All Questions
3,559
questions
1
vote
1
answer
83
views
Best Free Direction Field Plotter?
Can you recommend one for a first or second year calculus course?
Ideally the website that can plot direction fields:
is free
is 100% WYSIWYG (does not require any coding or markup or anything of the ...
- 564
3
votes
3
answers
155
views
Relearning math after long COVID using AoPS or developmental math textbooks?
This is a little bit of a niche topic.
I've dealt with a pretty bad dose of long COVID that has caused some serious gaps in my mathematics (basically causing terrible arithmetic skills and a really ...
- 369
0
votes
2
answers
176
views
Example of a phenomenon from real life where there is a limit going to infinity
I haven't been able to find examples in real life where we have a function or sequence such that the limit goes to infinity when the independent variable goes to infinity. The only one so far is ...
- 121
13
votes
9
answers
1k
views
Is it meaningful to add a number to itself a fractional number of times?
(Migrated from the math stack exchange, where I received an apt-seeming suggestion to pose the question here, at the math-educators stack exchange)
I introduce my young kids to basic math concepts in ...
- 233
4
votes
1
answer
218
views
How does learning math differ from learning second foreign languages (L2)?
Peer-reviewed publications analogize learning math to learning a L2. But what are the DisAnalogies and CounterArguments? How can you distinguish learning math from learning L2?
Luciana Oliveira, ...
- 351
1
vote
2
answers
211
views
A high school level proof that $a/b > 0$ [closed]
Is there a high school level proof of the following?
If $a,b > 0$ then $a/b > 0.$
- 301
11
votes
3
answers
1k
views
Arithmetic books for adults
I'm trying to learn arithmetic from scratch again. Even though I can use it, I'm not sure if I can teach it to someone and I believe if you can't teach something properly, there might be loopholes in ...
- 301
0
votes
1
answer
191
views
Which are the most used Greek letters in math textbooks?
I am looking for a list of the most frequent Greek letters used in high school and college textbooks or some other corpora. I've realized my students don't know Greek letters and I would like to teach ...
- 1,482
8
votes
4
answers
272
views
Should one include the unit in the variable? E.g. should one write $x^\circ = 30^\circ$ or $x = 30^\circ$?
I sometimes come across equations like
$x^\circ = 180^\circ - \frac{360^\circ}{n}$
where I would write
$x = 180^\circ - \frac{360^\circ}{n}$,
or like
$3 \text{ cm} + x \text{ cm} = 5 \text{ cm}$
where ...
- 1,811
11
votes
6
answers
4k
views
Is patching up a student's poor solution better than providing a good solution?
A student benefits from their attempt at a solution or proof being checked by the teacher. My own view is that, if the student's work is poor, it is best just to provide a model solution or proof in ...
- 239
4
votes
2
answers
356
views
Proof by Contradiction vs. Proof of Negation
In constructive mathematics we make a distinction between "proof of negation" and "proof by contradiction". You can read a great account of the difference in this blog post of ...
- 23.2k
2
votes
2
answers
196
views
How to introduce the use of Greek letters in high school?
I am looking for any hints or experience reports or materials/potential difficulties about how to introduce the use of Greek letters in high school Math/Physics.
- 1,482
3
votes
3
answers
318
views
What is the maximum value of the sum of the digits of the sum of the digits of a three-digit number?
The following is an elementary-level Math Kangaroo multiple choice question:
What is the maximum value of the sum of the digits of the sum of the digits of a three-digit number?
A. 9
B. 10
C. 11
D....
- 39
25
votes
6
answers
4k
views
Students confusing "object types" in introductory proofs class
In my intro to proofs (and discrete mathematics) class, I see a common mistake where students make nonsensical statements because, for lack of a better term, they confuse the types of the mathematical ...
- 361
12
votes
7
answers
1k
views
Introductory Books easier than Dover
I'm looking to books introducing different topics of math with fun for my son, to give him a taste of different areas.
My son roughly understands A-level topics until single variable calculus (of ...
- 665
0
votes
1
answer
107
views
Where can I find a summary of typical material (e.g., mathematics) taught in US elementaries and high schools?
The reasons for my question are complicated but basically I need information about different subjects, mostly languages (Eng, Spa, Fre), math, and sciences, as taught in different grades in elementary/...
- 11
1
vote
0
answers
108
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Math curricula\programs or any experience using "The Road to Reality" as the\a primary textbook
Primarily a reference request, collaborator search-tips requests, and question-improvement request (including improveent by deletion and re-posting to more appropriate stack, meta, wiki, etc). Rank ...
