Questions tagged [mathematical-pedagogy]

for questions on general considerations and problems of teaching mathematics, i.e., issues specific to teaching mathematics yet relevant to various contexts and courses.

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3answers
2k views

How many of “The Seven Laws of Teaching” are still relevant for teaching maths today?

Wikipedia shows that in 1886 John Milton Gregory outlined his "The Seven Laws of Teaching"; asserting that a teacher should: Know thoroughly and familiarly the lesson you wish to teach; ...
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7answers
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How do you handle the frustration of having to GRADE student exams / homework?

A math student may write very long and detailed answers, just because he or she does not know what to look for, for example in Geometry proofs. Or - a student may just write an arbitrary step without ...
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Why are most college level math textbooks black and white only?

Why are higher level math textbooks almost completely black and white? I can't think of any math textbooks on a subject more advanced than calculus that uses colors. Edited to add that the comments by ...
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Which works better for learning 6 * 7 = 42: saying “six sevens are forty-two”, or “six times seven equals forty-two”?

When memorizing and recalling the times table, I learned to say "six sevens are forty-two", and always wondered what it would be like to learn to say "six times seven equals forty-two&...
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3answers
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Why do we typically only teach high-school students affine transformations of elementary functions?

A standard pre-calculus curriculum consists of the study of elementary functions: Polynomials, rational functions, (circular and hyperbolic) trigonometric functions, exponential functions, their ...
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Worth introducing a mandatory short module on $\LaTeX$ into a mathematics degree?

On Mathematics StackExchange for a particular instance, it is highly recommended that questioners mark up their questions using $\LaTeX$. A surprising number of mathematicians and student ...
2
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0answers
203 views

Which areas of maths should underperforming western countries focus on?

I am not sure which StackExchange to ask this question but I am interested in the relative underperformance of Western countries such as Australia, US, UK compared to other higher performing countries ...
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1answer
113 views

Successor to School Mathematics Study Group (SMSG)

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 ...
2
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1answer
260 views

Are there any university programs that “supersize” calculus courses?

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, ...
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How to teach the Pythagorean theorem in a satisfying way to high school students?

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 ...
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Finding the Balance in a Math Question (Teaching)

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 ...
2
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2answers
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How do we explain to a little child that a date in 2020 and a date in 2021 are not necessarily a year apart?

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 ...
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1answer
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Do my students know elementary algebra; do they just use online calculators or external help; and is this ok?

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 ...
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Advice on teaching abstract algebra and logic to high-school students

NOTE: This question will soon be duplicated, as I didn't make clear that I was a high school sophmore in the beginning. At first I thought it didn't matter, and somewhat arrogant to mention, but in ...
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4answers
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How do you teach students about the concept of a proof?

I get this question a lot from new students who are taking their first proof-based math class. They are struggling because they don't have that fluency with proofs, to begin with. They don't know ...
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1answer
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Resources for Unit Rates

I am currently mentoring my little brother in mathematics. There is an issue with the pedagogy of unit rates. For example when given the following concept " 11.00 U.S. Dollars to 20 Planet X ...
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0answers
193 views

Do you avoid examples or test questions that showcase an algorithmic plug'n'chug approach?

If we accept that there's not much learning from doing the "same" questions, like find the derivative of $x^2$, and $x^3$, and $x^4$ due to the algorithmic way of how it's done, then what ...
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2answers
548 views

Teaching Mathematics to a Younger Sibling

I always wanted to teach my siblings mathematics, and one, ten years of age, is particularly eager. For the purposes of specializing recommendations, I will add he can use arithmetic up to ...
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Prerequisites to study Laplace Transform completely?

Hello to all the professors who read this. I'm an electrical engineering undergrad student. I wanted to ask for advice on what I should learn beforehand to fully grasp the Laplace transform. I also ...
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1answer
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Relational understanding for a specific topic

I want to aproach the undertanding of the trigonometric function based on the concept of relacional undertanding, but I have problems to came up with and problemic situation for it. I mean I don´t ...
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2answers
230 views

How can I teach $\frac{300}{200}$ to 10 years old students while s\he knows canceling the zeroes rule?

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\...
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Math websites/apps for high school students

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 ...
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1answer
267 views

If a computer could be programmed to do a math test, then should those tests be changed?

Not only do calculators have solving capabilities, but some computer programs or websites also provide step-by-step solutions to questions (here is WolframAlpha's). Although I understand a logical ...
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3answers
318 views

Transitioning proof based math courses online

I'd love to learn from anyone's recent experiences teaching online proof based math courses, especially those that have a large group of students who will be working asynchronously. My usual proof ...
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Teaching aid for online mathematics course

Crossposting from the math.stackexchange (Question) Online classes will start again as the semester will start, I bought an XP-Pen deco 03 to help me with online teaching. I will be teaching ...
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2answers
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Fear of notation and hazily-appeared writing in Mathematics

I am looking for literature related to fear of notation in mathematics. It is even heard that the font size and font type make a reader reluctant to study mathematical literature, often lecture notes,...
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2answers
261 views

Appealing thinking games, that are easy to make; easy to learn, and easy to play

$\color{Green}{\text{My Question in short}}$: Unprovable claim: Someone who is familiar with 100 thinking-games, and plays 30 of them reasonably well, is more prepared to go to math than the average ...
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7answers
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How can teachers warn students about common mistakes without causing the student to make the mistake?

