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 ...
- 4,980
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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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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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, ...
- 151
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 ...
- 7,485
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
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 ...
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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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 ...
- 5,762
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 ...
- 7,485
8
votes
Accepted
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 ...
- 7,485
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 ...
- 1,941
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 ...
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7
votes
Reusing homework exercises from previous terms
For me, the answer is simply that homework is not collected, graded, or scored. I assign odd-numbered problems from standard textbooks, expect that students check the answers at the back, and I ask ...
- 24.3k
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 ...
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7
votes
Accepted
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 ...
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7
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, ...
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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 ...
- 20.1k
6
votes
Collaboration on math homework assignments?
What level of mathematics are you looking at? When you say discrete math is this an undergrad course for general students, math majors or a grad course?
My experience has been that for undergrad ...
- 1,018
6
votes
Accepted
Collaboration on math homework assignments?
As I see it, the key issue with allowing collaboration on homework assignments is how to suitably assign grades, and in particular how to be seen to be 'fair' in the process of doing so. The approach ...
- 5,762
6
votes
Accepted
Is it appropriate to assign an extra credit homework question on the "next" session?
In general, I'd think that anything that helps students to break out of a tendency to passivity is good. Initiative should be rewarded, looking ahead is good, and so on.
Sure, if there is a pervasive ...
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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 ...
- 530
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.
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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, ...
- 421
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 ...
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5
votes
Accepted
Research/Anecdotes supporting WebWork, MyMathLab and other computerized, immediate feedback HW
Some of these links are old but I don't think WebWork has changed that much:
research at Rutgers about their calculus courses
this post has useful summaries and description of various aspects of ...
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5
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Can homework play a substantial role in the assessment of understanding in university math?
This is not a full answer to your question, but these comments do not fit in the comment box.
Homework and exams measure different things.
If you want to make sure that it is the student's own ...
- 3,720
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.
...
- 10.2k
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 ...
- 7,999
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