# Questions tagged [teaching]

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### How should I introduce the concept of a function to a precalculus student?

My brother has not taken a math class in $10-15$ years. He is studying for the GRE so I have been teaching him a chapter or two from my precalculus book. So far, he has learned (and excelled at) basic ...
2k views

### Greatest common divisor applications

What are some real-life applications of gcd? I am looking for a motivating way of introducing this topic in an elementary number theory course.
276 views

### How to teach to draw graphs of quadratic equations without knowing calculus?

In the country I'm living we learn how to draw the graph of quadratic equations such as $y=x^2$ or $y=x^2+5x+3$ before knowing calculus (in fact we don't even learn calculus until we begin the ...
234 views

### Repeating basic material in exercise class at university

I am a teaching assistant in mathematics at a university in Continental Europe. The course for which I am an assistant is a third year course, so usually the students are expected to know the basic ...
137 views

1k views

### Teaching Models for Mathematics (like 5 E's in Science)

I want to find and know about teaching models in mathematics. There's such a model for teaching science: the 5 E's model: Any suggestion (books, references, etc.) would be greatly appreciated.
528 views

### Why “plug in numbers” when solving inequality?

Let me use this example, Solve $x^3-4x>0$ After factorization, we have $$(x+2)x(x-2)>0$$, in order to have product of several numbers positive, even(0,2,4,...) of them have to be negative ...
956 views

### Is it better to provide students with guided notes or to have them write their own notes, or both?

When I taught calculus, I posted my notes after the lecture. Then I had the students fill out a mid-quarter evaluation, and a lot of them wanted me to post my notes before class. What I started ...
649 views

### Teaching algebra to visually impaired or blind students

I am currently writing an independent project investigating the teaching and learning of algebra for students with a visual impairment. I am struggling to find literature specifically about teaching ...
192 views

3k views

### Students strictly follow the steps and notations in sample problems without understanding them

It's just an observation, but I'll be highly appreciated if anyone with experience in teaching (or TA-ing) lower-division calculus can explain this phenomenon in detail. I'm one of a TAs who's ...
263 views

### How important is it to show students an application of the topics seen in an undergraduate course?

I am currently designing a proof-based Math course for my University. I already designed and ordered all of the theoretical content in the course and included some ad hoc exercises for practicing each ...
400 views

### Elementary physics course for pure math student

Are there any mathematical departments which present the course "elementary physics" for pure math undergraduate students, separately? Is there a way to present this course with the most pure ...
218 views

### How can I be more prolific as a maths teacher with my visual handicap?

I have a chronic visual handicap and am in need of adequate level of accessibility support while learning and teaching mathematics from and to the visually challenged as well as the sighted. I'm ...
889 views

### As a TA, how to reduce imprecise notations/statements in students' exams

I'm not a course instructor, just a TA of the first quarter calculus course who lead discussion sections and grade exams. When grading the midterm, I found large number of students showed some ...
47 views

### clasification of teaching licensures and certifications particularly for teacher-students

There is a lot of certification and licensure tests for teaching (math and etc) particularly for teachers and teacher-students (PACT, Praxis & PPAT, edTPA, RESA, ... in US and TAT in India and etc)...
### Should $\varphi$ be monotone in the integration by substitution?
I'm trying to calculate $$\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}}\sin t \cos^3 t\,dt$$ using integration by substitution \int_{\varphi([a;b])} f(x)dx=\int_{[a;b]} f\left(\varphi(t)\right)|\varphi'(t)|...