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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6
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1answer
172 views

Easy and good book on combinatorial problems

I am searching for a book on combinatorics and/or mathematical puzzles for very beginners in easy English. The book should not contain detail mathematical expressions, will contain easy understanding ...
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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 ...
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3answers
275 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 $f^{-1}(x)$...
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4answers
416 views

Surrounding a subject and strangling it to death versus concentrating on the main point

Standard calculus textbooks begin by introducing limits, including limits of a fraction as the numerator and denominator approach $0,$ limits of a fraction as the numerator and denominator approach $\...
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3answers
163 views

Advice for Community College Interview Statistics Demonstration

In a few weeks i'll be interviewing at a community college in California for a tenured Mathematics position. They've asked me to present the following in only 12 minutes. I'd appreciate any ...
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0answers
100 views

Research on how to teach math to children - what proven approaches are there to teaching math effectively? [closed]

I posted a related question on the Math.SE, but was directed here where I'm asking an similar but different question. I've been tasked with helping to redesign a math curriculum for an enrichment ...
4
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0answers
175 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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0answers
197 views

Introduction of the power set as a collection of *labels* or *names* for subsets

The way that naïve set theory is usually presented in undergraduate education is via very concrete examples of sets, often involving non-mathematical elements. When power sets are treated, having a ...
12
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2answers
185 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: "...
8
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4answers
683 views

May we permit identities to be established by equivalent equations?

A trigonometry text like Sullivan's Algebra & Trigonometry often has a prohibition like this (Sec. 7.3): WARNING: Be careful not to handle identities to be established as if they were ...
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3answers
2k views

Pedagogy, mathematics and Dieudonné's Foundations of Modern Analysis

I've heard from a friend of mine that Dieudonné's Foundations of Modern Analysis is "painful reading" and "a little outdated"; however, my teacher actually suggested it to me, describing it as a "...
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9answers
7k views

Can mathematics be learned by ONLY solving problems?

Here is the concept: Student is presented with a problem. He/she may not even understand what is being asked, or may attempt. Students reads a solution to the problem. In it there may be ...
13
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7answers
1k views

Problem “seeing” the perimeter of a figure

I was helping a home-schooled student with her homework when we came upon several images of figures that we were supposed to find the perimeter of. In several of the figures, some of the lengths were ...
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3answers
4k views

What math courses should be taught to undergrad electrical engineers: a 40 years update

I was browsing IEEE xplore the other day and found this gem called "What Mathematics Courses Should an Electrical Engineer Take? A Report on the National Study of Mathematics Requirements for ...
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3answers
360 views

What is the ULTIMATE Calculus syllabus

After such amazing answers I got here for a related question (link at the end if someone still wants to share with me their views)... Here is the concept: If you were to create the ULTIMATE Calculus ...
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9answers
2k views

Examples of Artistic Works with Mathematical Aspects

There are many examples of artistic works which have some mathematical aspects. A high school or undergraduate math teacher can use them as interesting examples in his/her teaching. e.g. In a ...
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3answers
1k views

Should I teach Laplace Transforms? How much?

My question is in the title. Let me elaborate and give some context: I'm teaching a first differential equations course, essentially for engineers, at the university. I'm developing the syllabus ...
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6answers
704 views

Too much motivation?

This is something that I felt like was difficult for me in some classes, especially lower division differential equations and linear algebra classes. I know professors want to motivate certain topics ...
2
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0answers
90 views

what is the standard subdivision or classification of calculus related rates problems?

I am working on a project where I have to group/classify calculus problems. Now with most the calculus topics, it's usually obvious how it's divided in various textbooks, but when it comes to related ...
13
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2answers
1k views

How early to start “abstract” math education, or, How to prevent smart kids from never getting exposed to math?

Everybody who is in graduate mathematics had a moment where they realized that mathematics was "their thing", and they decided to dedicate their academic career to it. I don't know of many people who ...
6
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2answers
297 views

How can I improve my problem solving/critical thinking skills and learn higher math?

I'm a rising sophomore in high school. So far, I've taken Algebra One, Two, and Geometry in school. I want to learn higher math such as precalculus/trigonometry, calculus, linear algebra, and more, so ...
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6answers
2k views

Is there any difference between teaching calculus for math and engineering students?

In our university both math and engineering students attend in the same calculus classes. There are arguments in our department about the possible influences of this approach on students. It seems ...
3
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3answers
4k views

Difference between whole numbers and decimal numbers

Clearly, whole numbers specify how many elements there are in a collection while decimal numbers specify how much of a substance there is in a lump---but only after a unit of that substance has been ...
14
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4answers
885 views

What is the right way to order the topics in a first ODEs course?

This question is long but I am asking for educated opinions on a question of math education and for this reason I'd like it not to be closed on the grounds that it invites subjective discussion. ...
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6answers
6k views

How to teach math to someone who is neither [really] willing nor able to understand it?

