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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 ...
NiloCK's user avatar
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20 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:      
Joseph O'Rourke's user avatar
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 ...
guest's user avatar
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15 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, ...
Bernard Bagnall's user avatar
11 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 ...
Xander Henderson's user avatar
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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 ...
dijksterhuis's user avatar
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 ...
Sciolism Apparently's user avatar
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 ...
Yuval Filmus's user avatar
8 votes

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

I think you're focusing too much on 'the answer'. I suspect the teacher was tired and busy, and quickly needed to come up with an exercise of a suitable level that was worth completing. If I was ...
Jessica B's user avatar
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8 votes
Accepted

What are the minimum criteria when checking homework for completion only?

This is going to look a lot like Jeffery Thompson's answer, with some slight modifications (I was working on this answer when his appeared). First off, I agree entirely that you have to decide what ...
Xander Henderson's user avatar
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8 votes
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Should homework be graded in an undergraduate math course?

I should preface this by saying that I am working in the US, at a large public university that serves a population that largely consists of first-in-family college attendees, low income students, and ...
Xander Henderson's user avatar
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8 votes

What's the point of exercises without answers?

To add to Namaste's answer above, two of the thing we're trying to teach in math is literacy and competency with the algorithms used to solve problems and the ability to solve problems for which you ...
Nate Bade's user avatar
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7 votes

Benefits of students grading each other's (or their own) homework or quizzes?

A benefit that can be expected is to help student realize how important it is to write mathematics in a language (e.g. English; French in my case). I have often been confronted by students who ...
Benoît Kloeckner's user avatar
7 votes
Accepted

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

For a history of how Geometry textbooks (and the way they were used) in the United States evolved from the mid-19th century into the 20th century, see: Herbst, P. (2002) Establishing a custom of ...
mweiss's user avatar
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6 votes

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

I teach at community college. I often publish the homework problems at the beginning of the semester, listed by section. I have never had a student work ahead (that I know of). And I have had a few ...
Sue VanHattum's user avatar
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6 votes

What are the minimum criteria when checking homework for completion only?

It depends on what you are assigning the homework for. The learning objectives of an assignment should determine your rubrics for assessment. You need to ask yourself why you are assigning the ...
Jeffery Thompson's user avatar
6 votes

Supplemental text for undergraduate real analysis

Understanding Analysis by Stephen Abbott is a very gentle and solid introduction to undergraduate analysis. Good exercises, too.
David Steinberg's user avatar
6 votes

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

As others have said, Euclid was often used as a reference book rather than what we now call a "textbook". Students were often required to memorize and reproduce the contents. For example, at Oxford, ...
Scott Eberle's user avatar
6 votes
Accepted

Mental Health in Mathematics

At my university, students with learning challenges receive extra time during exams. Based on this, I can tell you that there are quite a number of them in the math courses that I have taught. Some ...
Mikhail Katz's user avatar
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6 votes
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Should we use quizzes to replace homeworks?

I swapped to what you propose in my calculus classes. Grading calculus homework is miserable: If you grade on correctness, students use the solutions manual If you grade on completion, students use ...
Chris Cunningham's user avatar
6 votes

Homework in a Flipped Classroom

A flipped classroom course does typically have less homework than a lecture one to account for the time spent out of class doing things like watching videos, but it's pretty common to still have some, ...
Henry Towsner's user avatar
5 votes

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

Think of the pedagogical goal of the problem as being to generate discussion about assumptions being made, just as you are doing. The goal is not to come up with a pre-determined correct number. ...
user52817's user avatar
  • 11k
5 votes

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

Having taught gifted math to elementary school students for over 25 years, I was delighted to see that your 6 year old daughter was given this question. However, as I read further, I discovered that ...
Amy B's user avatar
  • 8,017
5 votes

Making solutions to all problems freely available

I teach a highly selective Liberal Arts College. If you don't assign a component of the final grade to the homework, the majority students in a typical introductory class just won't do it or, if they ...
ncr's user avatar
  • 2,986
5 votes

How cheating on homework affects student questions

Imagine a scenario where you don't have a hypothesis about your students' unwillingness to ask questions in class or during office hours. Your question may just boil down to: "How do you get students ...
Nick C's user avatar
  • 9,709
5 votes
Accepted

Selected Exercise for Linear Algebra Done Right Edition 3

See Syllabus for linear algebra using Axler's "Linear Algebra Done Right" for current/past courses being taught with the text as the primary text in a linear algebra class. In particular, see MIT's ...
amWhy's user avatar
  • 2,095
5 votes

What's the point of exercises without answers?

Texbooks can be used for: Self-study. In this case they have a healthy dosage of theoretical material and a bunch of exercises, which have answers. Guided study, when the teacher explains theoretical ...
Rusty Core's user avatar
  • 1,317
5 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)

I put this as a comment, but maybe it deserves an answer to prevent it from being dismissed outright. My comment: Why not use LaTeX? It might seem a little overbearing (and admittedly I've used it ...
searchengine27's user avatar
5 votes

Generating system of equations with unique solutions

If you are looking at intersecting the zero sets of two polynomials in two variables, then by Bezout's theorem you should anticipate that the number of solutions will be equal to the product of the ...
Steven Gubkin's user avatar

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