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86 votes

How to give exercises when students can use ChatGPT

I wouldn't bother at all. Just base your grades 90% on proctored exams where using the internet is prohibited. Those who will cheat on homework and quizzes will fail miserably and that will be their ...
fedja's user avatar
  • 3,939
46 votes

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

L1 language competence requires thousands and thousands of hours of practice to reach. We don't realise it only because much of it happens so early in life. Nonetheless huge amounts of early schooling ...
Jack Aidley's user avatar
34 votes

How to give exercises when students can use ChatGPT

I don't think ChatGPT fundamentally changes the ability to use unauthorized aids. Many other source of help have existed for a long time (other students, copying, Chegg, paid tutors, Google, books, ...
guest troll's user avatar
27 votes
Accepted

Students understand during course but can't solve exam

Do NOT give exam questions that are intentionally more challenging than homework or in-class problems. I would recommend precisely the opposite. The point of the exam is really a spot-check that ...
Daniel R. Collins's user avatar
20 votes

How to give exercises when students can use ChatGPT

Here are some suggested changes for dealing with ChatGPT, in no particular order. Note that these are based on our discussions in (mathematics and natural sciences) teacher education, so they are not ...
Tommi's user avatar
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18 votes
Accepted

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

Probably evolution. Our brains are not purely, perhaps not even mostly programmable computers. You can learn to walk naturally. Doing a kip in gymnastics takes practice. Similarly, your brain is ...
Guest troll's user avatar
17 votes

How much symbolic calculations before plugging in actual values?

Speaking from an American perspective, your son's approach strikes me as much more natural. For instance, to solve your problem We have three points $M(7;-2)$, $N(0;t)$, $P(3;1)$. Find $t$ so that ...
Matthew Daly's user avatar
  • 5,629
14 votes

How to give exercises when students can use ChatGPT

ChatGPT is stupid. This is not an opinion, but an observed behaviour. I've asked ChatGPT to calculate a number with 36 divisors and this went wrong, so I decided to learn the program how to perform ...
Dominique's user avatar
  • 2,165
12 votes

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

I believe there are people who develop mathematical competency without being taught but they are in the minority. No one taught me algebra, but I placed out of algebra by "intuition". I am ...
Amy B's user avatar
  • 8,017
11 votes
Accepted

How much symbolic calculations before plugging in actual values?

Calculate when you want an answer. Solve algebraically when you seek patterns. If the problem was "show that for any two points, you can find a third point along the y-axis that is collinear with ...
Cort Ammon's user avatar
  • 1,225
10 votes

Good Examples of Questions to have Students Ponder Over Without Paper

A possibility, requiring one definition: What is a tiling of the plane with an infinite supply of congruent copies of a single tile (technically, a monohedral tiling). This can go as deep as you'd ...
Joseph O'Rourke's user avatar
9 votes

Students understand during course but can't solve exam

I always make homework (from the textbook and online in WeBWorK) and written assignments MORE difficult than exam questions. I tell my students this, with the reason being “if you can run 10 miles in ...
BobaFret's user avatar
  • 836
9 votes

Simple combinatorics problems using division

You can do necklaces composed of colored beads. For simplicity the number of beads needs to be prime. If there are to be $p$ beads with $a$ choices of color, then there are $a^p$ ways to arrange the ...
Will Orrick's user avatar
  • 1,122
7 votes

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

Our minds are not well adapted to math. It is an abstract activity. And requires significant practice to sink in. We are not rule based systems. Not flawless computers. Our brains are optimized for ...
guest's user avatar
  • 157
7 votes

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

Generally, when we talk about improving a skill, we tend to refer to skills that are physical-based. For instance, a professional basketball player may be a strong three-point shooter because they go ...
FoiledIt24's user avatar
  • 1,291
7 votes

How to give exercises when students can use ChatGPT

I think that approaches like: "I don't care if the students cheat in exercises, they will learn their lesson at the exam." don't work well because dealing with large number of students doing ...
J Fabian Meier's user avatar
7 votes

How to give exercises when students can use ChatGPT

The Chronicle of Higher Education recently held a discussion on ChatGPT and other generative AI tools. While they were interested in the impact of these tools on academia in general, I think that the ...
Xander Henderson's user avatar
  • 8,224
6 votes
Accepted

Could you recommend a book for studying calculus 1?

I recommend OpenStax open-resource digital books from Rice University for all levels of college math, from prealgebra through calculus and statistics. For the student, they're free, can be shared and ...
Daniel R. Collins's user avatar
6 votes
Accepted

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

The analogy to driving a car or riding a bike is a bad one. I agree that once you learn those skills, is not unreasonable to spend some years without doing those and still have the skill learned ...
KCd's user avatar
  • 3,536
6 votes

How to give exercises when students can use ChatGPT

Explain to the students why using ChatGPT is not in their best interests in the long term in learning maths (or any other topic). I run into this problem with teaching programming, where software ...
Dikran Marsupial's user avatar
5 votes

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

The Fahrenheit and Celsius temperature scales are linearly related. A change of one degree Celsius is a change of 1.8 degrees Fahrenheit. The freezing point of water is 0° Celsius or 32° Fahrenheit. ...
Gerald Edgar's user avatar
  • 7,607
5 votes
Accepted

Is proof-based exercise-oriented math course without solution an effective way to teach pure math?

I have taught such courses and I don't think that a long list of exercises without solutions is good idea - at least it didn't work for me. It is because 1) students are not yet able to tell a ...
Fedor Duzhin's user avatar
5 votes

Good Examples of Questions to have Students Ponder Over Without Paper

Perhaps logic puzzles would work in this case. Some classic examples are: You're traveling along a road and arrive at a fork. Two guides are posted, but one always lies and the other always tells ...
Aeryk's user avatar
  • 8,019
5 votes

How to give exercises when students can use ChatGPT

I heard this news story about Professor Ethan Mollick, who addressed this problem by requiring students to work with ChatGPT to write their essays. This involved improving its drafts, looking up ...
Shawn V. Wilson's user avatar
4 votes

Good Examples of Questions to have Students Ponder Over Without Paper

Since Benjamin Dickman mentioned The Tokyo Puzzles in the comments, I'll include a couple of the questions from that book here that I thought fit the prompt nicely; neither requires a pen and paper to ...
Mike Pierce's user avatar
  • 4,845
4 votes

Is proof-based exercise-oriented math course without solution an effective way to teach pure math?

This sounds vaguely similar to an "inquiry-based learning" course. So although this isn't what you are describing (notably the lectures), you may find resources at the Academy of Inquiry Based ...
kcrisman's user avatar
  • 5,986
4 votes

Importance of exercises for learning mathematics

From my own experiences as a undergrad math major, I would say that good, quality exercises are one of the best tools for teaching math to people. Paul Halmos was right: "The only way to learn ...
Justin Benfield's user avatar
4 votes

Exercise database

WebWork maintains an Open Problem Library. It is not necessarily "easy" to construct your own problems on WebWork, but the system is constructed with purposes like these in mind. In particular, if you ...
Opal E's user avatar
  • 4,043

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