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1st time math teacher 1st test feedback appreciated

I'm not a math teacher but I've stepped into the role to assist a small private school who lost their math teacher during the holidays (I'm a mechanical engineer by trade). The course is Algebra 1 (...
Dan S's user avatar
  • 19
6 votes
3 answers
331 views

Is there any research on the impact of dismissive language (e.g., 'it's just...') in mathematics education? [closed]

I am curious about the effects of certain phrasings in educational contexts, particularly in mathematics. In fields like physiotherapy, using phrases like "it's just lifting your leg" can ...
Humberto José Bortolossi's user avatar
3 votes
2 answers
251 views

Some whiteboard program specialized for "typing" with latex support

Answers to the Previou question seem to suggest some whiteboard programs with latex support. However, my impression is that they are mostly designed for "handwriting" with some electrical ...
Keith's user avatar
  • 133
2 votes
2 answers
164 views

International mathematical olympiad-type competitions at lower levels, and if they exist, their educational usefulness?

Educators in many countries have found that preparing highly motivated students for national and international mathematical olympiads can be useful in training them in mathematical ways of thinking. ...
tell's user avatar
  • 131
5 votes
7 answers
3k views

Alternative approaches in basic mathematical operations

Sometimes awareness of alternative approaches of different origins may be helpful for students to improve their creative skills in mathematics. What would you suggest as alternative methods in basic ...
Janaka Rodrigo's user avatar
4 votes
2 answers
187 views

Infinite descent method in geometry

What are the examples we can use to explain infinite descent as an efficient method of proofs in geometry? I think one of the best may be proving medians of a triangle are concurrent by the infinite ...
Janaka Rodrigo's user avatar
7 votes
6 answers
2k views

How can we motivate that Newton's method is useful?

If you teach Newton's method for finding roots of real functions on the high school (or freshmen) level, I think some students may reason like a variant of the following: Why do I need learn such a &...
Julia's user avatar
  • 1,275
5 votes
4 answers
275 views

Are some natural languages better for expressing mathematical concepts than others?

I don't know if this is the best stack exchange for this question, but I couldn't think of a better one. Please migrate it to an appropriate stack exchange, if this one is not appropriate. Anyway, my ...
user107952's user avatar
0 votes
0 answers
91 views

Looking for resources about visualizing in mathematics

I have learned some useful tools/books to visualize some MATH concepts: Visual Group Theory (MAA Problem Book Series) 1st Edition. The paired website with this book is GroupExplorer Visual Complex ...
138 Aspen's user avatar
  • 109
0 votes
1 answer
475 views

How did Grigori Perelman , got all the necessary theory and materials to prove the Poincaré conjecture?

The Poincaré conjecture is one of the millennium problems which have been solved by the famous mathematician Grigori Perelman . As per I know he worked on the problem in isolation for 8 years. I ...
Sillyasker's user avatar
0 votes
2 answers
133 views

In what ways could or couldn't having students do homework in $\LaTeX$ for extra credit be helpful for them at the college level? High school level? [duplicate]

Do you think having students turn in homework in $\LaTeX$ say for extra credit is helpful for them at the college level? At the high school level? There could also be a few assignments that have to be ...
Matthew Albano's user avatar
2 votes
1 answer
997 views

Do you think with the advent of Desmos/GeoGebra, the Moore Method is more accessible to high school?

When I was a grad student, I taught a Calculus I course during the summer. Somehow I came across Robert Moore and I ended up reading his book which I connected with. Rather than being a great student, ...
Matthew Albano's user avatar
19 votes
4 answers
3k views

Whether to tell students how difficult (you think) a problem is

Background: Most textbooks end a section with a set of questions ranked either by topic or by difficulty. A distinction is often made between "exercises", which are for directly practicing a ...
Nick C's user avatar
  • 9,719
4 votes
0 answers
70 views

OER text for the mathematics of fair division

I'd like to design a course with a unit on fair division, and I'm looking for an OER text to use. The course will be a general education seminar, so students won't be expected to have any mathematical ...
Jared's user avatar
  • 2,223
6 votes
3 answers
2k views

What are common mistakes that students will make when solving "What's the original price" percentage problems?

Take this question for an example: A smartphone is now $\$500$ after a $20\%$ discount. What was its original price? Now, this is an example of a type of math problem that students face usually in ...
CrSb0001's user avatar
  • 295
6 votes
1 answer
193 views

are there Evidence-Based Justifications for Mandatory Mathematics Education in School Curricula?

I am currently working on a project to secure funding from our city council for our university. Participants from various academic disciplines are invited to contribute. The primary challenge I'm ...
Humberto José Bortolossi's user avatar
9 votes
3 answers
571 views

Best practices for Proof Revision/ Proof Portfolio?

