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4
votes
1answer
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 ...
2
votes
3answers
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 ...
5
votes
1answer
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?
0
votes
0answers
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 ...
29
votes
21answers
5k views

How to answer questions about the purpose of learning math?

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 ...
2
votes
2answers
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 ...
8
votes
2answers
257 views

Question about function notation

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 ...
3
votes
4answers
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 ...
8
votes
2answers
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 ...
1
vote
1answer
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 ...
5
votes
0answers
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 ...
14
votes
8answers
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 ...
2
votes
3answers
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?
2
votes
3answers
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 ...
1
vote
1answer
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!
4
votes
2answers
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 ...
1
vote
3answers
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 ...
9
votes
5answers
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 ...
5
votes
6answers
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 ...
3
votes
2answers
140 views

Clearest verb phrases for operations

What is the clearest way to indicate various operations along the following lines: $f(x) = 3x$: The function $f$ multiplies its input by 3. $g(x) = x-5$: The function $g$ decreases its input by 5. $h(...
4
votes
1answer
139 views

Relationships amusingly difficult to graph

Long ago, when I was the student, I encountered a bunch of stories that we were asked to illustrate with graphs. I seem to remember that it was a set of around 10 examples. One involved some two ...
0
votes
1answer
112 views

Teaching Hours for AP Calculus AB [closed]

What are the estimated hours for teaching AP Calculus AB for students aiming for a 5? Similar question, how many hours of practice will the student need to put it. Some Clarifications based on ...
6
votes
3answers
207 views

Am I responsible to help a student who does not understand/know some prerequisites of a course?

I am teaching Calculus III this semester and a student signed up for this course after completed Calculus I and II in a different institution. I quickly realised that this student does not understand ...
10
votes
1answer
202 views

How strict are you with prerequisites? [closed]

I've been thinking a bit of this comment and the following one: "(Look at all the complaints we get about kids who can't combine fractions!)" "Because it is not about you. Not about ...
6
votes
2answers
137 views

Is there online geometric construction software that models physical constructions?

In this weird pandemic school year, I'm doubly interested in technology integration to help my virtual (high school) students as much as my in-person students. I've been particularly eager to get ...
3
votes
4answers
271 views

Teaching calculus in AP without the limit definition

Years ago as a college freshman I was taking my first calculus course. Another freshman skipped it because he had calculus in Advanced Placement in high school. I mentioned we were learning the limit ...
2
votes
2answers
179 views

A wow video to teach Calculus

I am teaching Calculus (one and also several variables). I would like to create questions in which students would watch a short video and then answer a question related to the content of the video. In ...
5
votes
1answer
113 views

Do people usually teach solving a linear differential equation by inverse operators in an undergraduate course?

For the following linear differential equation $$a_ny^{(n)}+\cdots+a_1y'+a_0y=Q(x),$$ most books teach the method of undetermined coefficients, variation of parameters and Laplace transforms. ...
1
vote
2answers
139 views

How to summarize textbook material?

I'm taking a discrete math course. The textbook we use is such a pain to read because the amount of material is very overwhelming. For example, chapter 1 alone is 115 pages. And every subsection, 1.1-...
6
votes
1answer
190 views

The dimension theorem and pedagogy

The dimension theorem (the rank-nullity theorem) can be explained in many ways. I consider it as a consequence of the first isomorphism theorem/splitting lemma. When I teach undergrad matrix-theoretic ...
5
votes
1answer
229 views

How important is it to come up with or learn an elementary solution?

Note: by "elementary" I mean "without using more advanced theory and tools". Students are sometimes required or encouraged to solve very difficult problems using limited number of ...
1
vote
1answer
64 views

Resources for Unit Rates

I am currently mentoring my little brother in mathematics. There is an issue with the pedagogy of unit rates. For example when given the following concept " 11.00 U.S. Dollars to 20 Planet X ...
3
votes
1answer
81 views

Resources for Unit Conversions

I am working with a college student who was placed into a pre-college level math class. She's in a unit that covers a lot of unit conversions (simple ones, like 5 km = ___ miles or 3 yards = ___ cm ). ...
1
vote
1answer
33 views

Setting up a new Ximera course with randomized values in problems

I'm working on converting a course to make it free to the students, and I'm considering using Ximera. What I haven't found online is documentation for/information on tips and best practices for ...
1
vote
0answers
174 views

Do you avoid examples or test questions that showcase an algorithmic plug'n'chug approach?

If we accept that there's not much learning from doing the "same" questions, like find the derivative of $x^2$, and $x^3$, and $x^4$ due to the algorithmic way of how it's done, then what ...
43
votes
20answers
11k views

How to explain that winning the lottery is not a 50/50 distribution?

When casually discussing with my 13 yo child about probabilities, he told me there is a 50% chance to win at the lottery To what I said no, there is a 1 chance over 90 million (I roughly estimated ...
4
votes
2answers
590 views

Advice: How to cite literature for high-school students?

Suppose one were writing a book aimed at high-school students (and their teachers), where "high-school" in the US means grades 9,10,11,12 (where college/university starts at 13). The book is ...
1
vote
1answer
73 views

Questions relating to inclusion-exclusion principle [closed]

Today I came across the inclusion-exclusion principle for the first time. I believe I have understood it, however when I tried solving some questions on it, I got severely stuck. I couldn't solve any ...
5
votes
1answer
280 views

Choice of textbook for an undergraduate abstract algebra course

Currently a 5th year PhD student, and I've been fighting tooth and nail to teach one of our junior-year honors sections in undergraduate algebra next fall (desperately hopeful we'll be able to return ...
10
votes
6answers
2k views

What is the right notation to use in multivariable chain rules?

The following "chain rule" is in my multivariable calculus course: If $f$ depends on $x$ and $y$, but $x$ and $y$ depend on $t$, then $\frac{df}{dt} = \frac{\partial f}{\partial x} \frac{d ...
2
votes
2answers
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, ...
1
vote
2answers
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 ...
5
votes
4answers
971 views

Examples of real-life vector fields for vector calculus

My two main ones are Electrostatic force field $\mathbf{E}\left(\mathbf{r}\right)=\frac{Q}{4\pi\epsilon_0 \left|\left|\mathbf{r}\right|\right|^3}\mathbf{r}$ and Gravitational force field, $\mathbf{F}\...
2
votes
2answers
519 views

Teaching Mathematics to a Younger Sibling

I always wanted to teach my siblings mathematics, and one, ten years of age, is particularly eager. For the purposes of specializing recommendations, I will add he can use arithmetic up to ...
2
votes
2answers
178 views

Would this be a good way of teaching about symmetry?

Symmetry is an important concept in mathematics and it has a built-in aesthetic appeal. The following shows how different types of symmetry relate to one another. Start with the equation $f(x) = -x^2 ...
3
votes
3answers
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 ...
4
votes
5answers
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 ...
0
votes
0answers
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.
2
votes
1answer
67 views

Appropriate context for teaching derivative (undergraduate/graduate)

(Repost from MO, where the question will eventually be closed.) This question is related to lectures I have to make concerning differential calculus in one variable, but the students are quite ...
1
vote
1answer
260 views

Should students get another chance at a math question because of English troubles?

The question is John has locked a 4 digit combination lock with each of the numbers 0-9. He knows the numbers 1,4,6, appears exactly once, but he does not remember the position of the numbers and he ...

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