaching a course in mathematics-for-liberal-arts majors and it's the last math course they'll ever take. It has almost no ...
14
votes
4answers
527 views
Fun math for young, bored kids?
For 6 months, I'll be organizing, as part as my volunteer work in an NGO, math classes with small groups (~10 students, aged 16 or 17). These classes are not compulsory, but students willing to stay ...
5
votes
2answers
342 views
Interesting but elementary properties of the Mandelbrot Set
I suppose everyone is familiar with the Mandelbrot set. I'm teaching a course right now in which I am trying to convey the beauty of some mathematical ideas to first year students. They basically know ...
2
votes
0answers
160 views
Have Changes in Applications Made Linear Algebra More Central/Urgent?
In the days when my father taught civil engineering (some decades ago), mathematical applications seemed to be mainly "scientific." (This was the "space age.) Hence the most important branch of ...
8
votes
2answers
375 views
Is there any toy for learning algebraic manipulation of fractions?
Is there any toy for learning algebraic manipulation of fractions? If you don't know of any, how would you design one?
What I'm imagining is something similar to a Rubik's cube whose manipulation ...
13
votes
4answers
206 views
Should the domain of a function be inferred?
It is a common practice to have students of elementary algebra infer the domain of a function as an exercise. I believe this is contrary to the spirit of the definition of a function as a collection ...
39
votes
19answers
2k 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 ...
4
votes
2answers
579 views
Simpson's Rule and other Newton-Cotes Formulas
I am curious about the value of Simpson's rule (also called the parabolic rule or the 3-point rule) for approximating integrals. The calculus text I am now teaching from uses this rule any time an ...
18
votes
4answers
2k views
Teaching Introductory Real Analysis
I am currently helping teach an introduction to real analysis course at UC Berkeley. The textbook we are using in Rudin's "Principles of Mathematical Analysis" (aka baby rudin).
I am trying to find ...
-3
votes
1answer
578 views
How to engage extremely proficient math kid who hates math? [closed]
Well hate is probably too strong, maybe "doesn't enjoy" is a better description.
I have a 5 year old son who generally doesn't like math, though he is extraordinarily talented. I'm looking for books ...
0
votes
1answer
125 views
A good training field for formal rule application?
I'm tutoring a would-be Russian 7-grader who seems to have difficulties in understanding and application of formal rules (identities). I'm looking for a way to improve it, but I don't want him to try ...
0
votes
1answer
137 views
Interesting non-stem questions about Koch/Sierpinski fractals
Exam time and I am having a hard time finding any inspiring questions about fractals for our "contemporary math" course.
We found the perimeter and area of various Koch snowflakes and Sierpinski ...
7
votes
2answers
316 views
Share my maths video on the internet [closed]
I make some videos of math courses on the internet and some of them are in English. I want to find some where to upload it. Who can help me with this issue? I only know about Youtube, but that is ...
4
votes
3answers
486 views
Mathematical misconceptions and how to combat them
There are a lot of common misconceptions when it comes to math. A common one that has already been addressed on this site is $1 \neq .999\cdots$, as is that imaginary numbers "do not exist". Another ...
33
votes
1answer
1k views
Is Lagrange's theorem the most basic result in finite group theory?
Motivated by this question, can one prove that the order of an element in a finite group divides the order of the group without using Lagrange's theorem? (Or, equivalently, that the order of the group ...
6
votes
3answers
340 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 ...
