All Questions

From reviews on Amazon of the various high school math texts by Mary Dolciani et al of the SMSG, I assume that there might be a successor to the approach (referred to as “the new math”) taken by the ...

I noticed many seemingly reputable online sources have "incorrect" description of directional derivatives for real-valued functions in several variables. Here, by "incorrect" I ...

In the context of a standard undergraduate Calculus sequence, I've noticed there is a big emphasis on teaching the algebra part of Calculus. What I mean by this is that a student may feel more ...

(I was inspired by the comments in this answer to ask this question.) I have some multiplication table cards from Kumon that have a list of commonly mistaken multiplications: $7\times 8,4\times 8,11\...

I have been professionally tutoring a wide range of students (from elementary school through graduate school) for many years. Most of them are from the United States. I generally focus on helping my ...

I am running into problems explaining to my students in high school what exactly is sample space in probabilities, especially with identical objects. For example, according to Q6.2.3 of this UIC ...

My child in grade 3 often needs a reminder because in a task where he needs to do addition he would subtract instead of adding or v.v ignoring the signs given in a task. He would also forget adding ...

I have a college student who I've been tutoring over the past two semesters. He's a hard worker and quite bright. Unfortunately, I do not feel like I am having much success in helping him learn ...

I had an idea to improve education in my country with the help of textbooks by popular authors. I thought to publish videos on YouTube with comments and practical explanations about what the author ...

In several online high school teaching resources (I do not want to single out any) I see that $a-b$ is referred to as the conjugate of $a+b$ with no restriction on $a$ and $b$. I can understand that $...

In a previous question, I asked about the pros and cons of teaching rings before groups in abstract algebra. Recently, it has come to my attention that there is a third approach - a unified approach - ...

This question concerns teaching a proof of the theorem that if a polynomial $f \in k[x]$ over an infinite field $k$ is the zero function (i.e. $f(a) = 0$ for all $a \in k$) then it is also the zero ...

Main question: Does anyone have any good/interesting applications of the rational root theorem or ways to teach it that don't involve conveniently ignoring computer-based tools in order to avoid rote ...

I am teaching Linear Algebra this semester, with pre-recorded classes and weekly meetings, and the students have a few short and simple exercises to solve every week, which count a bit (20%) to their ...

I know that undergrad math books use colors, like Gilbert Strang in his undergrad Linear Algebra textbooks and Measure, Integration & Real Analysis by Sheldon Axler. Many first year calculus ...

There are $50$ bacteria at 10:00 and each divides simultaneously into 2 every 20 minutes. The process of dividing into two is known as binary fission. Let $n$ be the number of fissions that have ...

I am interested in learning graph theory, and from many resources I came to know that Douglas West's Introduction to Graph Theory is a good textbook. But since I am doing self-study, it is at times ...

We can spend a lot of time thinking of material which we have basics for without ever studying the original ideas from a textbook, for example, once one has finished regular derivatives, it is pretty ...

I have a quite broad questions. I'm a math teacher in Switzerland (high school level, school year 9-12). We teach following topics (among others): quadratic equations, quadratic functions, system of ...

I've been working with a teacher, helping her with tech. One of the things I help with is to convert PDF formatted quizzes or tests to DeltaMath for the students to take online. The issue that I face ...

To evaluate $\sqrt{-1}$ $\times$ $\sqrt{-1}$ we cannot use $\sqrt{A}$ $\times$ $\sqrt{B}$ = $\sqrt{AB}$ as the result would be 1. I know (?) that we must first respect that the initial numbers ...

A natural way to reason about Euclidean geometry using modern mathematical language is to define Euclidean space as an affine space $A$ directed by a finite-dimensional real vector space $V$. However, ...

The critical points of a function $f(x)$ are candidates for local extrema, i.e., if a function changes from increasing to decreasing, or vice versa, it must happen at a critical point. Is there an ...

Most differential calculus courses begin with the theory (and analysis) of differentiation, followed by computations, and likewise integral calculus courses. That's a lot for a three credit course, ...

