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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25
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2answers
1k views

What methods successfully identify and eliminate severe math anxiety?

What methods are effective in identifying and eliminating severe math anxiety, this most terrible and unfortunate part of modern mathematics education? This question is not about ordinary math anxiety ...
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6answers
681 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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6answers
968 views

How to present $\Bbb Z/n\Bbb Z$ to highschool level audience

I have the oportunity to talk to a highschool class about mathematics, the topic I got to present are the integers modulo $n$, ie, $\Bbb Z/n\Bbb Z$ , however I don't want to be very heavy and formal, ...
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5answers
773 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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4answers
526 views

Elementary physics course for pure math student

Are there any mathematical departments which present the course "elementary physics" for pure math undergraduate students, separately? Is there a way to present this course with the most pure ...
24
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5answers
1k 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 ...
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7answers
4k views

Why are we so careful in saying that dy/dx is not a fraction?

Calculus instructors are mostly very careful to explain that $\frac{\mathrm{d}y}{\mathrm{d}x}$ is not a fraction, and multiplying both sides of an equation by $\mathrm{d}x$ is nonsense, wrong, or evil....
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3answers
555 views

Is there any math text reader device to help children who cannot see?

I don't teach school math but as a part of my voluntary activities in some NGOs, sometimes I am in this special situation. When I was in a school for special children who cannot see I came across a ...
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6answers
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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 ...
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2answers
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Students who know high-level math before going to college

There is a high school in the city I live in which has some high-level math courses in their curriculum. It's a special math class mentored by some university lecturers, and the children basically do ...
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3answers
288 views

Any suggestions on how to approach recursion and induction?

Much mathematics is intimately tied to recursion, be it in definitions (like factorials and integer powers) and proofs by induction. This is also very relevant in computer science and programming. ...
24
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1answer
639 views

Is there a Piagetian age at which proofs can be comprehended?

I am wondering if there is literature on the developmental age (pre-adolescent?, adolescent?) at which the notion of a "proof" can be understood? I am less interested in mathematical proofs and more ...
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7answers
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Notation Conflict between Teachers and Textbooks

In mathematics notation plays an important role in clarifying the subject. A bad notation could be confusing. Recently I use a logic textbook which has a very nice approach and content but an ...
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1answer
204 views

Reference request for studies on gender in math examples, homework problems, or math exams

I am looking for a study or reference on gender in math problems given in mathematics. In math texts or even on math exams, if there is a word problem involving people, these people or "characters" ...
12
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2answers
194 views

Course-based undergraduate research experiences in math

"Course-based undergraduate research experiences" (CUREs, or CBEs) are being explored in various STEM fields, especially biology, chemistry, geology. Here is one geology link that gives a flavor: "...
12
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2answers
350 views

Mathematics and the hermeneutic circle

Many students, teachers and parents view problems as confrontational. Many students develop a self concept in mathematics based on failed attempts to easily win such confrontations. This leads me to ...
11
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1answer
368 views

Use of symbolic math apps in teaching

Symbolic math apps, such as Mathcad, are extremely useful in doing exploratory/experimental math. I've frequently used it to run numerical checks on mathematical expressions I've derived; put up quick ...
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3answers
229 views

Targeted group game for 8 or 9 players

I am a graduate math student and I believe that a nice way to raise the mathematical skills of people(especially students!) is to familiarize them with games and encourage them to use their minds and ...
5
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4answers
907 views

Mathematics Education in Africa

It seems there are few well-known professional mathematicians in Africa. It is mainly because of the poor quality of elementary/undergraduate mathematics education in African countries. Question 1. ...
5
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3answers
320 views

When discussing inverse functions, how can our notation and methods reinforce student understanding?

Yesterday in my precalculus class, I decided to teach students how to find the formula for an inverse function in a new way (to me). In this curriculum, they have already used the notation $f^{-1}(x)$...
5
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1answer
319 views

Propositional and predicate logic, with quantifiers: Is there any research when it is ideal to explicitly teach in mathematics education?

In terms of helping students to understand propositional and predicate logic, with quantifiers, is there any research regarding when it is most advantageous for students studying mathematics, to first ...
3
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1answer
149 views

Existing Tools for Math Expression Equivalence Logic

Note - this question was posted here and garnered some decent replies before it was closed as off-topic in Stack Overflow. Online systems, such as ALEKS, Cengage's WebAssign, and even Khan Academy ...
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14answers
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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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5answers
630 views

How to get through the boring stuff?

It frequently happens that there's some material I have to cover which is, frankly, boring. The subject itself may be boring, or it may be the particular exercises, but in any case I have to get ...
14
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4answers
518 views

Is there research for or against such an approach in teaching calculus?

Copying from Calculus Made Easy by Silvanus Thompson (2nd ed., 1914): CHAPTER I:TO DELIVER YOU FROM THE PRELIMINARY TERRORS The preliminary terror, which chokes off most fifth-form boys from ...
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5answers
469 views

Hands on activities for a college history of mathematics course

I will be teaching a course in history of mathematics to juniors/seniors who are math and math education majors, many future school teachers. It should include highlights from antiquity to early 19-th ...
12
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7answers
923 views

Name the heuristic: exploiting the legitimacy of the questioner

As a child, I made frequent use of a particular 'trick' in order to make short work of many different problems. The general form is to be presented a question which wants a definite (numerical) answer,...
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0answers
302 views

Books on meta-cognition that would be relevant for those involved in mathematics?

