# Mathematics Educators Stack Exchange Community Digest

## Top new questions this week:

### Are there any proofs of Euler's Formula that do not rely on calculus?

The most common way I have seen Euler's formula $$re^{i\theta} = r(\cos\theta+i\sin\theta)$$ introduced in a classroom environment is to substitute $i\theta$ into the series expansion of the ...

calculus complex-numbers

### Teaching Calculus I to engineers

I am in a research project where one of our jobs is improving the first year university experience for our students. One of the topics we are looking into is changing the way we teach our introductory ...

### Acceptability of creative questions in assessments

I am a math teacher and I have been for a decade now. One of the foundations of my philosophical approach to teaching has to do with Synthesis. For the purposes of this query, I consider Synthesis to ...

secondary-education exams general-pedagogy test-design critical-thinking

### How is $\frac{a}{b}$ interpreted?

I was having a discussion with a colleague who is in the process of writing some curriculum, and we ended up having a discussion about what $\frac{a}{b}$ (with all the standard restrictions) meant. We ...

definitions fractions division

### How to teach integrals motivated by the work done in moving an object?

I am now teaching Calculus of several variables this semester. In apllications of integrals, the problem of finding the work done in moving an object under a force $F$ is one of the most common ...

mathematical-pedagogy calculus physical-sciences

Awhile back I was very weak with my trigonometry so I came to this site asking for help, and it turned out the few answers I got made a huge difference. I excelled at the trigonometry section in my ...

## Greatest hits from previous weeks:

### Can we save the word "unique"?

Increasing numbers of students seem to be using the word "unique" incorrectly. A common example: Question. Define the term "one-to-one" for a function $f$. Answer. Every $x$ has a unique ...

language-use

### Examples of vocabulary that have different meanings in Mathematics compared to "everyday" English

I am asking this question here to obtain a nice reference list. I am asking for examples of words which have different connotations or meanings in Mathematics compared to English as taught in ...

reference-request vocabulary english-language-learners

### 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 ...

exams cheating

### Helping students who make no effort to figure things out for themselves

When I was a student, it was very much frowned upon to ask for help without making an effort, like how math.stackexchange.com operates (for the most part). In the high school where I work, it is ...

secondary-education

### Why do you need to distinguish between apparently identical objects in probability?

In the math class I taught today I was asked a question, and I was unable to give a good answer. The problem was as follows: A certain factory produces throat tablets. In each pack, there are from 48 ...

probability teacher-development

### How should a student's inefficient calculation be pointed out?

One time I watched a student solve the equation $0 = (x-2)^2-9$ for $x$ like this. \begin{align*} 0 &= (x-2)^2-9 \\0 &= (x^2-4x+4)-9 \\0 &= x^2-4x-5 \\0 &= ...

secondary-education mathematical-pedagogy algebra students-mistakes teaching

In an exam we have Question (5points) find $\lim_{x\to\infty}(x-\sqrt{x})$. A student answered: $\lim_{x\to\infty}(x-\sqrt{x}) =\lim \sqrt{x}(\sqrt{x}-1)=\infty \cdot\infty=\infty$. My question ...