All Questions
3,686
questions
1
vote
2
answers
263
views
Responding to students' questions that aren't directly relevant to their exams
What would you suggest as the best way to deal with students' questions that seem irrelevant to their upcoming exams?
When I was studying for my university-entrance exam, I came across a couple of ...
- 955
9
votes
0
answers
143
views
Course materials for developing a mathematical theory from "natural questions to ask"
Educational setting.
I'm teaching math courses - typically consisting of lectures, weekly homework sheets, and an exercise class where the homework questions are discussed - for undergraduate and ...
- 1,695
0
votes
2
answers
319
views
How to explain square meters?
How can we explain to students these ideas?
A square with 4 sides measuring 25 cm each does not have an area of 1 square meter.
A shape which is not a square can have an area of 1 square meter.
Is “...
0
votes
1
answer
238
views
Limitations of applying the factor theorem
Here are three situations in which students might try to apply the factor theorem.
Proving that $x + 1$ is a factor of the polynomial $x^3 + x + 2$ can be done using the factor theorem by showing ...
- 955
7
votes
5
answers
2k
views
Should I really just "shut up and calculate"? On learning at a good pace without sacrificing rigour
This question is about getting realistic expectations for how a university student actually does and should learn maths. I'm becoming increasingly suspicious that my approach is detrimental, but I don'...
- 458
9
votes
5
answers
1k
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Models for spherical geometry
Context: I am an associate professor at a small liberal arts institution in the US.
I am currently preparing to teach geometry this fall. Our course is mostly focused on Euclidean geometry (it's ...
- 1,409
1
vote
0
answers
70
views
If a student earns a non-ABET accredited engineering degree, when can they take the FE or PE exam?
I just recently had a student (U.S. university) ask "How long would I have to wait until I could be eligible to take the FE or PE exam if I earned a non-ABET accredited engineering degree?" ...
- 71
1
vote
1
answer
215
views
A Question about Answer Keys
I am a HS math teacher and just started a job that adopted a new curriculum at the last minute. It gave us the tasks but did not provide any answer keys. Of course, I know how to work through the math ...
6
votes
4
answers
640
views
What mathematical topics are important for succeeding in an undergrad PDE course?
I am a student helping to develop a remedial course for other students who have recently failed the undergraduate PDE course at our university. The topics are provided from the syllabus in the ...
- 71
0
votes
1
answer
171
views
What would constitute as a good justification of why a divergent limit is divergence for highschool teaching?
For example, consider $\lim_{x \to -\infty} \frac{x}{e^x}$, what would constitute as a good justification that the limit diverges too infinity?
It's pretty easy to justify convergent limits ...
7
votes
3
answers
2k
views
What's it called when multiple concepts are combined into a single problem?
A lot of students complain about "never being shown that before". What's the idea called when you test multiple concepts or one or two new ones along with some old ones in a word problem, ...
- 303
1
vote
1
answer
181
views
Are there differences between graphs, diagrams and charts?
"Can you explain the distinctions between graphs, diagrams, and charts, and provide definitions for each of these concepts? Specifically, is every graph considered a diagram? Are graphs ...
- 1,935
2
votes
1
answer
374
views
Sources on inequity in precalculus sequence
I'm trying to put together some thoughts on the importance of a strong college precalculus sequence (mainly I'm thinking College Algebra, where much of my experience is) for addressing socioeconomic ...
- 3,927
6
votes
7
answers
2k
views
How to explain that integral calculate areas?
I teach internal combustion engines theory in a technical school. I have an elementary knowledge of calculus and my students lack even this.
I want to intuitively explain them what is the pdV integral,...
4
votes
3
answers
321
views
do you know a mind-boggling/curious historical facts that will inspire and attract young people?
I am trying to compile a list of mind-boggling/curious historical facts in mathematics that will inspire and attract young people (9–11 years old) to the discipline of Mathematics. Do you have one ...
- 1,935
3
votes
0
answers
114
views
Books with Glossaries
I am seeking example math books that have a glossary.
I would especially be interested in an example that has a list of symbols,
a glossary, and an index.
I am working on a book (aimed at graduate ...
- 29.5k
5
votes
1
answer
606
views
Theory-practice order vs practice-theory
I heard that there were some studies on what is the best order for teaching math. But I cannot find any papers (probably my English is too poor to google this paper correctly).