28
votes
6
answers
2k
views
Calculus problems arising from real research problems
I am visiting my in-laws for the holidays. My sister in law is a statistician. She asked me to take a stab at a calculus problem which was coming up in her research. The Lambert $W_0$ function is ...
- 23.2k
4
votes
1
answer
149
views
About instructor's manual in math textbooks: principles, design, uses and impact
It is common that school math textbooks are supplemented with instructor's materials (answers, hints and guidelines).
Are there scientific studies on how instructor's materials impact math teaching?
...
- 1,482
8
votes
3
answers
2k
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Problem set recommendations for a student who has taken classes through Calc III, but has very weak fundamentals
I know an undergraduate who just finished calc III, and really struggled with it. However, it seems like a lot of the issues are coming from skills which should have been established during algebra, ...
- 211
-2
votes
1
answer
115
views
On doing scientific research [closed]
What I want to ask is: can I use the results of others when doing scientific research, whether it is math, physics or other science, without trying to prove them myself or try to verify them? For ...
- 159
-1
votes
1
answer
166
views
Learning, exams, math degree
I have only passed the one fourth of my courses so far, which means like one year of the maths undergraduate studies. I live in a different place from where the university i study at is and try to ...
- 159
6
votes
11
answers
786
views
How to explain to a ~$12-16$ year-old student who is weak at maths, that $\ 38 \times 27 \times 14 = 27 \times 14 \times 38$?
How to explain to a ~$12-16$ year-old student who is weak at maths, that $\ 38 \times 27 \times 14 = 27 \times 14 \times 38,\ $ and that $\ 3.4 \times 10^{-6} \times 2.1 \times 10^{-5} = 3.4\times 2.1 ...
- 904
14
votes
4
answers
428
views
Pedagogical insights to be gleaned from AI attempts to ‘learn’ mathematics
Some ChatGPT answers have been posted on (and removed from) MathOverflow, and there was a resulting MMO discussion.
In that discussion, @darijgrinberg said:
When I tell it about its errors, it "...
- 906
0
votes
1
answer
82
views
Suggestion for IB program Analysis and Approaches SL book?
What is the most suitable book for the IB program Analysis and Approaches SL for a student with significant weaknesses?
I had suggested the book from HAESE Mathematics yet he finds it particularly ...
2
votes
2
answers
139
views
Suggestions for Virtual Blackboard?
From time to time I need to teach mathematics to my students remotely. I would like to approximate writing on a blackboard together.
The subjects I teach are geometry and pre-calculus. So I would like ...
5
votes
0
answers
79
views
English version of the "Spécialité Mathématiques" French baccalaureate course (for a Ukrainian refugee)?
The highschool where I'm teaching welcomes a Ukrainian refugee who is in "classe Terminale" (ultimate highschool grade in France).
The math teacher who has this student in charge is not that ...
- 231
5
votes
2
answers
245
views
How to teach the concept of probability distribution?
I observed that my students do not understand what a probability distribution is.
We do not treat probability axiomatically on the course, so the required level of understanding is knowing all the ...
- 5,940
1
vote
3
answers
179
views
Where to learn axiomatic geometry from Hilbert's axioms?
I have found that math is relative easy for me to study but I have problems in geometry. I often omit some obvious steps as I think the problem visually but not from axioms. What would help me for ...
- 13
4
votes
1
answer
80
views
Research Into Self-Learning at Undergraduate Level and Above
My motivation for this question is personal. I'm a software engineer and I study mathematical logic as a hobby. Subjectively, it feels like I make the most progress after asking a question on the Math ...
- 271
7
votes
9
answers
6k
views
When did math start to be a hated subject in schools and universities?
Mathematics is currently considered one of the most hated school subjects, (at least in Brazil it is but I think it is a worldwide and cultural phenomenon.) My question is when did this start to ...
- 1,482
1
vote
3
answers
336
views
What are some examples of mathematical errors in computer algebra systems (CAS)?
Computer algebra software is easily and freely available for students nowadays but they still have mathematical errors. For instance, ask them to solve the simple equation $a x - b = 0$ for $x$. The ...
- 1,482
-2
votes
1
answer
182
views
Why do we use polysemy?
From Polysemy - Wikipedia:
Polysemy (/pəˈlɪsɪmi/ or /ˈpɒlɪˌsiːmi/; from Ancient Greek πολύ- (polý-) 'many', and σῆμα (sêma) 'sign') is the capacity for a sign (e.g. a symbol, a morpheme, a word, or a ...
