All Questions
3,692
questions
1
vote
0
answers
73
views
What are the books followed by the Chinese imo trainees?
We all know that china has been very dominant in the mathematical olympiads. I was very curious to know what are the books and problem sets these trainees use to tease such level of mathematical ...
- 193
-3
votes
1
answer
150
views
Are the standard of questions provided in reputed institutions like MIT, Stanford, Oxford, etc., as good as the problems of IMO?
I did not win the International Mathematics Olympiad, so I was very curious to know the standard of questions asked in the graduate and undergraduate courses of maths and computer science in ...
- 193
4
votes
1
answer
148
views
Strategies for Designing Challenging Yet Feasible Quiz Problems for Upper-Level Math Courses
In the past semester, I taught two 7-week courses: discrete math and algorithms designs (which is essentially still math) for undergraduate CS students. I implemented weekly 25-minute quizzes ...
- 579
8
votes
1
answer
159
views
ADHD superfocus and motivation for mathematics
I am almost surely ADHD, although undiagnosed. I have colleagues in mathematics who also are, but diagnosed. I have an extremely talented and successful graduate student who is (diagnosed) ADHD.
It is ...
- 6,133
-2
votes
0
answers
49
views
intersting poblems about central and and inscribed angles in a circle [closed]
I am looking for interesting problems and exercises about central and inscribed angles in a circle, preferably questions that involve applications.
- 1,931
4
votes
1
answer
288
views
Problem of the Week for College Students
Trinity's Problem of the Week and Purdue's Problem of the Week were both weekly problems that were excellent for college math clubs to tangle with at their weekly meetings. However, both of them are ...
- 49
6
votes
7
answers
1k
views
Special topics for introductory probability
I am helping to design a low-level college course whose purpose is to teach critical thinking, logic, finance and probability. I have been tasked with developing the probability section. I am ...
- 163
7
votes
2
answers
3k
views
Any examples of calculus sequence that deemphasizes calculation tricks?
I'm considering creating a series of classes that explore deeper ideas in calculus without overemphasizing the various computational tricks used in integration and differentiation.
My vision is ...
- 261
2
votes
0
answers
150
views
Which Books Comprised The Houghton Mifflin Modern Mathematics Series
Around the 1960s a collection of math books by authors such as Mary P. Dolciani, William Wooton, Edwin F. Beckenbach, Ray C. Jurgensen etc. started to appear which were part of a series of books ...
- 173
1
vote
0
answers
96
views
"Tools" (literarily) for solving linear or quadratic equations
Since a few weeks, I teach as a tutor (not from that school) a support course in a German 9/10 class. I quickly noticed a horrible lack of basics. (Partly based on just different names - I had to ...
- 111
7
votes
6
answers
318
views
Loaning students calculators during exams
Context: I am an associate professor at a small liberal arts institution in the US.
I find in my introductory business math course that students sometimes fail to buy a calculator for the course, ...
- 1,419
7
votes
1
answer
632
views
Bridging the gap between students' intuitive problem-solving abilities and expressing ideas through formal writing
Seeking guidance on how to assist students who possess a solid grasp of problem-solving concepts, allowing them to intuitively arrive at solutions, yet encounter difficulties when it comes to ...
- 71
3
votes
1
answer
214
views
What age group is this puzzle appropriate for?
I have created the following simple tiling puzzle for children.
The puzzle consists of 9 tiles shown below (4 pieces of type A, 4 pieces of type B and 1 piece of type C):
The goal of the puzzle is to ...
3
votes
2
answers
2k
views
Where can I find new types of problems regarding graduate level mathematics?
Though not an undergraduate student , I just wanted to know where can I find hard new types of problems regarding the problems in graduate level mathematics. As per my information , standard books ...
- 193
9
votes
5
answers
2k
views
Requesting a Polynomial System of Equations
I am teaching a course in commutative algebra, and it includes a project where the students research on a particular topic, solve a small problem and present it to the class.
I usually give my ...
2
votes
1
answer
164
views
Help finding a YouTube channel for Linear Algebra
I remember watching a youtube playlist on a video about equation of a plane and about vectors in 3D. The video was fully animated in 3D and had good sound effects too. I feel like it had a clock ...
2
votes
2
answers
434
views
How to motivate ‘unless’ = ‘if not’, with etymology?
My undergrads still reckon Nelson Lande’s 2 motivations for ‘unless’ = ‘if not’ (below) too abstract, formalistic! They crave simpler intuition! Thus I want to proffer a 3rd motivation, this time with ...
