84 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
  • 3,831
54 votes

Natural origins or learned habit: Why do students skip concepts before applications?

Students have the tendency to just try to learn the examples and skip the concepts. Is there a name for this phenomenon? Has it been studied? Does it have natural origins, or is it taught in prior ...
Justin Skycak's user avatar
41 votes
Accepted

Is there a fair way to increase the grade of students who did not do well in exams?

With respect to considerations of this kind one should reflect on one's information sources. For every student who exhibits to the professor hard work there are other students who have worked just as ...
Dan Fox's user avatar
  • 5,843
36 votes

Parentheses around negative numbers

It is not a good idea to against a convention, unless you have strong reasons for it. That said, you might not want to punish those going against the convention, either. An obvious reason for having ...
Tommi's user avatar
  • 7,009
36 votes

Natural origins or learned habit: Why do students skip concepts before applications?

An observation that I've made in the past is this: Math is hard because by its nature it's taught at TOO HIGH a level compared to other classes. Consider: Does the curriculum make time and space to ...
Daniel R. Collins's user avatar
33 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
29 votes

Students can't seem to grasp the intent of tangent lines and getting general trends of derivatives from graphs

Sadly, these students seem to think of math as a bunch of rules. You have done great work, and probably gotten them a little closer. But they are resisting the reasoning that can't easily be put into ...
Sue VanHattum's user avatar
  • 20.2k
29 votes

When is it appropriate to warn about the difficulty of a subject?

I know this is generally accepted as normal behavior by teachers, but personally, if I ever find myself tempted to attach disclaimers like "don't worry if you feel overwhelmed by this", then ...
Justin Skycak's user avatar
26 votes

How do/should administrators estimate the cost of producing an online introductory mathematics class?

I can answer a small part of this. -- The most important part of the costs that administration overlooks during these kinds of efforts is the cost of maintenance of the online course content that is ...
Chris Cunningham's user avatar
26 votes

Why don’t we teach a topological view of continuity instead of epsilon-delta?

Yes. You are crazy to be spending time on another effort to bring real analysis style rigor into a calc 1 course. In this case, even off brand real analysis. Instead of a "different" way ...
guest troll's user avatar
24 votes

Is there a fair way to increase the grade of students who did not do well in exams?

Follow your syllabus Presumably, you gave every student a syllabus at the beginning of the course, and this syllabus outlined standards for grading. The grades you assign at the end of the term ...
Xander Henderson's user avatar
  • 7,698
21 votes

What can I do when advanced undergraduate and/or early graduate STEM students cannot perform correct math manipulations?

I am really at a loss as to why this is happening and what should be the correct remedy, as it seems that it is not easy to address this late into their study. Also there seems to be no improvement ...
Justin Skycak'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
  • 7,009
20 votes

Students can't seem to grasp the intent of tangent lines and getting general trends of derivatives from graphs

When a concept just won't stick, no matter how many ways you explain it, that is usually a sign of a gap in the student's background knowledge. So I'd recommend searching for the gap. Of course, you'...
user22788's user avatar
  • 854
17 votes

Parentheses around negative numbers

Others have talked about legibility, so I want to address the importance of the parentheses in an expression like $$17\color{red}{-}(\color{blue}{-}59)$$ from the perspective of educational psychology....
Justin Hancock's user avatar
17 votes

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

I'm going to respond from an applied math (or maybe CS) perspective: Part of the problem is that the functions that you look at in high school and the standard calculus sequence are unrealistically ...
Adam's user avatar
  • 5,382
16 votes

Why do we teach linear algebra in precalculus classes?

Vector algebra is a standard 3rd-semester calculus topic (e.g., see OpenStax Calculus 3, Ch. 2-3). This includes calculations of the dot product, cross product, and related values. Standard ...
Daniel R. Collins's user avatar
16 votes

Any examples of calculus sequence that deemphasizes calculation tricks?

As you undertake the journey, you should read about the Calculus Reform movement of the 1990s. A unifying idea of the efforts was to increase conceptual understanding by using symbolic computational ...
user52817's user avatar
  • 10.5k
15 votes

Why don’t we teach a topological view of continuity instead of epsilon-delta?

You aren't crazy because Leonard Gillman wasn't crazy. See Emphasizing order relations rather than metric concepts in real analysis The family of all open intervals (A, B) about a point L assuredly ...
Marc Shelikoff's user avatar
15 votes

Students can't seem to grasp the intent of tangent lines and getting general trends of derivatives from graphs

I taught physics for 25 years at a community college, and the situation you're describing is one that I'm very familiar with. (I also got the oportunity to teach first-semester calculus a couple of ...
user23001's user avatar
  • 151
15 votes

When is it appropriate to warn about the difficulty of a subject?

I can remember two teachers warning us about the difficulty of a subject. The first warning was by a teacher of measure theory and probabilities. In the first half of the semester we'll study ...
Stef's user avatar
  • 546
15 votes

Natural origins or learned habit: Why do students skip concepts before applications?

Have you heard the story of Von Neumann and the train problem? The Train problem is a classic one. You have two trains heading towards each other, one going at 30 km/h the other going at 45 km/h, ...
Yakk's user avatar
  • 379
15 votes
Accepted

How does a math Olympian fare in undergraduate maths courses?

Mathematics is many things. Solving tricky problems is part of it, but there is also learning theory and new concepts and ways of thinking, and even developing routine. I would expect a person with ...
Tommi's user avatar
  • 7,009
14 votes

What can I do when advanced undergraduate and/or early graduate STEM students cannot perform correct math manipulations?

I'd like to offer a bit of a frame challenge here. Whenever I made these sorts of mistakes during my mathematics education it was normally because I didn't understand what the symbols in the more ...
andypea's user avatar
  • 257
14 votes

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

In video game animation, each second thousands of equations need to be solved with code. You can't tell a computer "look at a graph"! Your students need to think beyond the setting of ...
KCd's user avatar
  • 3,456
13 votes
Accepted

Seeking Advice on Allowing Students to Skip a Quiz in Linear Algebra Course

I do recommend dropping a certain number of quizzes to handle cases like this. You don't want a policy that makes more demands on your time and labor. This is common enough to be familiar to students. ...
Daniel R. Collins's user avatar
13 votes

How to teach pure mathematics to a well-educated adult who did badly in maths at school

As a person self-studying pure maths right now, I recommend the book "How to think about Analysis" by Lara Alcock since its very readable and the way Lara explains things, the concepts ...
muuzzmolz's user avatar
  • 171
13 votes
Accepted

Natural origins or learned habit: Why do students skip concepts before applications?

A relevant idea from the literature is the theoretical framework of "concept image and concept definition." It has been very popular since it was introduced, and you can find studies that ...
Justin Hancock's user avatar
12 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
  • 1,728
12 votes

Why don’t we teach a topological view of continuity instead of epsilon-delta?

If you want the comment on the approach yourself rather than on whether you should try to implement it, the key words in your post are Given epsilon I just need to show that the set of solutions to $L−...
fedja's user avatar
  • 3,831

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