All Questions

I had a question from a student which I'm unable to answer. We were practicing the rule $\int \frac{f'(x)}{f(x)} \, dx=\ln(f(x))$. A student noticed that if applied naively it gives the following ...

I'm a fairly new private math tutor, and I'm good at math (I have a BS from Caltech with lots of graduate level math), but becoming good at teaching math is something else, which I strive to improve ...

In Germany, one usual example to start teaching about integrals is to look at a simple (piecewise constant or with constant slope) functions that make up a water flow vs. time diagram and ask about ...

When you teach about slope in Algebra 1, should we relabel the slope formula to: $$m = \frac{y_b-y_a} {x_b-x_a}$$ and also temporarily relabel the slope-point formula to: $$y−y_a=m(x−x_a)$$ where ...

Ok, this may be a ridiculous question and if so, you guys will shut it down. But I didn't know where else to ask it-it certainly doesn't belong on Math Overflow. Does anyone know if anyone ever ...

For concreteness lets keep our discussion to calculus courses where there is a balance of proof and computations (computing limits but also doing epsilon-delta proofs) I can understand that in more ...

I'm a private math tutor. I'm fairly new at this, and this semester is the first time I've been tutoring for a statistics class at a community college. I enjoy experimenting and learning about ways to ...

I’m trying to negate the underlined formula(in the attached picture)but can’t seems to comes in terms with my solution. Your expert inputs are welcomed.

My institution is now in the process of "standardizing" our calculus classes. One issue we have is the variation among instructors in grading problems. I am interested if there are ways to objectively ...

This question came up in my diffyqs discussion today. I was curious as to what you fine people had to say. My intuition says it can't happen because the derivative is mostly positive... but my ...

Is there some single, persuading visualization that can be used to convince students of the intuitive truth of the fundamental theorem of calculus, in the form $$ \int_a^b f(t) \, dt = F(b) - F(a) \;?...

I am now pretending to be a newbie student. I write the following sample space for the Monty Hall problem (It is a famous brain teaser, I assume you know it). $$ S=\{ (C,G1),(C,G2), (G1,G2), (G2,G1) \...

I don't understand why common core: High School Algebra II (NYC, NY, USA) removed so many topics. I think these ideas are pretty important and useful (especially since a handful of these topics come ...

I feel that the common core: High School Algebra I (NYC, NY, USA) curriculum is too short and tedious. For one, it can be completed in 5 months even with a lot of prolonging. For me, there isn't a ...

I am teaching a math class where the students, most of them, tell me that they can understand the materials given by me during the course. I test them during the course too and they seem to get it. ...

I'm going to be giving a five minute "elevator pitch" presentation to undergraduate math majors in order to advertise an introduction to statistics class that I'll be teaching in the spring. It's an ...

One easy integration of $\sec x$ substitutes $u=\sin x$, viz.$$\int\frac{\cos x}{1-\sin^2 x}\,\mathrm{d}x=\frac{1}{2}\ln\left|\frac{1+\sin x}{1-\sin x}\right|+C.$$Multiplying top and bottom by $1+\sin ...

I am in charge in my institution of a class where students prepare math interviews to enter university. Part of the time is devoted to the review of the topics of PreCalculus and Calculus the students ...

Looking for the necessary hardware to share, in real time streaming, the writings and drawings done in a paper or notebook. It looked like something easy to find but after two hours goggling, nothing ...

Cubic polynomials are crucially important in computer graphics: for example, cubic Bézier curves/surfaces, and cubic splines, which have many practical applications. Essentially visual continuity ...

I was teaching elementary school kids (aged 10) about the mean. The intuition I gave them is roughly as follows: You are trying to find a value such that the sum of all the distances from the mean ...

For finding counter examples. That does not sound convincing enough, at least not always. Why as a object in its own right the study of Cantor Set has merit ?

I am teaching a mid-level calculus course, and I see my students making the freshman's dream mistake of thinking that every function is a homomorphism. In particular, they think that exponents can be ...

For simple expressions with easily derived canonical forms (eg polynomials and simple rational expressions), is there a way to leverage existing tools to verify that two expressions are equal when ...

What is the name for a situation where the obvious thing turns out to be true, but the reasoning is more complicated? In abstract algebra we can say the rational numbers - the fractions, $\mathbb{Q}...

