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0answers
28 views

Low-tech ways of visualizing multivariable and vector calculus

One way, which is the most obvious, is do sketches of 3d shapes that tend to be the ones that we can all draw (like rectangle, cone, cylinder, sphere, etc.) Another way is by analogy so even if we can'...
7
votes
3answers
276 views

What to do when uncertain about a question while tutoring

I tutor various math subjects online for a large tutoring company. I know that as a math tutor, it's my responsibility to be able to explain any concept in a way that makes sense to the student, or to ...
5
votes
0answers
53 views

Transition into a non-explicit sample space world

This is one of the problem taunting me over years while explaining probability. In most of the high-school as well as graduate textbooks, there are at most very few lines to deal with this problem. ...
2
votes
0answers
61 views

Trying to explain(understand?) combinations

Let us assume that we have 30 balls( 7 green, 10 black, 13 white). I was trying to explain to someone how we count the number of possibilities of getting 3 greens, 3 black, and 3 white balls in a ...
2
votes
0answers
55 views

Intuition explanation about Lebesgue measure zero of the rational numbers

This is a question about the intuition of the rational number having measure zero. Let us consider followng proof: Let $I = [0,1]$ and $Q = \mathbb Q \cap I$ and let $\lambda$ be the Lebesgue measure. ...
1
vote
1answer
116 views

Can I motivate kids to do math by giving them candies?

I am talking about literally asking for kids' time/attention by offering them candies: not giving them tasks about summing real candies, etc. I try to teach math from time to time to my relatives of ...
1
vote
2answers
156 views

How can I teach $\frac{300}{200}$ to 10 years old students while s\he knows canceling the zeroes rule?

I am teaching math to a 10 year old student. He learned that $$\frac{300}{100}=\require{cancel}\frac{3\cancel{00}}{1\cancel{00}}=3$$ and $$\frac{6000}{300}=\require{cancel}\frac{60\cancel{00}}{3\...
9
votes
1answer
172 views

College undergraduate geometry courses

I am interested in learning how a course in geometry is employed today at undergraduate colleges/universities in the U.S. On the one hand, such a course seems to serve as an optional (rarely required) ...
-3
votes
2answers
230 views

Missing Step in Most Proofs of the Irrationality of $\sqrt{2}$ [closed]

Numerous online resources parrot the usual proof by contradiction of the irrationality of $\sqrt{2}$. These all rely upon the assumption that the rational form (say, $a/b$) is in its simplest ...
1
vote
0answers
37 views

Exercises for explaning homothety, homothetic center, similarity on line and plane, free vector and vector space

I need the collection of exercises for such topics as: maps and transformations, composition of maps homothety, rotation homothety, homothetic center similarities of the line and the plane free ...
8
votes
6answers
4k views

Why we have to be so precise in Geometry?

Previously I've explained some basic things of graphs to my kid, such as planar, $V-E+F=2$. Now when I introduce geometry, he asked, "Why we have to be so precise in Geometry?" Indeed, in ...
4
votes
1answer
166 views

What are some famous problems, which are not difficult to understand, for senior high school students

I hope I am asking my question in the right forum. I am trying to introduce some mathematical problems (Better to be famous in the math community) to a group of senior high school students with a ...
1
vote
0answers
63 views

How long should we spend on teaching students the basics of subject?

Highschool-courses, at least in my country, are structured in a way that you tackle with a higher level of a given subject after some time constraint. So, after one year, you get to a higher class ...
1
vote
5answers
213 views

Practical case for solving with system of 2 equations

When I teach basic math I want to emphasize on it's power (algebraic part for starters) as a tool for solving certain problems you cannot solve with naked brain, so that one models a problem with ...
4
votes
0answers
45 views

Looking for papers with teaching-oriented style

I am looking for papers that have the similar style to Hervé Lehning's 1989 The American Mathematical Monthly article "From Experimentation to Proof" (PDF link via lehning.eu). It's like ...
17
votes
4answers
3k views

Does this property of subtraction and division have a name?

Addition and multiplication are commutative. Denoting $\circ$ as either such operation, we have $$x \circ y = z \Leftrightarrow y \circ x = z.$$ Subtraction and division have a similar property, where ...
0
votes
0answers
99 views

What should the time limit for this high school math competition topology round be?