For example, if you're teaching integration of $\int \frac{dx}{1+x^2}$, would you mention the common wrong answer of $\ln\left(1+x^2\right)+C$? -- For myself, I very rarely mention common mistakes ...
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2answers
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What is “mastery” in a mathematical topic?

This question was prompted by looking at Khan Academy's website to see how a comprehensive lecture series could be done and often I see the word, "mastery". To me, I'd think mastery is ...
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2answers
497 views

Logic and proofs in secondary school

Inspired by the question When do college students learn rigorous proofs?, I became curious when pupils in secondary schools learn about proofs, what kinds of proofs they are, how rigorously they are ...
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2answers
240 views

Math Education for Students who use Right-to-Left Written Languages

Does anyone know of any studies or have personal experience dealing with difficulties (if any) faced by students studying mathematics if they come from countries which use languages written from right-...
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5answers
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Concrete way to teach addition and subtraction of fractions

I am teaching 4th-grade kids. The topic is Fraction. Basic understanding of a fraction as a part of the whole and as part of the collection is clear to the kids. Several concrete ways exist to teach ...
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3answers
590 views

Looking for a HIERARCHY of math subjects

If you were to "map" mathematics onto a tree structure where the top is "Mathematics", and then below it the different branches, then sub-branches, etc. What do you suggest is a good structure, for ...
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How rigorous should high school calculus be?

In the UK, calculus taught in secondary school focuses mainly on computation of derivatives and integrals and solving simple differential equations. There is a small amount of discussion about limits ...
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2answers
173 views

Has a List of Fundamental Mathematical Skills been compiled?

... in the literature. I an wondering is there a (considered) list of "fundamental mathematical skills". I am not sure can I give a solid definition of "fundamental mathematical skill". What I mean ...
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1answer
150 views

Are there any online question bank of mathematics questions?

I know Dr. Martin Greenhow and his team of Brunel University London have developed online questions and I have used some of these at the following url: http://maths-for-all.co.uk/engineering-...
3
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1answer
165 views

The spatial thinking course for primary school - what to use?

We're planning to run the project for first two grades of the elementary school kids, in which we want to facilitate the spatial thinking development along with the regular arithmetic course and make ...
2
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2answers
334 views

How actually are prime numbers taught in elementary school in United States and how easily do students learn what they're being taught about them?

I read the question https://math.stackexchange.com/questions/1593091/how-to-explain-why-study-prime-numbers-to-5th-graders and according to the body of the question, some students sigh. Also according ...
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2answers
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What would you recommend for the math thinking course for school?

We're going to make a new math course for kids as intermediary between middle and high school with math profile (for preparation to entrance exams to high school), and before the main part (arithmetic,...
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1answer
349 views

Let P be a polygon

I've encountered the following misunderstanding. I pose a question (to undergraduates in the U.S.), for example: Let $P$ be a polygon of $n$ vertices. Is it true that every triangulation of $P$ ...
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1answer
469 views

Taxonomy of bad proofs

I am interested in finding examples of poorly written proofs that exemplify the types of mistakes made by undergraduate students in their first year or two of writing proofs. I am interested both in ...
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0answers
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Is There Book on Collection of Theorems? [closed]

For example, there is a book titled "Synopsis of Elementary Results in Pure and Applied Mathematics: Containing Propositions, Formulae, And Methods Of Analysis, With Abridged Demonstrations" (...
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3answers
133 views

How to teach integrals motivated by the work done in moving an object?

I am now teaching Calculus of several variables this semester. In apllications of integrals, the problem of finding the work done in moving an object under a force $F$ is one of the most common ...
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Is there a numerical base that is in any way “better” for simple mathematical calculations than others?

I want to know if there are any numerical bases that are notably well-suited for humans to learn and use at an elementary or grade-school level. I know that different numerical bases (i.e. decimal/...
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1answer
193 views

Misdirected, Side-Tracked, and Distorted Ramanujan: Problems in Basic Math Education?

I read that- “The tragedy of Ramanujan was not that he died young, but that his genius was misdirected, side-tracked, and to a certain extent : distorted. The years between 18 and 25 are ...
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4answers
234 views

How to convince parents that Mathematical puzzles/games help students in their academics too

I write content and conduct workshops for an education firm and also in schools where I try to make them realise how beautifully mathematics and rational thinking complement each other (on elementary ...
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368 views

How do I convince my teachers that a book on maths must focus on conceptual understanding?

I am a senior teacher at this school. We have to select the textbooks for the upcoming session. I am proposing that we have to select books (in maths) that focus more on conceptual understanding and ...
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Should high school teachers say “real numbers” before teaching complex numbers?

Before complex numbers are introduced in senior high school courses, should we emphasise that solutions (e.g. to quadratic equations) are real solutions? If we do, then when non-real numbers finally ...
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2answers
209 views

How should one approach the concept of “plus or minus”, such as in the numerator of the quadratic formula?

The numerator is structured like: $$(-b)\pm\sqrt{b^2- 4ac}.$$ Is it confusing or acceptable to distinguish between the following two things? An idiom; and What is or seems to be a compositionally ...
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Why is it possible to teach real numbers before even rigorously defining them?

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 ...

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