I have been tutoring a wide range of math subjects for many years. Recently, I began tutoring a girl in high school geometry (in California, for context). This semester of the course is starting with ...

Robert Ash (1935-2015) touts in the Preface to Real Variables with Basic Metric Space Topology, I rely especially on one of the most useful of all learning devices: the inclusion of detailed ...

I'm planning to teach a series of lessons on expanding and factoring binomials using a certain visual method for my edTPA assessment. Each lesson is pretty much going to be structured the same way in ...

I plan to work with my students on solving real-world problems through modelling them. Now it is my idea to follow the modelling cycle below. The idea is to find with the help of two values that have ...

I am looking for a book or any resources related to this book. It is called Pattern and Structure Mathematics Awareness Program (there is a book one and book two). I have tried to order it but it is ...

The cross product is an important vector operation in in any serious multivariable calculus course. In most textbooks that I'm aware of, right after the definition, we always introduce the ...

Judea Pearl, in his book "Probabilistic reasoning in intelligent systems" uses a handful of stories over and over again, each time to demonstrate a different point. (His "Alarm" ...

This question applies to solely books already accompanied by an ISM ("Instructor's Solution Manual) — access is restricted to instructors. Some don't even sell a SSM (Students' Solution Manual) ...

Some students have sniveled that most examples of Bayes' Theorem use non-integer numbers. I want to try a Bayes' Theorem chart that uses just single digit Natural Numbers $\le 9$. To complete the ...

We are now in lock-down, so while homeschooling my son I get to se exactly what he does for math. He has been getting a huge amount of repetitive practicing of really simple math, despite being quite ...

From one textbook we use in our High School - Transcription: A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases of the trapezoid. And from ...

I am currently advising a student at his final project (it is a graduation course for people who will become math teachers). We've chosen to pick some basic mathematical rules which are (or at least ...

I am to give the following for an interview: "a short 7–10-minute teaching demonstration on logarithms. Please consider this as your first 10 minutes of introducing logarithms as if you have not ...

I've been pretty dissatisfied with the way the Pythagorean theorem is usually taught, mainly for two reasons: The chosen proof feels like magic and I don't feel like I have a better understanding of ...

In conceptually motivating the $\epsilon-\delta$ definition and proof of a limit, I realized a new way of choosing the $\delta$. For example, consider $\lim_{x\to 4}\sqrt{x}=2$. In the "standard ...

I posted this question earlier today on the Mathematics site (https://math.stackexchange.com/q/3988907/96384), but was advised it would be better here. I had a heated argument with someone online who ...

We’re precalculus honors teachers. In this year of Covid and reduced instructional time, what topics can we cut (Demana textbook) that would not hurt our kids in either calc AB or BC?

I am giving tutoring to a high school student since more than one year and half. He is about 17 years old. He has excellent results in mathematics, being best student in his class for the last year ...

I know someone I really like, but sadly, that person has absolutely no experience in math or mathematical thinking above third grade mathematics (+, - are fine, but division already makes problems). ...

As we try to work and teach in the midst of this pandemic, some problems arise when making online math exams. My question is simple: What could be an interesting basic differentiation question such ...

I’m a master student in Turkey. I’m researching math textbooks from different counties to compare them for my thesis. However, it is really difficult to find them. I need your suggestions. Or is there ...

I talked with my friend on December 29 2020. Then I talked with him again on January 03, 2021. Q: What was the year when you last talked with your friend? A: 2021. Q: And what was the year the ...

I'm looking for a simple way to define mathematics to primary/elementary school teachers and explain some of the confusion children have. I'm hoping some Algebraist could help me properly state the ...

I am looking for a simple solution to the following problem: I would like to create a math quiz with n questions via LaTex (printable, in pdf) where question 1 is chosen randomly from question bank #1,...

Background I know the question in the title is very broad so I will try to explain it as succinctly as I can. Half my time is spent on as a researcher on didactics, while the other half is devoted to ...

I was trying to figure out the distinction of a root and a zero and found people in such discussions make distinctions between equation vs. expression vs. polynomial without defining them. What is ...