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.
2
votes
2answers
181 views
Can a rule be formulated to explain this to 7 year old?
I'm trying to teach math to my 7 year old daughter. I'm teaching following type of equations.
$$\cdots - x = y$$
I'm able to explain her the rule that:
when $\cdots- x = y$, we can always ...
9
votes
4answers
848 views
What is an intermediate definition for a tangent to a curve?
Most students come to calculus with an intuitive sense of what a tangent line should be for a curve. It is easy enough to give a definition of a tangent to a circle that is both elementary and ...
3
votes
2answers
227 views
For teaching: Combinatorial Construction Riddles
Can you give examples of combinatorial construction riddles, approachable by gifted high school students?
Examples:
Find a finite set $A$ and $B \subset 2^A$ such that any element of $A$ is covered ...
7
votes
1answer
291 views
Some maps of the land of mathematics?
This question is motivated by a little anecdote. I was at home teaching some secondary school math to a relative. At some relax time, he glanced at a book I had over the table - it was some text about ...
4
votes
5answers
603 views
Differential Geometry of curves and surfaces: bibliography?
Dear all, next year, I will probably teach a one-semester course of Differential Geomtry of curves and surfaces. Its content must be something along the lines of the first four chapters of Do Carmo's ...
20
votes
6answers
1k views
Why do we need to prove $e^{u+v} = e^ue^v$?
In this book I'm using the author seems to feel a need to prove
$e^{u+v} = e^ue^v$
By
$\ln(e^{u+v}) = u + v = \ln(e^u) + \ln(e^v) = \ln(e^u e^v)$
Hence $e^{u+v} = e^u e^v$
But we know from basic ...
32
votes
5answers
6k views
+50
Why is Pi equal to 3.14159…?
Wait before you dismiss this as a crank question :)
A friend of mine teaches school kids, and the book she uses states something to the following effect:
If you divide the circumference of any ...
10
votes
7answers
2k views
Topic for a high school-level math elective?
I'm looking for ideas for a 15-hour mathematical enrichment course in a Chinese high school. What (fairly) elementary subject would you suggest as a topic for such a course?
...
6
votes
5answers
374 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 ...
1
vote
3answers
684 views
Advice for young girls who think of mathematics as an unnecessary thing? [closed]
I had many interaction with young girls when I was a private math teacher. Most of them have an assumption that learning mathematics is not necessary for them, because they just want to be a house ...
6
votes
9answers
526 views
Motivating implications of the axiom of choice?
What are some motivating consequences of the axiom of choice (or its omission)? I know that weak forms of choice are sometimes required for interesting results like Banach-Tarski; what are some ...
22
votes
5answers
1k views
Quotient geometries known in popular culture, such as “flat torus = Asteroids video game”
In answering a question I mentioned the Asteroids video game as an example -- at one time, the canonical example -- of a locally flat geometry that is globally different from the Euclidean plane. It ...
5
votes
3answers
555 views
Books that develop interest & critical thinking among high school students
I heard about Yakov Perelman and his books. I just finished reading his two volumes of Physics for Entertainment. What a delightful read! What a splendid author. This is the exact book I've been ...
27
votes
12answers
3k views
Why 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) ...
14
votes
12answers
4k views
How do I explain 2 to the power of zero equals 1 to a child
My daughter is stuck on the concept that 20 = 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 concept ...
11
votes
9answers
1k 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, ...
5
votes
6answers
923 views
Why Doesn't This Series Converge?
I am teaching a Calc II course and came across the following series when finding the interval of convergence for the Taylor series of $f(x)=\sqrt{x}$ centered at $x=1$:
$$
\sum_{n=2}^\infty ...
6
votes
10answers
1k views
False beliefs in mathematics (conceptual errors made despite, or because of, mathematical education)
Over on mathoverflow, there is a popular CW question titled: Examples of common false beliefs in mathematics. I thought it would be nice to have a parallel question on this site to serve as a ...
2
votes
2answers
354 views
Is most of the GM-AM Inequality in its codicil?
Let’s define the codicil of the Geometric Mean – Arithmetic Mean Inequality to be the statement that if the means are equal, then all the terms are equal. Then: I conjecture that most of the GM-AM ...
2
votes
2answers
177 views
What are good elementary examples for teaching/introducing/learning about Intuitionistic Logic or Heyting Algebras?
For example, I have heard of a topological one wherein negation means the interior of the complement (but still would like a reference).
9
votes
4answers
2k views
Is “locally linear” an appropriate description of a differentiable function?
In this answer on meta, Pete L. Clark said:
I think the question concerns the idea that a differentiable curve becomes more and more like a straight line segment the closer one zooms in on its ...
6
votes
2answers
258 views
What are some deep questions that are applicable to first graders in regards to adding zero?
I'm trying to come up with some math problems (word or otherwise) that get to the meaning of adding zero, but I'm getting stuck because it seems just too simple to me.
I have come up with questions ...
9
votes
11answers
3k views
What concepts were most difficult for you to understand in Calculus?
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
8answers
4k 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.
3
votes
2answers
839 views
How to explain Real Big Numbers?
Mathematicians, and esp. number theorists, are used to working with big numbers. I have noted on several occasions that lots of people don't have a clear understanding of big numbers as far as the ...
9
votes
7answers
1k views
What should the high school math curriculum consist of?
"Life is open book."
With the advent of widely accessible, inexpensive (or even free) computational tools and Computer Algebra Systems (TI-89, Wolfram|Alpha, etc.), much of what traditionally ...
8
votes
7answers
857 views
Can this standard calculus result be explained “intuitively”
Recently I stumbled upon someone who said he wanted to understand why
$\arctan x = \int\dfrac{dx}{1+x^2}$
At first I was confused. This is an easy result in any integral calculus course. But then he ...
11
votes
9answers
581 views
Sources of problems for teaching/tutoring young mathematicians
I am tutoring several talented students, middle school level and early high school level, in mathematics. I am always looking for new sources from which to draw questions. Can anyone recommend books, ...
19
votes
9answers
2k views
How do you define functions for non-mathematicians?
I'm teaching a College Algebra class in the upcoming semester, and only a small portion of the students will be moving on to further mathematics. The class is built around functions, so I need to ...
2
votes
2answers
492 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.
4
votes
5answers
475 views
Usefulness of Conic Sections
Conic sections are a frequent target for dropping when attempting to make room for other topics in advanced algebra and precalculus courses. A common argument in favor of dropping them is that ...
69
votes
18answers
2k views
Good Physical Demonstrations of Abstract Mathematics
I like to use physical demonstrations when teaching mathematics (putting physics in the service of mathematics, for once, instead of the other way around), and it'd be great to get some more ideas to ...
206
votes
33answers
17k views
Do complex numbers really exist?
Complex numbers involve the square root of negative one, and most non-mathematicians find it hard to accept that such a number is meaningful. In contrast, they feel that real numbers have an obvious ...
46
votes
17answers
2k views
What are some good ways to get children excited about math?
I'm talking in the range of 10-12 years old, but this question isn't limited to only that range.
Do you have any advice on cool things to show kids that might spark their interest in spending more ...
