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30
votes
5answers
38k views

Software to create video tutorial of mathematics topics

I came across many video tutorials on youtube regarding mathematics. I found this video amazingly simple to understand for students. I want to know about the tool/software used for it or similar ...
30
votes
6answers
3k views

How to motivate an adolescent who has fallen behind in conceptual development?

I tutor a 16 year old girl. As far as I can tell, she has average talent and interest in math. However, her knowledge of math is that of a 10 year old or even below. She knows the basic operations on ...
29
votes
10answers
10k views

Is this homework problem on counting triangles within a 4x4 grid too vague?

My six-year old daughter was given this maths problem for her homework: Given a regular square grid of 4 × 4 dots, how many different triangles with one dot in the middle can you draw? We were ...
29
votes
13answers
7k views

What do you say to students who want to apply Banach-Tarski theorem in practice?

Once when I was talking about Banach-Traski theorem (paradox) I said: OK! This is Banach-Tarski's theorem which is against our intuition but provable from our intuitive axioms! It says you can ...
29
votes
11answers
3k views

What are the arguments for and against learning the multiplication table by heart?

I think, a lot of students are bothered by learning multiplication tables by heart, in particular when it comes to numbers greater than 10. Why should one learn (or not learn) these things by heart?
29
votes
11answers
27k views

Why should kids learn how to use a compass and straightedge, and not rely on a drawing program?

I am curious why it is necessary for people to learn how to use compasses and straightedges in geometry, and not just rely on a drawing program. I have a couple ideas, but I might be missing ...
29
votes
10answers
9k views

Why do we teach even and odd functions?

I've been either a student or an instructor in Precalculus or Calculus 1 at about 6 institutions now, and teaching the definition of even functions (where $f(-x) = f(x)$) and odd functions (where $f(-...
29
votes
10answers
5k views

Is Euclid dead? or Should Euclidean geometry be taught to high school students?

Apparently Euclid died about 2,300 years ago (actually 2,288 to be more precise), but the title of the question refers to the rallying cry of Dieudonné, "A bas Euclide! Mort aux triangles!" (...
29
votes
11answers
4k views

For calculus students, what should be the intuition or motivation behind series?

I've noticed that series are one of the most difficult portions of calculus for new students to learn. I think the level of abstraction has to do with this. Limits, derivatives, and integrals, as ...
29
votes
14answers
2k views

Revisiting topics from previous courses

I teach calculus to students who have almost all taken calculus before. (Primarily first-year college students who took calculus in high school but didn't perform well enough to skip the course.) ...
29
votes
11answers
4k views

Are the words “easy,” “basic,” “clearly,” “obviously,” etc., ever helpful?

This is a very basic fact from... It then clearly follows that... Obviously, we have... The proof is trivial... I could add plenty of other phrases to this list that mathematicians are prone to use ...
29
votes
11answers
5k views

When asked to by a religious university, how can an instructor make a mathematics course spiritually uplifting?

Several religious universities, such as Brigham Young University, ask all instructors in every area to try to make their courses spiritually uplifting. This is something included in student ratings. ...
29
votes
7answers
2k views

Mathematical education by country

Depending on the university, there are always slight differences in the syllabus and the structure of the standard material undergraduate students learn. But I also noticed that undergraduate ...
29
votes
3answers
11k views

Difference between high school and college calculus courses

I am curious why students who take calculus in high school often do so poorly in college calculus. I am an instructor at an engineering college and I've noticed a decent number of students who have ...
29
votes
6answers
1k views

What is the rationale for the absent (+) in mixed fractions?

Why are students taught to represent one and a half as $1 \frac{1}{2}$ rather than $1 + \frac{1}{2}$? This mode of expression seems standard at least throughout North America. I believe that it is bad ...
29
votes
3answers
510 views

What Math(s) Ed literature is accessible to the working math(s) educator?

This site is - as far as I'm aware - for what I would term working maths educators. That is, on the whole the users of this site are not researchers in mathematics education. Rather, we are the ...
29
votes
7answers
2k views

Teaching logic with a proof assistant

I am thinking about teaching a university-level "introduction to proofs" class (mainly for math and CS majors) making use of a computer proof assistant like Coq. I feel like there is a lot of ...
29
votes
4answers
3k views

Books about elementary mathematics written like a good undergraduate textbook

I've never seen any really good expositions of elementary mathematics (middle school or earlier). A good college-level textbook, written for people with an interest in mathematics, reads like a novel ...
29
votes
5answers
4k views

What fraction of the population is incapable of learning algebra?

In the comment thread of this academia.SE question, the following generated some strong reactions: My very different (community-college) perspective is that the math discipline will end up as a ...
28
votes
17answers
6k views

Examples of Innumeracy

I read Innumeracy by John Allen Paulos and would like to share more up-to-date and relevant examples of innumeracy to motivate my grade 8, 9 & 10 students. Are there any websites, blogs, books, ...
28
votes
13answers
9k views

Should I be teaching point-slope formula to high school algebra students?

I'm student teaching this semester, and so far I'm loving it! Our next section in the book teaches point-slope formula, and my cooperating teacher (a 24-year veteran teacher) is convinced that point-...
28
votes
10answers
1k views

What are argument one can give to students on the definition $0^0$?

From high school to introduction courses in university, the expression $0^0$ is some (psychological) problems. High school students just apply it to their calculator and either the result is $1$ or ...
28
votes
9answers
4k views

Teaching by Slides, Yes or No?

Mathematicians use (Powerpoint/Beamer) slides for their lectures. My question is about using slides for teaching math. There are several positive and negative arguments about teaching by slide show. e....
28
votes
6answers
6k views

Misuse of parentheses for multiplication

I'd like to raise the issue of constant misuse of parentheses in the U.S., and I'm wondering if anybody else shares the same feelings, has had the same issues, knows any history behind it, and can ...
28
votes
8answers
3k views

Is there a good age/level to start learning mathematical proofs?