- 1,482
1
vote
0
answers
116
views
Quality of a solution in mathematics
How can you determine a quality of a solution for a mathematics problem in general ?
If you try to explain too much then solution becomes bit longer and it takes time to go through causing less ...
- 701
4
votes
0
answers
191
views
When dealing with sequences, should we teach students to start at 0 or 1?
The reason I prefer starting at 0 is due to a computer science background and also, I think it helps to start at 0 because there are certain reasons that demand it (in particular, combinatorics) and I ...
- 835
5
votes
4
answers
2k
views
Point Deductions - Exams and Quizzes
With regard to an undergraduate statistics course, I am developing a standardized list of point deductions with the TAs (doctoral students) so that graders are consistent in what they are taking off ...
- 161
6
votes
0
answers
151
views
Online math quiz: students make short video explaining solution
I am teaching high school math. My students are generally hardworking and competent. Class sizes are about 35.
We were recently forced online due to the pandemic, and I have been searching for a way ...
- 619
1
vote
0
answers
133
views
What is the text for "the other second-term course in analysis at MIT?"
My question comes from first few paragraphs of preface of "Analysis on Manifolds" by James R. Munkres, as excerpted below:
A year-long course in real analysis is an essential part of the
...
- 11
3
votes
6
answers
991
views
Is this motivation for the concept of a limit a good one?
tldr: There is a simple intuitive definition of a limit for monotone sequences, and I suggest that it can be used to motivate the (more complicated) standard definition. I am asking for feedback on my ...
- 425
6
votes
0
answers
68
views
Potential topics for a university level mathematical thinking module
Social science training typically involves statistics as equivalent to "quantitative methods", particularly statistical modelling but also some material about data quality and exploratory ...
- 161
10
votes
1
answer
168
views
How to explain the concept "Without loss of generality" (through examples)?
This is not a precise question. I am curious to know how do you present to your students the (imprecise) concept of "without loss of generality", and how to use it correctly/incorrectly.
I ...
- 425
7
votes
3
answers
203
views
Encouraging students to see value in things that can't be measured
It's very tempting for a student who is overly excited about mathematics to discount intellectual work in other fields, particularly the humanities, where the nature of knowledge and knowledge ...
- 3,858
2
votes
0
answers
128
views
Split in pedagogy of propositional logic
In some sources where I read about propositional logic, it is shown that the propositions come with a truth value baked into the sentence. In other books, it is said that the truth value a proposition ...
5
votes
8
answers
9k
views
What do you do in order to drag out lectures?
I posted earlier about how I was surprised that a typical Calculus 1 course that meets 3-4 hours each week for 15 weeks only barely manages to reach the fundamental theorem by the end of the course. ...
- 105
2
votes
1
answer
503
views
Help needed to find 7th & 8th grade completed math samples
I am trying to find samples of completed homework, class work and tests for 7th and 8th grade math in the US. I can find a million blank workbooks but not copies that students have completed with ...
- 29
1
vote
1
answer
750
views
Why can't students master math simply by passive reading?
Yearly, at least one student emails me this question, after wholly relying on passive reading then failing the exam. They successfully remember and can regurgitate everything from the textbook and ...
- 351
0
votes
3
answers
419
views
To improve in Math, why precisely must most students slog at exercises, unlike driving that AI still can't automate?
Too many parents ask why students need to buckle to problems to succeed at math — like end of chapter questions in textbooks. Bewildered, they analogize to lasting skills that — after acquisition — ...
- 351
4
votes
1
answer
177
views
Why is there variation in the meaning of "Standard form" for a quadratic?
I'm teaching this year out of "Precalculus with limits" by Ron Larson [7th ed], and the following expression appears in the unit introducing polynomial functions:
$f(x)=a{(x-h)}^2+k$
He ...
- 409
6
votes
3
answers
1k
views
Geometry in the Community College Curriculum
As many Americans know, the “traditional” high school sequence is:
Algebra 1
Geometry
Algebra 2
PreCalculus
Calculus
For those who take developmental education at the community college level, it ...
- 369
3
votes
2
answers
1k
views
What is a good pacing for a Calculus 1 undergraduate course?
I am going to teach a Calculus 1 course next semester, and I have 15 weeks for the course material. The class meets MWF for 50 minutes each. I have taught this class before using the same syllabus, ...
- 105