# All Questions

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### How to handle the situation when you made a stupid mistake in front of the class?

I don't know whether you guys have made a similar experience but it just happened to me: I made a very stupid mistake in front of the class. I can't really tell you how it happened and I feel too ...
8k views

### How do I show students the Beauty of Mathematics?

I teach many high school students, and all of them complain about being unable to fully understand mathematical concepts. I try to show them the joy of learning and deepen their understanding through ...
11k views

### Why are triangles so prevalent in high school geometry?

A colleague and I recently discussed what we call the "Triangle Trap." High school geometry covers a very large unit reflecting the common core: Classifying Triangles Triangle Angle Properties ...
6k views

### Imbuing a six year old with a sense of mathematical wonder

My six year old started school a few months back and he's loving it. This first year is more about social skills than anything academic and I like that approach. But we're spending some time at home ...
4k views

### How can I give feedback that is not demotivating?

Background: To cope with online education, I taught linear algebra using a variant of the flipped classroom. I recorded videos and put them up on YouTube and students presented the content in these ...
4k views

### Uninsulting way to say “this will eventually be easy”

When presenting a proof, there are usually a lot of parts which look like "obvious", "routine" manipulation to me, and between zero and two genuinely insightful steps. I want to point out the ...
2k views

### Metonymy in mathematics

Metonymy is a figure of speech where a word or another expression is used to mean something other than its literal meaning. This phenomenon is not restricted to the "usual human languages" (such as ...
2k views

### Examples why university education is important for future high school teachers

At my university, the students in math are mixed up (1/3-1/2 are bachelor/master students, the rest are future high school teachers). A problem arising very often is the discussion dramatically ...
2k views

### What are some great books for exploring mathematics? (not kids' books and not textbooks)

People often think of math as facts and procedure - dry stuff. But it is so much more, even at basic levels. What books about mathematics have you been inspired by? There are some real treasures out ...
2k views

### Reasons for (not) distinguishing $f$ from $f(x)$

Formally, if $f$ is a function, $f(x)$ is a value. So for instance, $f$ can be continuous, but not $f(x)$. In teaching at school and university, notation is quite often mixed up, e.g. the function is ...
12k views

### Should I change my take-home exam policy because of one suspected cheater?

This is just the third semester I've been teaching, but I've been tutoring for many years. At the moment I'm teaching to community college students a "Business Calculus" course whose curriculum is ...
1k views

### Questions with “round” answers only?

Textbook writers are blessed with only solving problems with neat answers. Numerical coefficients are small integers, many terms cancel, polynomials split into simple factors, angles have ...
2k views

### How can I help a student who has a “wrong” kind of enthusiasm?

Alice (not real name) is a student in one of my Math 100 (calculus) classes. It's a course offered by my college as a dual credit course at a high school, so the whole class is about 17/18 years old, ...
9k views

### Dividing by zero

I was having a discussion with a friend and fellow mathematics teacher the other day when the topic of dividing by zero came up. She is the department head and had this in a questionnaire she gave to ...
5k views

### How should I answer questions about the purpose of learning math?

What are some good answers to questions e.g. "why do we need to study square roots"? Of course the answer depends highly on who is asking. For the scope of my question, I have a student in ...
4k views

### Is there any proof of the fundamental theorem of algebra that can be introduced to undergraduates who have just completed Calc III?

I am aware of three proofs of the fundamental theorem of algebra, using: Liouville's theorem The fundamental group of the punctured plane, or Multiplicativity of field extensions together with the ...
6k views

### What to do when you get “the empty stare”?

First, I am not a professor, but I was a teaching assistent for a couple of courses. One time I took over a few sections for a friend who was also a TA. The course was 'math for chemists' (I think it ...
8k views

### Justifications for: Why learn mathematics?

I wonder how you teachers walk the line between justifying mathematics because of its many—and sometimes surprising—applications, and justifying it as the study of one of the great ...
9k views

### How can teachers warn students about common mistakes without causing the student to make the mistake?

For example, if you're teaching integration of $\int \frac{dx}{1+x^2}$, would you mention the common wrong answer of $\ln\left(1+x^2\right)+C$? -- For myself, I very rarely mention common mistakes ...
3k views

### What happened to the Moore method?

I always read about the Moore method with great enthusiasm. Somehow I always felt that it should be how we do it in an ideal world, but it is impossible to use because of time and other constrains. ...
4k views

### Rings before groups in abstract algebra?

The default approach to teaching abstract algebra seems to be groups first, then rings. However, occasionally a textbook pops up (e.g. Childs' A Concrete Introduction to Higher Algebra or Hodge et al'...
2k views

### Are there any benefits to having an entire course's homework problems available from day one?

I am designing a course for the upcoming fall semester, and I am tossing around an idea in my head. While planning which topics to cover each week and how to set the pacing of the course, I figured I ...