All Questions

As I was being observed today, an administrator asked me for a practical application of parabolas. I responded by talking about objects in free-fall. Afterwards as I was re-thinking this conversation ...

In Norway we will have a new national mathematics curriculum for all ages including high school beginning august 2020. A fundamental change is the new focus on so called algorithmic thinking. In ...

My daughter’s 5th grade teacher gives some pretty impossible questions and I don’t think she understands the material she’s teaching. For example, this question has no context from previous questions ...

The 1st fundamental theorem of calculus: $$\frac{d}{dx}\int_a^xf(t)\,dt = f(x),\quad x\in (a,b).$$ No textbook says that this can be generalized into the scenario where x is less than a and where f ...

I would like to teach the German Tank Problem to bright students with little prerequisites. They are 16 year old high school students with a lot of maths competition experience, but no prior knowledge ...

I was talking recently with my daughters about non-planar graphs, like $K_{3,3}$, $K_5$, and the 7 bridges of Königsberg. They got pretty interested in it, and seemed to catch on to the core ideas. ...

Many years ago when learning complex maths we used complex maths as an example in the quadratic equation to find real roots. My nephew is struggling to deal with complex maths, as his teacher is ...

So this is a somewhat neat idea I stumbled onto late in thinking. It involved refactoring the pedagogy of analysis maths. The typical discourse or dialectic is analysis versus synthesis. Here, I ...

I'm starting a repetition with my students in 5th grade after they learned in elementary school how to sum up larger natural numbers (also 5- to 6-digits) by writing down that calculation. As ...

I would like to impress college students (undergraduates in the U.S.) that there is more to planar geometry beyond what they learned in high school. I would like to show them beautiful theorems they ...

My school is hyped about the promise of co-curricular education and they are giving the math and science teachers paid days off to develop lesson plans that synergize our learning goals. I'm on ...

I read this is the mathematics educators stack exchange so hopefully this is the right place for this question. I was curious what is your favorite math toys, manipulatives, math games, or tools to ...

There are a lot of "proofs" of the identity $e^{ix}=\cos x+i\sin x$ in textbooks, using either differential equations or power series. However, I find those proofs often misleading, because it appears ...

In most of books on elementary algebra, intermediate algebra and college algebra, the degree of the non-zero polynomial $$f(x)=a_nx^n+\cdots a_1x+a_0$$ with $a_n\neq 0$ is defined to be $n$. But I ...

I was teaching Fourier transform for engineering students. Since I didn't want to go into rigourous proofs during class, I often use intuition, just give students an idea to persuade them with the ...

In mathematics, one can hardly study any mathematical concept unless it is clearly and rigorously defined. For example, without the definition the fundamental group, it is almost impossible to teach ...

I am teaching my daughter, who is currently about $46$ months old, additions. She is very curious and asks a lot of good questions. For example, when I told her that $2+6=8$ and $4+4=8$, she asked me ...

The context is explaining to calculus students how to integrate rational functions by using partial fractions decomposition. As we all know, partial fractions decomposition is a method to write every ...

I am curious if it is true that one can learn more from hard problems, or from easy problems. I heard that we all learn a lot more from doing harder problems, because we have to learn all of the ...

This seems like a stupid question . I just don’t understand why the algebra textbooks I see don’t really address this with students. I boy that I am tutoring brought it up and I was slightly ...

In teaching elementary set theory, suppose we refrain from emphasizing historical decisions that were made in theory construction. Is there a danger that students may see the mathematical language ...

How to deal with a student who refuses to learn? I've met a few of those over the years as a a private-class math teacher. They don't want to learn anything about the subject. Some of them are just ...

Let $A$ be the set of all undergraduate mathematical courses in the US and define a binary relation $\leq$ on $A$ such that for elements $a,b\in A$ (that is, $a$, $b$ are undergraduate mathematical ...

First, I will simply observe that it seems to be standard practice, in elementary set theory, to define relations to be sets of ordered pairs. If we had the option of introducing a "symmetric ...

I am planning to teach (unofficially, I am a Grad student) a course in real analysis. Aim of the course is to understand the convergence of Fourier series. I want to start with the notion of ...

