# All Questions

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81 views

### Start drawing a graph

I want to give to my students instructions/advises for drawing (directed) graphs (with few nodes, less than 15) in draft mode (before drawing final one on the official test paper). But I really have ...
188 views

### Interesting Trigonometry problems

After explaining some basic trigonometry to my kid, such as $\sin (\alpha+\beta) = \sin \alpha \cos \beta + \cos \alpha \sin \beta$, Law of sines, Law of cosines, I wonder if there are some ...
244 views

### Why do we write numbers with decreasing place values?

This question came up while teaching ~16 year olds binary numbers. Why do place values increase to the left and not the other way round?
44 views

### Weekly Problem Sets for Lang's Undergraduate Algebra and Undergraduate Analysis [closed]

For Lang's Undergraduate Algebra and Undergraduate Analysis, I cannot find any weekly problem sets online. I've found that doing every problem in every section takes far too long, and without problem ...
5k views

What are some good answers to questions eg. "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 ...
200 views

### Logarithms chronologically before algebra

Do any textbooks or (somewhat?) standard curricula introduce logarithms and their applications in arithmetic without assuming the students know any algebra? (I do not mean just the use of logarithms ...
257 views

In the textbook I am using to teach mathematics to high school students I found the following illustration about composition of functions. I do not agree with this illustration. For me $g$ is the ...
524 views

### What is an algebraic explanation of why the product of the slopes of perpendicular lines is $-1$? [duplicate]

Q: What is a succinct, clear and purely algebraic explanation of why the product of the slopes of perpendicular lines is $-1$? Here I am aiming for high-school students (in the U.S.). I have a purely ...
207 views

### How do you teach students about the concept of a proof?

I get this question a lot from new students who are taking their first proof-based math class. They are struggling because they don't have that fluency with proofs, to begin with. They don't know ...
102 views

### How to create an online examination in a small class that ensures certain academic integrity

I am teaching a Calculus class with around 30 students. The classroom is about 100 m^2. So far I have been using myopenmath.com to assign homework problems to my students. Now I would like to deliver ...
106 views

### A video game for teaching the concept of a mathematical proof

Two students in my game development course would like, as a final project, to develop a video game for teaching mathematics. In contrast to the many other games for teaching maths, which focus mainly ...
3k views

### Replacement for the Pac-Man grid analogy

To most people, a torus is a donut-like shape. Topologists like to describe the torus differently: you start with a square, and "identify opposite sides". We can imagine gluing together one ...
246 views

### Are differential equations considered calculus and included in a calculus class or is it its own class?

Are differential equations considered calculus and included in a calculus class or is it its own class? Also, if it is its own class then what calculus classes does it come after?
255 views

### What is the motivation for teaching Factoring by Grouping?

This seems like such a niche trick to teach students when factoring polynomials. Like, the polynomials I've seen textbooks ask students to factor by grouping seem so cherry picked that I can't imagine ...
104 views

### I'm in 8th grade and just finished Algebra 2. What math would I do for the next 4 years? [closed]

I'm in 8th grade and just finished Algebra 2. What math would I do for the next 2 years? In what order would math I would do in 9th, 10th, 11th, and 12th grade. Thanks!
170 views

### Why is isolating for $x$ taught before factoring?

I'm currently working on some precalculus packages for students who need review. For inspiration, I'm looking at some prealgebra books and I'm wondering why isolating for $x$ is taught before ...
160 views

### When are students taught implicit and parametric representations of curves?

Do students learn implicit equations (such as $x^2+y^2-r^2 = 0$) and parametric equations (e.g., $x=a t^2,\;y= 2 a t$) in a first course in algebra, which in the US would be early high school, maybe ...
2k views

### Is there a name for paths that follow gridlines?

I'm writing up an activity where students are looking at pathlengths that follow along gridlines. Is there a word or phrase that is commonly used to describe those paths, but doesn't include ...
273 views

### Writing mathematics in real time for lectures using Latex

I am supposed to hold tutorial sessions for an undergraduate course in calculus. But the software provided by the university is not good at all. I saw the question suggesting to use Ziteborad but it ...
140 views

162 views

### What should be the bare minimum wrong answer threshold when self studying a math text?

I'm currently self studying a Linear Algebra text book due to the fact that I forgot the vast majority of it since I took the course 10 years ago. My general strategy is to take every single example, ...
104 views

### Where can I find a good course on tensor calculus not focused on applications and physics?

Where can I find a good course on tensor/ricci calculus not focused on applications and physics? I've been running into lots of tensor-theoretic stuff in differential geometry, so I don't know if ...
971 views

190 views

### Applications of abstract algebra outside of mathematics and suitable textbook

The question What are some good mathematical applications to present in an abstract algebra course? asks about mathematical applications of abstract algebra. What are some applications of abstract ...
396 views

### What's the common word for equations and inequalities?

My instinct is often that there should be some technical word for the common class of equations and inequalities. That is: statements that connect two numerical expressions, with a relational operator ...
42 views

### Recommendation for cheap practical graphics tablet?

I am looking a good,stable and cheap graphics tablet for online math educations that you use to use and love to use. I gotto prepare remote videos.