Questions tagged [exercises]

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-1 votes
3 answers
628 views

Why must most adults slog at exercises to improve at Math, but not driving that AI still can't automate?

Too many mature students ask why they need to toil at problems — like end of chapter questions in textbooks — to succeed at math. They contrast buckling to math exercises with lasting skills like ...
5 votes
7 answers
489 views

Are there any good exercises on point-slope form of a linear equation by itself?

Let's say we're running a basic algebra course and we're committed to showing proofs of everything we reasonably can. The development of equations of lines seems most straightforward in this sequence: ...
37 votes
14 answers
14k views

How to give exercises when students can use ChatGPT

I tried some math exercises we will give to students and ChatGPT does really well answering these. It excels at proofs and often gives details that were not our the example solution, and makes some ...
18 votes
9 answers
2k views

Good Examples of Questions to have Students Ponder Over Without Paper

A few times now I've found myself in a situation where I want to give a precalculus-level undergraduate student something to think about that's kinda fun and that's well outside of their coursework. ...
12 votes
8 answers
6k views

Why does math need to be practiced and exercised, when L1 Linguistic Competence is subconscious?

If 'linguistic knowledge is largely subconscious'3, why isn't math? Most math instructors sermonize solving exercises and problems. But a student challenged why students need practice — because most ...
2 votes
0 answers
118 views

Is there any way of explaining the Cayley/Beltrami–Klein metric to undergrads?

How to explain the Cayley-Klein or sometimes called Beltrami–Klein metric concept to find the distance between two points in a hyperbolic space to an audience with no higher education than maybe a ...
6 votes
2 answers
359 views

Effective Strategies for Helping Students Recognize Nonsensical Expressions? (HS - Undergrad Level)

I'm not entirely how best to pose this question, so that it fits within the guidelines (so edits / suggestions for modification are warmly welcome). I'm interested in exploring effective strategies ...
8 votes
3 answers
621 views

Simple combinatorics problems using division

I would like to introduce counting principles associated with each of the 4 basic operations (addition, subtraction, multiplication, and division) before introducing permutations and combinations in ...
5 votes
2 answers
275 views

How can I encourage students to show up for exercise classes?

I am doing a maths PhD and naturally that involves leading exercise classes for undergraduate students. The idea is that the students just show up and work through the problem set and I'm there to ...
13 votes
0 answers
194 views

What studies exist, comparing the efficacy of exercise sheets with or without worked solutions?

I've been tutoring mathematics at university level for over 10 years, and one of the more common requests from students is worked solutions for sheets of exercises. Most educators I've worked with ...
0 votes
1 answer
81 views

Which grade students should be able to solve applied economy / business / profit prediction exercises?

I've designed a few applied problems with business analytics/money calculations. However, I'm not sure which age (or rather, which grade) are those best to introduce. on one hand, solution uses only +...
5 votes
0 answers
343 views

Self study curriculum for a working professional who is enthusiastic about mathematics

I had some mathematics education during my high school and Electrical Engineering studies, but I never used any of them during my career as a software professional. Now I am again coming across Linear ...
1 vote
0 answers
94 views

Exercises for explaning homothety, homothetic center, similarity on line and plane, free vector and vector space

I need the collection of exercises for such topics as: maps and transformations, composition of maps homothety, rotation homothety, homothetic center similarities of the line and the plane free ...
14 votes
6 answers
2k views

How much symbolic calculations before plugging in actual values?

My son is in high school (France, 2nde) and I was watching how he solves math exercices. This led me to the following question: when are students expected to plug in actual values in their ...
9 votes
2 answers
270 views

Exercise database

edit: Thanks for all your answers so far. I have decided to develop my own solution, both because it is fun and I can then form it exactly as I want to. Once I am done (which might take some time, ...
3 votes
2 answers
225 views

Where to find good exercises for term operations?

I'm searching for exercises for practising operations with terms. They should involve working with decimal numbers and fractions (ideally one should convert decimal numbers to simple fractions like ...
6 votes
2 answers
1k views

Unconstrained/Constrained optimization real life example

I am in charge of some practice lesson for Calculus II. I have to show how to apply the theory for unconstrained optimization (mainly Hessian analysis) and constrained optimization (Lagrange ...
8 votes
3 answers
330 views

Solutions to exercises

I am teaching the exercise sessions for a 3rd year algebra course (intro to field theory, Galois theory and Algebraic geometry). The format of the course is as follows: for every 2 hour lecture by the ...
7 votes
4 answers
3k views

Students understand during course but can't solve exam

I am teaching a math class where the students, most of them, tell me that they can understand the materials given by me during the course. I test them during the course too and they seem to get it. ...
6 votes
0 answers
187 views

Questions similar to Wason Selection Task

The Wason Selection Task (described by Pete Clark here) is a great problem for getting students to grapple with all of the intricacies of logical implication. I will be teaching a discrete ...
4 votes
3 answers
382 views

Could you recommend a book for studying calculus 1?

I would like to practice a large quantity of exercises from limit calculation, derivatives, sequences and series and finaly integrals.
8 votes
3 answers
356 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 ...
10 votes
2 answers
1k views

Importance of exercises for learning mathematics

For me it seem to be obvious that exercises and exercise courses are important for undergraduates to learn mathematics and skills like finding a proof or writing it down. Was there any research ...
8 votes
1 answer
467 views

Is there a repository with K-12 math exercises and problems written in LaTeX (English or Spanish)?

I've been searching for a repository or a database with math problems (K-12 levels) written in LaTeX, but with no luck. Neither in Spanish (my student's language) ...
9 votes
3 answers
583 views

How many problems do we have to do as undergraduate mathematicians in order to learn a subject?

I'm wondering how many problems are needed in order to learn a subject, let's say Calculus of Several Variables. We know that the professors often assign us a list of problems to solve as homework, ...
1 vote
0 answers
68 views

How many problems do we have to do as undergraduate mathematicians in order to learn a subject? [duplicate]

I'm wondering how many problems are needed in order to learn a subject, let's say Calculus of Several Variables. We know that the professors often assign us a list of problems to solve as homework, ...
10 votes
1 answer
190 views

Software to organize and track your exercises

I am math teacher in secondary school and I have a few thousands of mathematical exercises in many Microsoft Word files. I tried to organize them in folders and keep track of new exercises to update ...
13 votes
0 answers
307 views

Exercises to go with Simon's "Representations of finite and compact groups"

I am teaching an independent-reading course from Simon's "Representations of finite and compact groups". I chose this book based on fond memories from a previous reading course in which I had ...
4 votes
1 answer
376 views

Abandon all hope, ye who enter my office!

The sentence in the title is inspired by a sentence on the gate of hell in Dante Alighieri's masterwork Divine Comedy (Part I: Inferno). I usually write it on my office door after exams when I think ...