I'm teaching a class small enough that I'm considering encouraging proof revisions (i.e. students taking a second try on proof based homework problems after getting feedback) for the first time. I'd ...
Mathprof's user avatar
  • 1,205
3 votes
2 answers
339 views

How to mention a long theorem in a presentation/beamer

I have to do a short presentation using beamer for 25 minutes about a topic. In the presentation i want to discuss the following proposition with a lot of conditions Proposition 2.8.5.8. Let $\...
Sophus Valentin Willumsgaard's user avatar
-4 votes
1 answer
107 views

Condense a logistic function around its midpoint [closed]

I have a function $$ f(x) = {1 \over 1 + e^{-k(x-0.5)}} $$ that plots a logistic curve that is symmetric around the point $0.5 / 0.5$. $k$ defines the steepness of the curve. I would now like to add ...
Fred's user avatar
  • 95
2 votes
1 answer
193 views

Define logarithmic function by functional relation [closed]

My son was working the other day with exercises such as: Find all the mappings $f:\mathbb{N}\rightarrow\mathbb{Z}$ verifying $$\forall m,n \in \mathbb{N}, f(m+n)=f(n)+f(m).$$ As another example: Find ...
Dimitris's user avatar
  • 165
18 votes
11 answers
4k views

Topological fun facts for high school students

I'm going to give a class to highschoolers about topology. I've prepared the beginning of the class where I introduce what is topology and give them different ways we use to describe spaces, but ...
bml64's user avatar
  • 311
4 votes
0 answers
212 views

Learn ring theory more fun

I asked this question at 'mathoverflow'. However, the character of this question does not match mathoverflow, so I am asking this question again on this site. Motivation: Among abstract algebra, I am ...
pokssin's user avatar
  • 149
8 votes
10 answers
2k views

How to explain (FALSE => TRUE) is TRUE [duplicate]

How do you explain that the implication $p \implies q$ has the value TRUE when $p$ is FALSE and $q$ is TRUE? It is difficult for students to accept that FALSE $\implies$ TRUE should have the value ...
Joseph O'Rourke's user avatar
6 votes
1 answer
632 views

Strategies for Fair Assessment in Mixed-Ability Undergraduate Math Classes

In my undergraduate courses (discrete math, linear algebra), students' backgrounds vary significantly. One group has a strong math foundation from high school, while the other, less prepared, ...
user avatar
11 votes
5 answers
2k views

Textbook For a Course on Classical Geometry

I have been assigned to teach a first year course in geometry the next academic year. This course has been running for quite a while in the university, but of late, has been thought of as redundant ...
Aravind Gundakaram's user avatar
10 votes
0 answers
198 views

Examples for advanced math courses based on measurable learning objectives

Background. I teach math at a German university (both undergraduate courses and courses for Master programmes), mostly for students who major in mathematics or very similar programmes. Students ...
Jochen Glueck's user avatar
-4 votes
1 answer
251 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 ...
Sillyasker's user avatar
5 votes
1 answer
231 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 ...
user avatar
12 votes
2 answers
555 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 ...
Jon Bannon's user avatar
  • 6,173
4 votes
1 answer
394 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 ...
user23487's user avatar
7 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 ...
dt688's user avatar
  • 173
8 votes
4 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 ...
Bilbo's user avatar
  • 271
2 votes
1 answer
270 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 ...
fire-bee's user avatar
  • 173
2 votes
0 answers
130 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 ...
Hauke Reddmann's user avatar
9 votes
7 answers
479 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, ...
AegisCruiser's user avatar
  • 1,427
7 votes
1 answer
683 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 ...
user1258481's user avatar
4 votes
1 answer
261 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 ...
Will.Octagon.Gibson's user avatar
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 ...
Sillyasker's user avatar
10 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 ...
Aravind Gundakaram's user avatar
0 votes
1 answer
254 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 ...
Broy Tennison's user avatar
-1 votes
1 answer
49 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?
Monika's user avatar
  • 7
6 votes
3 answers
311 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 ...
Fraïssé's user avatar
  • 749
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 ...
Dan's user avatar
  • 989
11 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 ...
bobble's user avatar
  • 375
0 votes
2 answers
318 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 ...
Sillyasker's user avatar
0 votes
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 ...
Sillyasker's user avatar
1 vote
1 answer
116 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-...
EngrStudent's user avatar
-4 votes
2 answers
276 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 ...
Humberto José Bortolossi's user avatar
6 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,...
Zuriel's user avatar
  • 4,275
9 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 ...
Justin Skycak's user avatar

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