When I participated in the 2019 John Hopkins Math Tournament, the team round consisted of two separate topics, 40 minutes per round, and 3 people per team. My team suffered on the topology round. Only ...
3
votes
4answers
300 views

When does thinking $(-8)^{1/3} = -2$ result in problems for an undergraduates?

In high school we learn that the cube root of $-8$ is $-2$. Much later some of us learn about the single valued natural logarithm of a complex number, and that $w^z = e^{z\cdot Lz(w)}$ when $w$ and $z$...
2
votes
1answer
71 views

Recommendation for Discrete Mathematics

I'm taking a Mathematical Structures course as a 2nd year math major. Our course textbook is Discrete mathematics and Its Applications, by Rosen. It's been very difficult finding good content on ...
2
votes
0answers
85 views

References for visualizing numbers in base 10 flats

Base 10 blocks (units, rods, flats and cubes) are a widespread manipulative material for teaching place value. However, piling rods on top of each other is not very stable, so it is not easy to build ...
2
votes
0answers
66 views

Math websites/apps for high school students

I am undergraduate math student who is interested in being a high school math teacher. I have been given an assignment to present to my class (for a total of about 20 minutes) a teaching tool or a ...
2
votes
2answers
119 views

Analogy for cylindrical shells

The analogy for cross-sections is easy since we can think of how slices of bread can make up a loaf. But what would be the analogy for cylindrical shells? Regarding shapes, apparently there's ...
28
votes
14answers
3k views

What's the point of learning equivalence relations?

I teach an introductory discrete mathematics course at a community college to math and computing majors, usually in their sophomore year. As is common, it's partly used as the first foray into formal ...
6
votes
1answer
240 views

Where does the compulsive use of three dots come from and should it be discouraged?

There are some students in freshman calculus/even precalculus who compulsively use the three dots $\therefore$ in every single step: https://en.wikipedia.org/wiki/Therefore_sign It's not "wrong&...
3
votes
2answers
125 views

Why are “homogeneous differential equations” in the standard ODE curriculum?

Here I mean a differential equation of the form $y'=f(x,y)$ where for some $\alpha$, we have $f(tx,ty)=t^\alpha f(x,y)$ for every $t$. I have no idea why this topic seems to appear in every ODE ...
9
votes
5answers
3k views

Math activities for fast-finishers

I am a math teacher for sixth graders and I am trying to think of some strategies to keep the students who finish their work quickly productively occupied. I would like to have a selection of ...
3
votes
1answer
81 views

The purpose of a particular rational function integration exercise

This might be a more appropriate question for math.stackexchange, but it's about a problem I'm considering giving my students, so here it goes. One of the later exercises in Section 7.4 of James ...
3
votes
1answer
137 views

Is there an arithmetic book similar to “Teach Your Child to Read in 100 Easy Lessons” by Siegfried Engelmann?

I have found Engelmann’s book (mentioned in subject) to be extremely effective. Is there an equivalent to this book for teaching Arithmetic? I believe the overall approach or method is called Direct ...
1
vote
4answers
285 views

How can I explain construction of the Bézout's identity to my kid?

My kid is soon 7 years old, he could understand fractions, linear equation and modulo operation. I've just taught him Chinese remainder theorem, looking to introduce some more basic number theory ...
3
votes
1answer
176 views

How much literature research should one do when designing a course?

For each mathematical subject on the undergraduate level there are many textbooks, often with quite different approaches to the subject. Some are just concise and rigorous, some focus on examples, ...
4
votes
0answers
79 views

Create a mathematical problem with randomized parameters

Recently I am using Moodle to create problems with randomized parameters. In Moodle, there is so-called Calculated questions that let me do this in a straightforward way. For example, I can simply ...
6
votes
5answers
171 views

Question formats for online tests, to deter cheating

I'm teaching calculus 1 online this term and anticipate being plagued by the perennial problem of cheaters. I have seen suggestions for how to arrange the testing time to accommodate for traditional ...
1
vote
2answers
91 views

Are books as old as J.E. Thompson's “for the practical man” series outdated?