-1
votes
1
answer
40
views
Ratio in Fractional Form [closed]
I have 3 puppies and 2 piglets.
Can you that ratio be written in this fractional form 5/2?
If yes, how would you describe this ratio as 5/2?
- 7
6
votes
3
answers
251
views
What to do with "wild goose chase" or "quantum leap"-types of incorrect solutions when you ask students to prove/show something?
So in an advanced mathematics course for engineers, there are often problems of the type:
Prove claim A.
Given equation A, show that you can obtain equation Z.
I am frequently faced with a problem ...
- 737
12
votes
11
answers
4k
views
Does a proof by induction have to explicitly refer to the principle of mathematical induction?
I teach high school math.
Some of my colleagues insist that a proof by induction should explicitly refer to the principle of mathematical induction, i.e. it must include the words "by the ...
- 821
0
votes
5
answers
264
views
Are logic textbooks wrong to teach ‘unless’ = ‘or’? How to motivate?
Most times in English, it’s ungrammatic to swap ‘unless’ with ‘or’! Aren’t the textbooks below wrong?
My undergrads can master Truth Tables, but still fail to intuit why ‘unless’ = ‘or’. How to ...
10
votes
12
answers
3k
views
Fixing wrong ideas about coefficients (e.g. subtract 3 from 3x to isolate x)
I tutor a student (9th grade, United States) who is in an algebra class. She consistently makes mistakes when dealing with coefficients.
The most common one is attempting to subtract away a ...
- 363
1
vote
2
answers
233
views
What will happen if someone doesn’t make it to the IMO team?
I am highly interested in mathematics, and solving Olympiad maths problems has been a type of hobby for me. But due to my age, I will never be able to give the olympiads a go again. I want to know ...
- 193
1
vote
1
answer
2k
views
How does a math Olympian fare in undergraduate maths courses?
I am a maths enthusiast and have been exposed to maths olympiad problems for some time. I wanted to know how does a math Olympian do in undergraduate courses of mathematics, statistics or computer ...
- 193
1
vote
1
answer
105
views
Speed math appropriate for middle-school students
There are many "rules" for speed arithmetic.
List of some reference links showing speed methods or rules:
https://ofpad.com/multiplication-tricks-for-mental-math/
https://ofpad.com/mental-...
- 111
-4
votes
2
answers
207
views
Order of operations pemdas
Why was the order of operations established in mathematics with multiplication taking precedence over addition, as dictated by the PEMDAS rule? What historical or practical factors influenced this ...
- 1,931
5
votes
4
answers
2k
views
How can we explain intuitively the convergence and divergence of these two series?
It is known that $\displaystyle\sum_1^{\infty} \frac{1}{n^{1.000001}}$ converges while $\displaystyle\sum_{n\text{ is a prime number}}\frac{1}{n}$ diverges. Though we can logically prove these results,...
- 4,255
8
votes
3
answers
1k
views
Is there a standard convention for interpreting ambiguous absolute value expressions?
Consider the expression
$$|x + 2|x + 3|x + 4|.$$
One way to interpret this is that there are two products being added together:
$$|x+2|x \hspace{1cm} + \hspace{1cm} 3|x+4|$$
But you could also ...
- 6,342
-4
votes
1
answer
105
views
PROBABILITY QUESTION [closed]
How to solve this probability question?f a, b, and c are in the range [0, 1], what is the probability that the quadratic equation ax^2 + bx + c has real solutions? justify your answer!
This question ...
- 1,931
3
votes
11
answers
3k
views
Importance of complex numbers knowledge in real roots
Many students question the importance of complex numbers in real life. We can find many important applications of imaginary numbers in Engineering field and physics. This question is not related to ...
- 955
1
vote
1
answer
90
views
Summer or Semester Programs which bridge to Graduate Mathematics
A few years back I had a student attend the MASS semester at Penn State. It was a fantastic experience for my student and it certainly helped him find a place in graduate school and I would wager it ...
- 10.7k
6
votes
11
answers
5k
views
How can I teach intuition why ‘If P then Q’ and ‘P only if Q’ mean the same, to first year undergraduates?
In every of my ten years as course instructor introducing first year undergraduates to proofs, I always project this quotation on the lecture screen, then dictate the whole caboodle word for word! But ...
- 89
2
votes
3
answers
166
views
Engaging Mathematical Riddles for Classroom Enrichment: examples and impact studies references
Hello fellow educators and math enthusiasts,
I am on the hunt for entertaining and thought-provoking mathematical riddles suitable for a classroom setting. My objective is to find riddles that not ...
