66 votes

Is this homework problem on counting triangles within a 4x4 grid too vague?

This is a bit of a can of worms. Let's unpack a little. We were given no additional information other than that stated in the page. This is your daughter's homework, not yours. Be careful with ...
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  • 4,850
65 votes
Accepted

Is it worth grading calculus homework?

The evidence says no What research I'm aware of is all about how giving any overall data about their own performance is actively harmful in promoting further learning. They learn considerably more ...
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  • 1,912
21 votes
Accepted

Are there any benefits to having an entire course's homework problems available from day one?

I always organize my courses with the totality of the course set from the outset whenever I can. I see this as being closely tied to your question concerning homeworks assigned. The benefits I see: ...
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21 votes
Accepted

Do you have an efficient way to view student responses to remote assignments allowing them to type math symbols and steps? (Middle + High school)

In a Google doc, one can "Insert/Equation" (marked by $\pi^2$). Then tiny pull-down menus appear in a top bar: Using these menus, I just typed this nonsense:      
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18 votes
Accepted

How much time to spend on a single question?

The key is not just that you spend time on a problem - it is normal to struggle with problems at the level you have described - but that you do so in a productive way. In fact, the notion of ...
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16 votes

Do you have an efficient way to view student responses to remote assignments allowing them to type math symbols and steps? (Middle + High school)

Consider to just review scanned or photographed handwritten homework. Yes, this is not as easy as looking at typed work, but consider: would you require typed work normally? So why now? If your ...
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  • 235
15 votes

How to give homework for integration techniques?

First of all, I try to be honest with my students by telling them directly and explicitly about the existence of such integration machines (It is silly of me assuming that they don't know that!). Then,...
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  • 4,316
14 votes

Is this homework problem on counting triangles within a 4x4 grid too vague?

I've come across some creative 10 year olds who produced solutions like So when there are questions set that seem closed you can allow it to be opened out and the child's exploration can begin, ...
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13 votes
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Motivating students to take homework seriously without grades

We tried something that worked nicely (though not for all students). At the beginning of the course we announced that there will be a quiz during the semester, and the questions in the quiz will be ...
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  • 318
13 votes

Abandon all hope, ye who enter my office!

I wouldn't put any such sentence on your door, just one in the syllabus explaining your make-up exam policy which should be determined at the beginning of the semester. You don't want to come off as ...
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  • 2,584
11 votes

Students' Messy Sheets: The Big Problem of Exams and Homeworks

Besides mastering the material in the course one thing that the students have to learn during studies is to communicate mathematics in written form. Almost nobody comes to university and is able to ...
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  • 2,932
11 votes

Motivating students to take homework seriously without grades

The following answer is just my opinion and might not address your particular situation. To oversimplify a bit, most students either want to do the homework for their own reasons (enlightenment, fun,...
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11 votes

Is it morally acceptable to complete math homework with a program oneself has written?

TL;DR Yes, as long as the teacher didn't explicitly forbid it, you wrote the mathematical core of the program yourself, the technique you are using doesn't twist the intent of the problem. Teacher ...
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  • 8,729
10 votes

Is this homework problem on counting triangles within a 4x4 grid too vague?

I think the key issue is with this part of the question: How many different triangles with one dot in the middle can you draw? Which depends on the context of how the subject is being taught I ...
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10 votes

Making solutions to all problems freely available

This is an opinion, but perhaps worth sharing: When I assign that I expect students (particularly lower division students, such as those in calculus or precalculus classes) to do on their own time, I ...
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10 votes

When Euclid was used as a textbook, what exercises did students do?

Euclid’s Elements was used as a Geometry textbook in essentially the same way that Virgil’s Æneid was used as a Latin textbook. Neither contained exercises anything else pedagogical, and both were ...
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10 votes

Generating system of equations with unique solutions

Generating systems. The same method that works for linear equations works also for polynomial equations. Starting with a solution in mind (in mathematics and computer science, we call this a planted ...
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9 votes

Motivating students to take homework seriously without grades

This won't directly help you, but the way I was motivated to do my homework as an undergraduate was that I had one-on-two tutorials every week. If you haven't done the homework and your tutorial ...
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9 votes
Accepted

What are the pros and cons of having students choose which HW problems are looked at?

Question 1: Will you tell your students which are the easy problems and which are the hard ones? If yes, you get the vonbrand scenario If not, how will the "strong students" know which are the ...
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  • 2,671
8 votes

Overload of Calculus homework assignments

In addition to having an online homework system if possible, you might also consider asking the students present a few problems in class. This would make the students at the very least care more about ...
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  • 2,916
8 votes

How is calculus possible in a small number of very long class periods?

Never been in such a bind teaching (as a student I had a full term compressed into some six weeks once, but I don't remember much of that), but I'd look for ways to split the subject "sideways", I.e. ...
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  • 12k
8 votes

What are the pros and cons of having students choose which HW problems are looked at?

Knowing (a little) of how student's brains work, you'll get $n - 1$ "easy" problem attempts + 1 "medium" problem attempt each time, period. You have to force their hand a bit. Perhaps give extra ...
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  • 12k
8 votes

Are there any benefits to having an entire course's homework problems available from day one?

I did this for an introductory calculus course at a US state university. My reason was that I wanted to assign more homework than my colleagues typically do. On the first day of class I warned ...
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  • 2,045
8 votes
Accepted

Is it morally acceptable to complete math homework with a program oneself has written?

I put my recommendation first, with my reasoning about the moral basis of school and homework underneath if you are interested. Recommendation It is not cheating and is probably more moral than doing ...
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  • 2,588
8 votes

Worksheet: Homology in Intro Lin Al

Personally, I think this seems very appropriate. A few points: You might reconsider using a two character name for a vector. $xa$ looks like a multiplication. Perhaps just label the vertices $V_1$,...
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8 votes
Accepted

Worksheet: Homology in Intro Lin Al

I have a dim memory of a simple exercise I came up with as a TA. It was something like the vector space over the reals of polynomials in two variables, including x^2, y^2, and (x+y)^2. I then asked ...
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