As I heard idea was: ...
0
votes
1
answer
124
views
Pythagoras and Trigonometry sequencing
In teaching the high school curriculum Pythagoras is usually bundled with Trigonometry. They might be justified by way of proof of some sort. They are used to solve 2d and 3d geometry problems for ...
- 957
5
votes
0
answers
161
views
Is it better to teach category theory in the background of type theory than set theory?
I have been going over some applied instances of category theory in Programming, and also by a book by conceptual Mathematics by Lawvrere, and I think an issue of applying category theory to real life,...
1
vote
0
answers
84
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MathArt contest about Aesthetic Conformal Image Mapping [closed]
At the moment a MathArt contest is running about Aesthetic Conformal Image Mapping were individuals and classes can participate:
https://www.freelancer.com/contest/MathArt-Contest-Aesthetic-Conformal-...
9
votes
1
answer
143
views
Where to distribute free math ed materials for informal settings?
I am a psychologist studying mathematical thinking and learning and I have been organizing a monthly math night at a local library. Each math night consists of a short presentation followed by several ...
- 193
5
votes
1
answer
310
views
What is the dimension of $\mathbb{R}$ over $\mathbb{Q}$?
Long time ago a student asked me what the dimension of $\mathbb{R}$ over $\mathbb{Q}$ is, and I said
$$\dim_{\mathbb{Q}}\mathbb{R}=\mathfrak{c}$$
where $\mathfrak{c}$ is the cardinality of the ...
- 153
4
votes
2
answers
262
views
how to read binary numbers?
Using decimal representation for numbers,
we read 10 as ten (not as one, zero)
we read 1011 as one thousand eleven (not as one, zero, one, one digit by digit).
But using binary representation, how ...
- 1,935
1
vote
1
answer
209
views
Calculus at competitive level or Olympiad level
What are the topics of Calculus which can be useful for competitive level and the students are not exposed to it ?
- 61
26
votes
14
answers
9k
views
How to teach pure mathematics to a well-educated adult who did badly in maths at school
My partner is a PhD student in philosophy and has recently developed a keen interest in learning pure mathematics. I am doing my best to teach her (I'm a pure maths PhD student myself) and it is ...
- 361
4
votes
2
answers
377
views
What is Algebra 1 and 2 as it is in US highschool education?
I am a pre-university student who wants to help students with Algebra 1 and 2 in high school. I am curious to how the curriculum was built and what the goal of teaching both algebra 1 and 2 might be. ...
- 171
11
votes
7
answers
3k
views
How can we best motivate the study of polynomials to high-school students?
We all know how important and ubiquitous polynomials are in mathematics. However, when faced with a (not so much in love with the subject) 14-year-old asking us why they should care about these things,...
- 219
1
vote
3
answers
175
views
Whole numbers as sets vs abstracted properties of sets
I recently landed on a book written for elementary school teachers which introduced the concept of whole numbers in the following manner:
We have a set $\{\alpha, \beta, \gamma\}$. There are other ...
- 447
12
votes
8
answers
929
views
Any meaning/interpretation for $\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+\dots (= \mathrm e)$ (sum of reciprocals of factorials)?
One common way to introduce Euler's number $\mathrm e$ is $$\mathrm e = \lim_{n\to \infty} \left(1+\frac{1}{n}\right)^n,$$ where the right-hand expression has an "interest rate interpretation&...
user18187
2
votes
1
answer
349
views
Teachers passionate in mathematics
One of the greatest mathematicians Andrew Wiles once told that it is really important to give students a chance to work with passionate teachers before starting secondary education, and it is not easy ...
- 955
9
votes
6
answers
2k
views
Can this be a better way of defining subsets?
I remember my high school days where subsets were defined in the following manner:
Given two sets A and B, if every element of B is an element of A, then B is called a subset of A.
A common ...
- 447
4
votes
4
answers
305
views
Recommendations for secondary student interested in maths
As a student attending a grammar school in the UK ,I have been fortunate to have access to various opportunities to showcase my mathematical abilities. These include participating in maths challenges ...
- 41
6
votes
2
answers
360
views
Demarcated "Proof Idea"
Michael Sipser's textbook Introduction to the Theory of Computation (now 3rd ed.) includes for each major theorem, a demarcated Proof Idea of length a paragraph to more than a page, prior to ...
