All Questions

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'...

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 ...

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. ...

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 ...

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. ...

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 ...

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\...

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) ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 $z$...

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 ...

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 ...

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 ...

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 ...

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 ...

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&...

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 ...

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 ...

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 ...

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 ...

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 ...

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, ...

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 ...

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 ...

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 ...

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&...

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” ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 &...

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 ...

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 ...

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 ...

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 ...

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 ...

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

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 ...