Mathematics Educators Stack Exchange
Mathematics Educators Stack Exchange

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1500 questions
17
votes
5 answers

Amount of concrete calculations on board?

Imagine that you are teaching a high school class in the last years of high school, an undergraduate class in university, or you are a tutor of a small group at university. Should one provide examples of concrete calculations in front of the class,…
Markus Klein
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11 answers

Looking for simple "interesting" math problems that cannot be easily solved without algebra

I often find students who dislike algebra. They prefer to work with numbers in solving problems. I believe there are many problems that are hard to solve without algebra. For example: Finding the value of $x$ such that the volume of a box without…
kiss my armpit
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11 answers

What's the most practical and efficient way to sort exams on paper?

There are a lot of sorting algorithms to sort a list on a computer, and a lot of theory about them. However, my problem is not how to sort a list under the quite well defined conditions of a computer, but to sort alphabetically a pile of exams (made…
Pere
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4 answers

Explaining the "siblings" paradox

This is a question I originally posted on Math Stackexchange. I've just seen a very good discussion of Monty Hall problem, and someone mentioned the "siblings" paradox. I've had some success explaining the Monty Hall, but ran into some tough…
PA6OTA
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7 answers

Why don’t we teach a topological view of continuity instead of epsilon-delta?

I would like a critique of this approach to teaching continuity to calculus 1 students. Show them that for an increasing function on (a,b) we have that (a,b) is contained in the set of solutions to $f(a) < f(x) < f(b)$. For decreasing function we…
user22312
17
votes
4 answers

Historically Motivating Concepts

I have been reading this site for a while, and was glad to find an entire tag devoted to "concept motivation," which is currently my area of interest. However, my particular focus has not been addressed. Skimming through standard textbooks used in…
user1598
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5 answers

Overload of Calculus homework assignments

I am a new calculus teacher in a high school for gifted students. I am the youngest teacher, I am not in my home country, and this country particularly values age and experience, so I have little room to discuss syllabi and homework assignments.…
Taladris
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7 answers

What are the differences between popular undergraduate abstract algebra books?

I will be teaching a year-long undergraduate introduction to abstract algebra in the fall, and I am quite looking forward to it! I need to choose a textbook, and I don't have personal experience with any that I think will be suitable. It seems that…
Frank Thorne
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4 answers

What are some good ways to motivate and introduce reasoning abstractly about abstract algebra?

I've found one of the hardest topics to introduce to students early on is abstract algebra. Even if they've already written proofs, it's hard for them to work directly from axioms. They seem to have problems with understanding why we view sets and…
adamblan
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6 answers

Where can I find resources for creating a mathematics “bridge course”?

I originally asked this over at MathOverflow, but it was suggested I might also find some good answers over here. My university department is in the very early stages of developing a "bridge course" or "introduction to proofs" course, motivated by…
Greg Friedman
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7 answers

Motivating students to take homework seriously without grades

Next semester I'm teaching a course where I want to grade a significant chunk of the homework for completeness without checking whether the answers are right, and separately post the answers and encourage students to check the answers…
Henry Towsner
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3 answers

How to build a class based on Project Euler?

Project Euler is a very popular self-challenge website where users complete various projects designed to test their number-theory intuition and programming skills. I've been considering various ideas for a first year introduction to proofs course.…
Brian Rushton
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12 answers

What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

The imagined students are in elementary school, say around 9-13 years old. I want to use rather precise terminology when talking to my students. However, it seems like we typically use the same terminology for a geometric figure and for its…
Improve
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1 answer

Is there any evidence about the effectiveness of "table proofs" in pre-college mathematics education?

I remember when I took geometry in high school, like most students it's where I was formally introduced to proofs. However, the way we went about them was strange, it really felt like symbol manipulation. We had a big list of axioms and postulates,…
Linear
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2 answers

Is there a math curriculum that is aware of CAS and the internet?

About 15 years ago, I heard a math education professor give a talk about how computer algebra systems would change the kinds of questions teachers would ask high school and first year college students. Exercises in factoring and polynomial long…
Noah
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