- 29.5k
4
votes
0
answers
170
views
What evidence is there in the literature that lessons geared towards dyslexic student help non-dyslexic students?
Dyslexic students sometimes benefit from informal analogies to things in the world which the student can see with their eyes, and/or touch with their hands.
Tentatively, we can conjecture that ...
- 183
2
votes
1
answer
110
views
Partitioning objects in combinatorics
When you come to explain dividing given n number of objects into k number of groups, is it good to describe the cases involved using an example to cover as many cases as possible in order to give ...
- 955
4
votes
0
answers
115
views
Activities that encourage students to create or evaluate mathematical notations
I'm looking for references about activities that encourage elementary school students to create or evaluate mathematical notations. do you know any?
- 1,935
34
votes
5
answers
6k
views
Why are there two inverses to exponentiation?
I'm not sure if this is more educational or more "pure math", but:
For multiplication and addition, there is exactly one inverse operation, namely division and subtraction.
For ...
- 2,689
4
votes
2
answers
369
views
Programming and computation-focused textbook for introductory linear algebra
tl;dr I am looking for references which cover introductory abstract Linear Algebra but with a programming / computational approach. The only one I found is the Jupyter guide to Linear Algebra
Long ...
- 739
6
votes
2
answers
1k
views
Topics covered in Calculus I and II (university level) that aren't covered in the AP Curriculum
I teach AP Calculus BC at my high school and we have AP Calculus AB as a pre-req for taking BC. So most of my students are coming in with a strong calculus foundation, and I can spend less time on the ...
- 2,061
4
votes
0
answers
102
views
Studies on the effects of using online platforms in teaching mathematics on students' beliefs about mathematics
Are you aware of any research examining the impact of utilizing online platforms in teaching mathematics, on students' beliefs about mathematics? To give you an example of the kind of beliefs that I ...
- 1,019
2
votes
2
answers
189
views
Are these explanations of variance and covariance intuitive?
When tutoring, I try to simplify concepts. I came up with these examples to explain the intention behind variance and covariance. Could you please help me find conceptual, pedagogical or mathematical ...
2
votes
2
answers
246
views
Should one study Laplace Transformation before Fourier Transforms?
(Im sorry if the question is out of the scope of the forum)
Hi, Im currently a Physics student. I have studied most of the Calculus. Now, according to the book Im using, there is chapter on "...
- 121
7
votes
1
answer
98
views
Joint Teaching of a First Year Engineering Maths Class
My department is considering using more than one lecturer (sequentially, not in parallel) to give lectures in our large first-year classes (e.g. 500 students doing engineering mathematics).
In other ...
- 703
0
votes
0
answers
115
views
Infinite descent method
We have plenty of examples in mathematical induction for advanced level mathematics students. Can we introduce infinite descent method as extremely opposite approach to mathematical induction and is ...
- 955
8
votes
5
answers
2k
views
Adjusting a Bonus Points System to More Equitably Benefit Struggling Students
I am a mathematics professor seeking advice on refining my grading system for future courses. I currently employ a bonus points system intended to provide a catch-up mechanism for students who may be ...
- 537
32
votes
7
answers
10k
views
Is it harmful to use the word "Cancel"?
Elsewhere, among a group of high school math teachers, I encountered a discussion of the term 'cancel'. Most (>20) people in the discussion had very strong feelings about why the term should be ...
0
votes
1
answer
140
views
‘Induction on’ vs ‘Induction with respect to’ in math
I heard one mathematician who said “induction on 𝑛” and another who said “induction with respect to 𝑛”. Do these two expressions mean exactly the same thing mathematically?
If so, then are they ...
guest
4
votes
4
answers
331
views
Good analogies for teaching error correcting codes
I'm trying to find a good real-world analogy (or even good visualization) for teaching about error correcting codes and erasure encodings. The most natural way to talk about it really is in terms of ...
- 143
19
votes
4
answers
4k
views
Why do we teach linear algebra in precalculus classes?
When I took precalculus, we learned about polynomials and how to factor them, we learned about trigonometry and lots of great and useful identities there, and we learned about matrices. They didn't ...
- 307
3
votes
0
answers
64
views
Are there any fun toy applications of representation and character theory for finite groups to physics?
Representation theory has very deep ties with physics, leading to incredibly profound and admittedly cool results such as the classification of particles in the Standard Model via mass and spin by ...
- 131