- 1,931
6
votes
3
answers
153
views
Game project using linear algebra
Throughout this year, I have been in charge of a linear algebra course aimed at engineering school. In this course, I asked my students to work on a final project involving finding a winning strategy ...
- 61
9
votes
6
answers
1k
views
Intuition for order of operations in compound transformations
This is a close cousin of the previous question asked here about transformations inside and outside a function and how they switch things around. I think some of the perspectives there will help here, ...
1
vote
2
answers
80
views
Online Probability Simulation for Compound Events
I'm teaching Grade 9 Probability. We need to compare Experiment Probabilities (Relative Frequencies) with Theoretical Probabilities for Simple and Compound Events.
I want to come up with and Online ...
- 957
4
votes
4
answers
330
views
Educational resources commonly address slant asymptotes. Why not general polynomial asymptotes?
Back in 2018, I wrote a post about asymptotes of rational functions in which I addressed not only horizontal and slant/oblique asymptotes, but also the general case of "polynomial asymptotes.&...
- 6,342
3
votes
0
answers
70
views
Examples of Financial Institutions that Compute Interest Atypically?
Are there examples of financial institutions that compound their interest more frequently than once-a-month? Are there examples of financial institutions that consider continually compounded interest ...
- 4,606
0
votes
1
answer
105
views
Chinese and Japanese most important high school textbooks
I would like to know the best high school math books from Japan and China. Can you suggest some books or free resources? I would like to compare the different approach betweeen China and Japan and ...
- 101
13
votes
18
answers
6k
views
What are some "deep" questions to explore in elementary school math?
My first grader is very advanced in math. Rather than doing more and more math and making school math even more boring for him, I recently decided to start going "deeper" rather than "...
- 373
1
vote
1
answer
109
views
Idea of using LLMs to help communicate ideas in math
What do you guys think about the ideas presented in this short text: https://github.com/yougetyourmanwww/AI-for-math/blob/main/AI.md
The text is about how LLMs like chatGPT can be used for when doing ...
- 19
9
votes
8
answers
4k
views
Why do most Analysis textbooks overlook, and fail to teach delta-epsilon proofs, using the K-ε principle?
When writing $\delta$-$\varepsilon$ proofs, it's common that the ''natural'' choice of $\delta$ leads to the final inequality in the form, say, $|\ldots| < \varepsilon+\varepsilon+\varepsilon$ ...
- 139
8
votes
2
answers
150
views
Cognitive activation vs cognitive load reduction
During my teaching training in Germany and in many professional development sessions, there has been repeated emphasis on the importance of cognitive activation and challenging tasks for effective ...
- 1,128
13
votes
5
answers
4k
views
Role of human math teachers in the century of AI learning tools
In view of recent developments of AI-based adaptive math learning systems like Squirrel, Aleks, Knewton Alta, or Math Academy:
Does a human math teacher play any reasonable role, or will those systems ...
- 1,128
2
votes
1
answer
354
views
Feedback from AI based learning to human based learning in math?
There are several AI based adaptive learning environments out there like Squirrel, KNewton or MathAcademy.
Are there any studies which try to extract from the (big) data of those learning systems ...
- 1,128
1
vote
3
answers
498
views
Basic skill requirement suspension
Oregon appears to have suspended the "basic skills" requirement for graduation; see this. What will be the effect of this on the mathematical proficiency of the graduating class?
Follow-up ...
- 2,102
4
votes
2
answers
135
views
What are some decent apps for Hasse diagrams?
What options are out there for software that supports interactively constructing, editing, and manipulating Hasse diagrams? Their semantics is significantly constrained, so garden-variety Let’s-draw-...
- 141
2
votes
4
answers
385
views
How can one lone picture prove the Triangle Inequality, $|x−y|≤|x|+|y|$, $|x|−|y|≤|x−y|$, and the Reverse Triangle Inequality?
I always showcase separate pictures of Triangle Inequality, and Reverse, to 16-years-old students in 1st class. I reshow pictures in 2nd class. I preachify
Please remember these 4 inequalities. ...
- 139
1
vote
1
answer
196
views
Identifying Trigonometrical proofs
How can we identify trigonometrical proofs from geometrical proofs, do we have purely trigonometrical proof of Pythagoras theorem as claimed by two high school students ? https://www....
- 955
3
votes
1
answer
106
views
Alternative to Quizlet live that supports latex formulas
With Quizlet Live you can play a flashcard game in classroom, where teams compete against each other. Since Quizlet doesn't seem to support rendering latex formulas, I am looking for a alternative ...
- 1,128