I'm not a teacher, I am a student. But in math, I am one of the best ones in my class so sometimes other people will ask me to explain stuff to them. And usually it works quite well: If I understood ...
9
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2answers
262 views

Explaining difference between natural numbers, integers, rationals, reals, complex numbers, Gaussian integers

I am teaching an introduction to number theory for high schoolers right now, and there seems to be quite a bit of confusion on what the difference between the natural numbers, the integers, the ...
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4answers
429 views

Calculus 3 Teaching Demonstration for Community College Teaching Position

Colleagues. In a few weeks I will be interviewed for a position at a community college. I got selected for an interview and the teaching demonstration is as follows: Assume you are teaching a ...
28
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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 ...
13
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7answers
751 views

When should we get into limits in introductory calculus courses?

All of the calculus textbooks I've used (teaching at community colleges) start with the first chapter covering limits. (Perhaps after a review chapter.) I think this order is wrong. Historically, ...
6
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2answers
189 views

How to introduce Wilson's Theorem?

What is the most motivating way to introduce Wilson’s Theorem? Why is Wilson’s theorem useful? With Fermat’s little Theorem we can say that working with residue 1 modulo prime p makes life easier ...
6
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4answers
332 views

Statistics Class Held in a Computer Lab

I'm looking into holding my basic statistics class in a computer lab in the future to avoid a lot of the by-hand computing that happens in statistics classes. For example, very few students get ...
8
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2answers
415 views

Learning math through fun rather than rote learning

Is it easier to remember something if it is expressed in a funny and/or fascinating way rather than by learning through repetitious exercises that hopefully instill the necessary understanding ? The ...
14
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4answers
495 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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2answers
219 views

How to catch students from different subjects' interest to math?

I have just started to teach Calculus to freshmans and sophomores who study non-mathematical subjects, e.g., international relations, psychology. They have to take few mathematics classes -including ...
4
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1answer
167 views

Erasing students' work - etiquette/guidelines?

What are some guidelines on erasing students' work such as on a chalkboard/whiteboard in a classroom or on paper in a private tutorial class? Usually this is for the parts of maths that involves ...
3
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3answers
451 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 ...
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3answers
593 views

Summary of the mechanism of reification

The concept of "reification" in mathematics education is interesting. Roughly, if I understand this correctly, one "reifies" processes into mathematical objects. Very recently, it occurred to me that ...
16
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3answers
344 views

How to invite humanities students to study mathematics?

This question comes from the perspective of an undergraduate math major who feels that much (although not all) of the mathematical discipline is a liberal art, rather than a science, and should be ...
35
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23answers
6k views

Imbuing a six year old with a sense of mathematical wonder

My six year old started school a few months back and he's loving it. This first year is more about social skills than anything academic and I like that approach. But we're spending some time at home ...
27
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4answers
840 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 ...
16
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10answers
4k views

Complex numbers in high school

Are complex numbers taught in high school in other countries? I am from Germany and complex numbers are next to never touched in high school with the exception of extra-curricular activities, for ...
7
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1answer
267 views

Why many people believe that: $\displaystyle c>0\implies \frac{1}{c}<0$?

I came across many people who believe the below false implication. I don't know why people believe it true in high school and middle school and also students in university level. Really I would like ...
3
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1answer
233 views

How to ask a student a question to get the answer '…integer not continuous…'

Context: a very basic level statistics package computer lab. A scatter plot is produced for one integer variable versus another integer variable. The students are asked why the points form a grid ...
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2answers
487 views

Developing mathematical stories

In a comment on a recent post, Steven Gubkin pointed out that in doing mathematics he likes to develop stories. This motivation for mathematics is perhaps familiar to many practicing mathematicians. ...
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7answers
1k views

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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4answers
649 views

Why are proofs by contradiction counterintuitive?

And how to make them intuitive? We are tasked to prove $P \implies Q$. So we assume $P$ and are trying to prove $Q$. We assume not-$Q$ ($\neg Q$) and derive a contradiction, establishing $Q$. There ...
7
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2answers
239 views

Ethics of looking at other proofs before submitting work

I am in my third year of undergraduate math, and now that classes are becoming more proof-based, many of my homework questions are proofs of relatively basic concepts that can be found with a quick ...
8
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3answers
271 views

Is proof-based exercise-oriented math course without solution an effective way to teach pure math?

In recent years I have seen several courses in pure math in the undergrad level (year 2, 3, 4) such as real analysis and topology where the entire course consists of: notes written during the lecture ...
9
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1answer
86 views

How to incorporate optional higher level mathematical content in an Engineering Maths course?

Our department teaches two very large first-year "Mathematical Methods" courses (600-ish students) to Engineering students. The syllabus is dictated by their (future) needs and covers a huge array of ...
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1answer
304 views

When are partial fractions taught? [closed]

Recently I had taken the SATs, and a question came up that involved partial fractions decomposition. $$\frac{x^2-4x+5}{x-3}$$ This is not the exact problem but a similar one. If the SAT math is ...

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