Question: Would it be feasible to teach undergraduate math students a "map"-centric view early on? If so, how early on? Now that I'm preparing for a phd program, I'm also reflecting on my ...

Just now I'm thinking a crazy reversed idea: Is it good to teach math to elementary students without starting from its real world motivation or making it intuitive first, but rather by realizing that ...

I would like suggestions for a good text on concentration inequalities (examples here https://en.wikipedia.org/wiki/Concentration_inequality). I am looking for sources (texts) that can give strong ...

I have found very little online that compares & critiques the MVP vs traditional curricula. Any suggestions & pointers would be welcomed. The MVP is an implementation of Common Core Standards ...

Question Does anyone have a nice list of "no effort" activities that parents can employ to promote numeracy? I am primarily interested in K-8 activities. Exposition Often parents ask me about what ...

I am teaching a very small intro to proofs class with Dana Ernst IBL book, and came to theorem 2.56. The section is about proof by contradiction but I felt that the solution I came up with is ...

A course that my kids are doing in conic sections insists that all positions are represented as standard 2D cartesian coordinates $(x,y)$ (i.e. row vectors), and all translations are written as 2D ...

This happens a lot when I try to explain the commutative property, mostly in elementary grade levels. I say 2 + 3 = ? and then the student usually replies with 5. Albeit they're not wrong, it's ...

Question: What are good examples of functions $f: \Bbb R \rightarrow \Bbb R$ (or $f: D \rightarrow \Bbb R$ with $D \subseteq \Bbb R$) which are not just given by "a formula" (or finitely many formulae ...

I am teaching a student basic equations. For now, I want him to drill: Multiplication Exponentiation (by exponents 2,3 4 and 5) Substituting values in first degree equations (what is $(x-2)(5x+3)+3x+...

If $a = \frac{x}{b}$ and $a = \frac{c}{b}$, and I solve for $x$ I get $x = c$. $b$ has been removed because it appeared in the numerator and the denominator. What is it called in English what ...

I have been thinking, is it possible, or a good thing to do when learning from a textbook without ever writing anything down. But have to verbally give out the solution from beginning to the end with ...

I'm covering section 2.5 of Stewart (on continuity) and stewarts treatment seems needlessly complicated. It seems like the following theorem would streamline a lot of it: If $f(x)$ and $g(x)$ are ...

What are good examples of proofs by induction that are relatively low on algebra? Examples might include simple results about graphs. My aim is to help students get a sense of the logical form of an ...

I often see a situation when professors use words "logic", "mathematical proof" and even prove logically while actually knowing that students are not even familiar with logic itself, i.e. no formal ...

Third grade grandchild had this for homework. I don't even know the intent here?

As you know, Art of Problem Solving includes 11 books that comes with their solutions and they are PreAlgebra, Introduction to Algebra, Introduction to Counting and Probability, Introduction to ...

I am teaching intro to Geometry using Moise and Downs textbook. It is an excellent text but somewhat old. Does anyone know if there are sample tests that are available for use with this textbook?

I am no professional educator; I am a student myself! But apparently I come up with useful tricks that help my younger brother do better in maths. I just want to hear your feedback, is all. My ...

Students often misuse the equals sign to indicate "I've done this operation" rather than the proper use indicating numerical equivalence. Eg. Tax is paid using the rule: \$3 572 plus 32.5c per \$1 ...

I have a 13-year-old nephew that liked learning with me, but I've recently moved 400km away. I wonder if it is possible to still learn with him long distance. The subjects I care about are maths and ...

I was recently at EPFL drone days and enjoyed a demo of a robot that could follow a black line like in the sketch (I can improve the sketch on demand): Then I remembered my good all times at the ...

** Edit Thanks everyone for some great suggestions. I should have been more clear though. I am actually looking for a college level proof that pertains to algebra or leads to algebra in some form. ...

In the U.S. students in grades $\{9,10,11\}$ often learn long division of two polynomials, e.g.: $$ \frac{x^4 + 6x^2 + 2}{x^2 + 5} = x^2 + 1 - \frac{3}{x^2 + 5} \;. $$ I believe it is fair to say that ...

This semester I am a TA for a Calc 2 course. At my first meeting with my instructor, he mentioned in passing that "Homework is always easier than an exam, because homework questions come from the ...