I'm sure Thompson's books were a fine series back in his time, but are they still worth recommending for, say, interested high-school students or prospective college students that want to brush up ...
50
votes
4answers
4k views

Future educators writing nonsense questions

I teach future elementary educators mathematics content courses. We play a lot in class with tasks like "Write a variety of word problems which would require the student to multiply 2.3 by 1.4&...
3
votes
1answer
218 views

How should mathematics tests be designed? [closed]

I am speaking about high school mathematics . Students have attended a mathematics course . By the end thereof , students are supposed to be able to: find the limit of a real function f as “x” ...
3
votes
1answer
124 views

How to make maths explainer videos?

I am a maths teacher and I want to make maths explainer videos particularly like this guy is doing. In fact, in my research, I came to know that manim is the latest tool for creating maths animations ...
5
votes
3answers
359 views

How to explain to undergraduate students what research means?

Background: I am a lecturer in computer science, but my research is mostly theoretic and mathematic, so I ask here. I want to encourage my undergraduate students to become research students after ...
8
votes
1answer
106 views

Grading in a way that lets students have a good and formative experience

This fall, I'll be a reader (i.e. homework grader) for the first time, and the course is a second-level linear algebra course, which is likely the first proof-based course most of the students will ...
16
votes
6answers
2k views

Are there direct practical applications of differentiating natural logarithms?

The textbook I am using to teach Calculus I includes in the exercises of most chapters a number of interesting real-world applications of the concepts from that chapter. However, the chapter on the ...
3
votes
3answers
468 views

How to word this exercise about converting “English” into interval notation?

I am writing an exercise for a precalculus homework assignment that deals with the topic of interval notation. The point of the exercise is to convert open, closed, and half open intervals described ...
4
votes
2answers
94 views

What is a good way to teach Taylor expansion of multi-variable calculus?

I found teaching Taylor expansion for multivariable functions rather challenging. It is a bit complicated to prove and to to compute. So what happened to me last year was that my students simply ...
12
votes
6answers
2k views

How do you explain concavity of a polynomial without any calculus?

How do you explain the concavity of a polynomial without any calculus? As the title suggests, I am struggling to explain when given a graph of a polynomial, how we determine when it is concave up or ...
4
votes
3answers
494 views

How to layout a solution to a trig equation?

I am interested in how you would encourage students to layout their working to a trigonometric equation. For instance, let's consider this problem: Solve the equation $6\cos x - 8\sin x = 7$ for $0 &...
1
vote
1answer
76 views

asynchronous teaching and requiring frequent email updates from students, and having these as the only part of their grade

Due to the COVID pandemic, classes at my school (small public liberal arts college) will be all online. I've chosen to try teaching asynchronously (via pre-made video lectures) starting next week. I ...
4
votes
1answer
130 views

Is there a study on how often modern teaching methods versus traditional methods are used in a math classes?

Most of the students I've encountered seem to have had the same sort of math education I've had, the standard lecture, book readings, homework problems and exams. In my own experience and in my ...
1
vote
1answer
64 views

What are some of the struggles that come with teaching introductory formal logic?

I'm currently an undergraduate student who wants to do research on the pedagogy of formal logic. As a result, I wanted to know what are some challenges that instructors (or even students for that ...
13
votes
5answers
949 views

Best form for slide / beamer presentation: display items in a slide as they are discussed or all at once?

I am preparing beamer slides for an online class, and I am unsure whether I should display different items in a single slide as they are discussed or all at once. To be more precise: I am teaching ...
3
votes
1answer
130 views

Learning strategies for high volume/pace learning?

Background: I am a graduate student in a mid-tier U.S. university, and I am struggling. I feel like I during my undergrad, I haven't aquired the neccesary skills to keep up with the high volume/pace ...
1
vote
1answer
88 views

What books are good to study Solid Mensuration?

Preferably I want those that contain the following topics: Solid Figures Polyhedrons Prisms Pyramids Prismatoid Truncated Prisms Cylinders Cones Spheres I've been ...
3
votes
2answers
149 views

Sharing notes in an editable format?

This question isn't really about lecture notes in themselves, like these questions (Hand out lecture notes or not? or Is it better to provide students with guided notes or to have them write their own ...

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