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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167 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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3answers
7k views

Good examples of proof by contradiction?

In later courses on automata theory, many students just seem incapable of getting a proof that a language isn't regular right, be it using the pumping lemma (see also the many questions on the matter ...
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3answers
345 views

Teaching number theory: geometric approach

Are there any books that are substantially based on a geometric approach to explain topics in number theory (elementary and more advanced)? If so, is such approach -- judging from your teaching (or ...
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24answers
7k views

Good, simple examples of induction?

Many examples of induction are silly, in that there are more natural methods available. Could you please post examples of induction, where it is required, and which are simple enough as examples in a ...
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0answers
68 views

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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6answers
791 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 ...
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8answers
2k views

Knowing mathematics does not translate to knowing to teach mathematics. Why?

Many brilliant mathematicians seem to make average or even poor classroom teachers. Is this an accurate assessment? Has there been any research to explain the phenomena? What is the difference ...
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3answers
981 views

Mathematical education slang

Amir Asghari recently asked a question about mathematical slang. He was "looking for "non-mathematical" terms or phrases that are used to refer to mathematical objects (of any kind) mainly for ...
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5answers
762 views

Descriptive Thinking vs. Formal Writing

Sometimes I come across some exam answers which describe a proof sketch or a counterexample very well but are not written formally. Such proofs show that a particular student understands the general ...
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1answer
240 views

Answering the Diversity Question for Mathematics Instructor Applications

As I apply for several other colleges who are hiring part time math teachers, I find myself wondering about this question as it is asked on ALL college instruction applications. Some of the questions ...
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5answers
963 views

Inability to work with an arbitrary mathematical object

This question is motivated by student responses to homework and quiz problems I have recently posed in an undergraduate real analysis course. I will share some examples and observations first, to ...
7
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1answer
206 views

Native language, writing, and mathematical problem solving

This question is meant to explore the intuition that mathematical thought does not most naturally proceed from writing in one's native language. The hackneyed and not entirely satisfying slogan that ...
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7answers
9k views

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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4answers
2k views

Lesson plan to self-teach real analysis to student with comp-sci background

For my background, I'm a software engineer currently studying for his master's degree in information security. But when that's all done, I plan on going back to mathematics to keep me busy. But with ...
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3answers
259 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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1answer
244 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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2answers
471 views

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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0answers
59 views

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 ...
5
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2answers
245 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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2answers
421 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
215 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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2answers
203 views

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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6answers
5k views

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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5answers
207 views

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
330 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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1answer
176 views

How can I deal with the time pressure of teaching a short course?

I am an undergraduate applied math student. In about a month, I will be teaching two nine-hour math courses (one precalculus, one calculus) to a small group of motivated high school students. My broad ...
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5answers
331 views

Is required reading of the text effective, and how can it be assessed?

This will likely depend on the class, of course. But I've asked calculus students in the past if (a) they regularly read the textbook and (b) whether this is helpful for them and (c) whether they like ...
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2answers
230 views

Good ideas on structuring a math class?

I have just started teaching mathematics up to secondary level. I don't have much idea as to how to handle the class. In order to make students learn well, how can we divide the time in order to put ...
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2answers
186 views

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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17answers
15k views

Unique candidate that fails

In the comments to David Speyer's answer here, he points out that "the distinction between 'if there is a formula, it is this one' and 'this formula works' is subtle." Does anyone have any simple, ...
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3answers
372 views

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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2answers
167 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
143 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-...
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1answer
197 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 $P$ ...
3
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1answer
162 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 ...
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8answers
538 views

How best to explain the logarithm to the mathematically naive?

Suppose you need to explain "What is a logarithm?" to an intelligent but math-phobic adult (or a student well-prior to her introduction to logarithms).1 I have used base-$10$, saying that, essentially,...
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13answers
4k views

How to teach binary numbers to 5th graders?

I already tried the direct approach, starting with "this is how it works". That turned out ok but took too long and was boring for all of us. My second attempt was using the twofingered alien. This ...
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14answers
7k views

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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2answers
203 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 ...
20
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1answer
329 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
78 views

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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11answers
10k views

Looking for simple “interesting” math problems that cannot be easily solved without algebra

I often find students who dislike algebra. They prefer to work with numbers in solving problems. I believe there are many problems that are hard to solve without algebra. For example: Finding the ...
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3answers
6k views

How do blind people learn mathematics?

I am interested in how blind people learn mathematics at any level, but particularly before college. Math is often taught using a lot of visualization; how does this work with blind people? My ...
2
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3answers
130 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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1answer
178 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
224 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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6answers
648 views

Would taking 5 minutes to explain the history behind a mathematical idea help stimulate learning the idea?

I read a paper in my "Research Issues in Mathematical Education" class that I have applied to the Undergraduate Calculus I and Calculus II class that I teach. I take five minutes to explain the ...
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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.) ...
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3answers
714 views

What teaching strategies can we learn from this logic puzzle going viral?

By now I'm sure everyone has run into the math puzzle where Albert and Bernard try to deduce Cheryl's birthday, which is all over social media, and even traditional media! If you don't know what I'm ...
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3answers
348 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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