I know from my experience I learnt proofs myself way before I learnt them in school and I felt it gave me a far better understanding of math. What is a good point to start learning proofs? what are ...
28
votes
14answers
4k 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 ...
28
votes
7answers
2k views

Good definition for introducing real numbers?

In the first lectures about calculus/analysis, you should introduce real numbers. Let's assume students know that rational numbers are. What are the advantages or disadvantages in the different "...
28
votes
10answers
8k views

How should a student's inefficient calculation be pointed out?

One time I watched a student solve the equation $0 = (x-2)^2-9$ for $x$ like this. $$\begin{align*} 0 &= (x-2)^2-9 \\0 &= (x^2-4x+4)-9 \\0 &= x^2-4x-5 \\0 &= (x+1)(x-...
28
votes
12answers
7k views

How to give my students a straightedge instead of a ruler

I'm having a "challenge" in my geometry classes getting students to avoid using rulers as measuring devices in constructions. As natural as that usage is, they're only supposed to use them to connect ...
28
votes
9answers
4k views

When handing back exams, what should we tell our students about the distribution of exam scores?

I've seen a variety of approaches to the day we hand back our exams. Show every score listed in order, so every student knows exactly how they compare to others Show an aggregated histogram, for ...
28
votes
4answers
2k views

Interesting things you learned while grading?

What are some interesting mathematical things you have learned while grading student work (or marking, if you prefer)? It is final exams time here, so if anyone can help cast a more positive light on ...
28
votes
1answer
5k views

Which product of single digits do children usually get wrong?

(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\...
28
votes
3answers
779 views

What is the evidence about the effectiveness of remediation in math?

At many colleges in the United States, incoming students are required to take placement tests in basic skills such as math and reading. Those who score below a cut-off are required to take remedial ...
28
votes
5answers
1k views

Wonder as motivation

Like all mathematicians, I have a deep appreciation of the beauty of mathematics. Many theorems I find amazing even after I fully understand their proofs. (Example: Euler's formula, $V-E+F=2-2g$. That ...
28
votes
4answers
4k views

Open-Source Math Textbooks

It seems to me that an open-source model could work quite well for textbooks, with issues being raised by the users of the book and different forks of the project being created for different ...
28
votes
6answers
2k views

What are non-math majors supposed to get out of an undergraduate calculus class?

When I teach a course for math majors (an analysis course out of Rudin, say), I have a more or less clear idea of what the students should take away from the course, having been in their shoes some 15 ...
28
votes
6answers
20k views

Early vs. late transcendentals

There seem to be two approaches to calculus education: Early transcendentals: introduce polynomials, rational functions, exponentials, logarithms, and trigonometric functions at the beginning of the ...
27
votes
15answers
4k views

How do I teach algebra?

I find that soon I'll be working with high school students that are struggling with math. In particular, we'll be talking a lot about algebra and some basic trigonometry. The latter I have experience ...
27
votes
10answers
8k views

Should LaTeX be taught in high school?

This semester, I was forced to learn LaTeX for my Real Analysis class. The professor wanted all homework assignments to be typed in LaTeX in order to produce "high-quality" work. At first I was ...
27
votes
10answers
3k views

Should figures be presented to scale?

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 ...
27
votes
8answers
2k views

Good motivation for the introduction of Lebesgue integral?

When students take a course on real analysis, they have likely learned about Riemann integrals. What is a good motivation why they have to learn a new way to integrate? A student don't want to hear ...
27
votes
7answers
6k views

What was the problem with New Math? Why did it end?

During the 60s, people in the US (and also in Europe), school curricula introduces New Math where students began with set theory in the first grade before learning to perform addition or ...
27
votes
6answers
2k views

How to encourage women to study mathematics?

What are different ways we can get women to study mathematics? In my own experience, the higher the math class, the less women in the class. Most women tend to go on the math education track and do ...
27
votes
5answers
2k views

Should word problems be reasonable?

I've recently run across a series of problems that didn't reflect reality. For example - An algebra problem with two teens on bicycles. The resulting times showed the bike was moving at 120MPH. ...
27
votes
7answers
1k views

Why does high school teaching in the USA require a teaching certificate while college/university teaching does not?

Original post: I have a math PhD. In the United States, I can teach at a 4-year university or a community college without any additional training. However, to teach mathematics in high-school I must ...
27
votes
6answers
815 views

How can we help students who are very anxious about math?

In many parts of the world, the majority of the population is uncomfortable with math. In a few countries this is not the case. We would do well to change our education systems to promote a healthier ...
27
votes
4answers
902 views

The Undergraduate Responsibility Gradient

We tell undergraduate students that they should study two to three hours for every hour they spend in class. We know that many students don't follow through with this nearly to the degree that they ...
27
votes
4answers
837 views

How to tactfully discourage casual, implicit disparagement of mathematics

I volunteer with a group that provides tutoring to kids from grades nine through twelve. The included kids have been determined to be 'at risk of not graduating high school'. Of course, many of the ...
27
votes
4answers
3k views

Students use WolframAlpha. Can we change calculus instruction to exploit it while discouraging 'cheating'?

(This question developed from a comment in the thread "Revisiting the chain rule".) Students know that WolframAlpha and other software/computational resources exist and will make use of them as they ...
27
votes
1answer
859 views

Do “gateway tests” work?

Here is an overview of the practice of "gateway testing", which explains it much better than I could: https://sites.lsa.umich.edu/michigan-math-in-action/2015/09/24/25-years-gateway-testing-at-...

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