The idea is that a student who is reading from beginning to end will always be provided with a train of thought. The student will have no motivation to stop, and memorize an unexplained product of ...

For example, Trigonometry was written by Wolf-Prize winner Israel Gelfand, one of the top mathematicians in the 20th century. I am wondering if other world-class mathematicians have written textbooks ...

There are lots of discussions out there about whether $1$ is a prime number (such as this one) and even about zero (such as this question, though note zero does generate a prime ideal in $\mathbb{Z}$ ...

edit: Thanks for all your answers so far. I have decided to develop my own solution, both because it is fun and I can then form it exactly as I want to. Once I am done (which might take some time, ...

I have been doing a little bit of experimenting when it comes time to review with the class in preparation for the final exam. The last handout I have been giving my students has usually been a ...

It seems to me that we all might benefit from an answer to this question, since math departments must defend their performance within their institutions. I imagine there will be standard answers like:...

I am planning to give my students a take-home examination on ODE. The main topic that I would like to cover is Linear Differential Equations of Order Greater than One. For example, I will give my ...

In the precalculus curriculum I am teaching (using Stewart's book Precalculus: Mathematics for Calculus, 7th ed.), we do a bit of polar graphing, which includes discussion of symmetry on polar graphs. ...

I'm thinking about teaching calculus by firstly introducing the asymptotic notations (big-Oh, little-oh, and $\sim$), secondly explaining their "arithmetic" (things like how to sum little-oh's and ...

I am about to teach a second year undergraduate class on applied differential equation (first time) and, while I won't have time to go into the details, I wanted to show my students the difference ...

I am preparing an introductory course on Game Theory for children (between 10 and 17 years old). In the course description, I want to include a prisoner's dilemma in order to catch children's ...

I'm worried that I'm bad at realizing when a question I've written requires little or no conceptual understanding to answer. Like, when I'm writing a question for a homework assignment or exam, I'll ...

I took Calc I in preparation for the CLEP. I did not learn about solids of revolution. Is this something that is normally part of Calc I and that most Calc II classes will expect that I can do already?...

Hi I've just discovered mathseducators stackexchange. As a maths tutor in the UK, I am irritated that some of my students - particularly GCSE and sometimes below - use the table method for expanding ...

Every good teacher knows that giving an informal explanation (that is, an explanation not based on strict definitions and maybe making use of metaphors, intuition, or everyday language) of a ...

I have been looking everywhere for the name of this form of equation of a line $y=m(x-x_0)+y_0$. It's not quite point-slope. It's the same form you would write in the linear approximation of a ...

Why is it popular to teach modulus via the example of mod 12 and analogue clocks rather than rectangles or tables that have a finite number of columns in each row, and infinitely many rows? It's ...

In undergraduate maths study, there are three main areas: analysis, algebra, and geometry. (There are of course other small topics as well, but they don't have to be learnt by every student.) I have ...

I want to emphasize the aspect of environmental education in my math class. Now I'm reasoning whether to do that with linear inequalities or terms with two variables - these are our next topics. The ...

There are many university ranking consultancies trying to compare one leading maths department with another and to conclude which one is better. Although this doesn't seem to be a very reasonable ...

I feel very confused when teaching students how to sketch a parametric curve like $$x(t)=e^{-t}t; y(t)=t^{2}+t.$$ Here students are supposed to know derivatives, increasing-decreasing,... In ...

In prob/stats, students mostly get the idea of mean/expected value, and variance/s.d. slowly sinks in. Even the third and fourth moments (about the mean) have "standard" interpretations - skewness ...

Someone asks the following question: Determine the values for the real numbers $a$ and $b$ such that $$\lim_{x\to0}\frac{ae^x+b\cos x}{x}=2$$ The students directly apply de LHospital's rule for the ...

I am teaching mathematical proof to kids (10th grade) and am of the opinion that proofs of theorems are a good place to start, where almost all of mathematics' important players come together. On ...

This is a question I asked on [Academia.se]. It did not get an answer, so I am re-posting it here. In the country where I live, university students studying mathematics usually attend lectures, ...