In 1992 Schoenfeld wrote an excellent "review" of (among other things) metacognition as it applies to mathematics: whether from the perspective of a student, or a teacher. Metacognition, as quoted ...
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1answer
585 views

Ideological Teaching in Logic Courses

Logic and its sub-fields are closely related to philosophy. There is an undeniable mutual interaction between one's philosophical point of view and his/her approach in teaching mathematical logic. In ...
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4answers
1k views

Topics that should be in an undergraduate math programme

According to your experience as students and professors, what are (and why) the courses that should be part of a math undergraduate degree, but that are missing in most institutions?
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1answer
440 views

The “rearranging” approach to teaching logarithms

Consider the following way to teach division: Division works this way: any product equation $xy = z$ can be rewritten as a quotient equation $x = \frac{z}{y}$. Just move the numbers in that way. ...
9
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5answers
461 views

What to do if there is a disagreement on fundamentals, e.g. axioms or inference rules?

Sometimes it happens that a person doesn't want to accept your argument, because he claims not all the inferences are valid. There's a famous example of Lewis Carroll, namely What the Tortoise Said to ...
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4answers
839 views

Complex analysis (Applied versus pure)

I am studying Electrical Engineering and I want to specialize in signal processing. However, I have to study complex analysis first (I am an undergraduate, so I lack some terminology). In your opinion:...
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4answers
473 views

Are puzzles a good way to interest pre-college students?

Nothing more quickly disspitates the myth that most people aren't interested in math than hitting them with a good puzzle and watching the instinctive human urge to solve it get to work. To be fair, ...
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1answer
283 views

How is math taught in elementry school in Finland?

I read on the internet that Finland has the best education system in the world at that in Finland, students are taught to love mistakes and that's how they learn and become smarter. I could not find ...
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5answers
924 views

Rigorous proofs vs. illustrative examples

No one would argue against the idea/ observation that proofs are very important in mathematics. Some people are trying to make their notations on a blackboard during a lecture as consistent as ...
12
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4answers
366 views

How do I get them to appreciate learning a new way of doing that thing?

A typical student mistake You see this: $$\frac{15}{4\sqrt{15}}=\frac{15}{4\sqrt{15}}\cdot\frac{\sqrt{15}}{\sqrt{15}}=\frac{15\sqrt{15}}{4\cdot15}=\frac{15\sqrt{15}}{120}.$$ You can see that the ...
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3answers
767 views

What is the pedagogical justification and history for using mnemonics to teach order of operations?

There was previously a question/rant here on MESE about why so many are still using the PEMDAS/BODMAS/BIDMAS/BEDMAS mnemonics to teach order of operations. The question was deleted (still viewable by ...
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4answers
294 views

Teaching mathematics and its charms to non-mathematicians

I am teaching English in Japan and I have a student who speaks English well, and to keep up his level, in our weekly lessons would like to learn some subjects related to my degree in mathematics. I ...
8
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3answers
2k views

How to Teach Averages (Arithmetic Mean) to a Teenager?

Suppose you had to teach averages to a teenager. For arguments sake let the question be; Find the mean of $2, 3, 4, 7$ Of course the simple answer is $\frac{2+3+4+7}{4}=4$ but in my experience the ...
8
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2answers
152 views

In introductory statistics hypothesis testing, why not always use P-values?

A test statistic is a measure of significance of a data set with respect to a claim. My statistics textbook is insistent that the students should be able to interpret the test statistic in two ...
8
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3answers
434 views

Advantages of using script letters

In which areas of mathematics is it traditional to use script letters, such as $\mathcal{ABCDEFG}$, and is there a pedagogical advantage to doing so?
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5answers
688 views

What are some common fallacies students make when they learn $X$ concept?

What are some common mistakes students often make, which may seem logical at first? I'm a student myself, but I'm curious of what some of the most frequent mistakes which happens. I'm thinking of ...
6
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1answer
315 views

Who is E. Kim Nebeuts?

I just learned the name E. Kim Nebeuts from the quote at the beginning of Joseph O'Rourke's answer to this question. Curious, I google searched. All I saw on the first 2 pages of results was things ...
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0answers
176 views

Mathematics Self-Efficacy Questionnaire

Good Day! I need help in finding a free validated and reliable tool in assessing (elementary or high school) students' Mathematics Self-Efficacy.
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3answers
453 views

Mathematical difficulty

There exist a large number of reasons why "mathematics is difficult". If one exclude "subjective reasons" such as: "math anxiety, math fear,..." and education factors ...
3
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1answer
127 views

Focusing on definitions for understanding in secondary education

I am a teaching assistant at a school. My job is mostly to help them solve problems given by their teachers. Students are at high school level. I assume the curriculum In Brazil is similar to the one ...
3
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2answers
194 views

How to teach mathematically about Fourier analysis and synthesis? [duplicate]

I have recently started teaching. It gets totally blank in front of the big crowd. Now, I am quite confused about how to start teaching the Fourier transform and Fourier series chapter. I want ...
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0answers
188 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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3answers
412 views

Could students learn a lot more from school if they're only taught number theory until way later?

According to https://www.inc.com/bill-murphy-jr/science-says-were-sending-our-kids-to-school-much-too-early-and-that-can-hurt-th.html, when students get taught a concept when they're so young, they're ...

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