23
votes
What benefit is there to obfuscate the geometry with algebra?
Tests seek to measure ability. Math ability, like most other forms of ability (including athletic ability), isn't solely dependent on one's ability to execute individual skills in isolation -- it also ...
- 6,111
21
votes
Accepted
What benefit is there to obfuscate the geometry with algebra?
Is your ultimate goal really just to teach cofunctions?
Or are you trying to teach cofunctions so that the students can apply them later?
I am speaking as a student rather than an educator, but math, ...
- 326
18
votes
What should I do if I have a student 'hiding' their working out?
It has been nearly a year now since I've made this question, and I think I've discovered a 'magical cure'. This one simple trick has worked for all of my classes with great success (I am feeling more ...
- 1,106
18
votes
What benefit is there to obfuscate the geometry with algebra?
This multi-step question requires students to understand and apply multiple concepts or strategies to solve the problem. The goal of a standardized test is not to provide a correctly-sequenced list of ...
- 1,404
16
votes
What is the quantitative data on effectiveness of "modern" teaching methods?
Consider a paper from this year: Setren, et. al., "Effects of the Flipped Classroom: Evidence from a Randomized Trial", Annenberg Institute at Brown University (2019). In their introduction, the ...
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15
votes
How to teach perseverance?
I believe that my students can learn best when they display perseverance (sometimes called grit). I'll discuss how I teach, model, and encourage mathematical perseverance.
Tell a story about ...
- 900
13
votes
Accepted
What is the correlation between students' contentment and educational quality?
From Clark, Richard, Paul A. Kirschner, and John Sweller. "Putting students on the path to learning: The case for fully guided instruction." (2012):
Even more disturbing is evidence that when ...
- 24.3k
13
votes
Accepted
Should I teach a subject I don't like?
This is a contentious and highly individual thing, of course, so all answers in this should be taken with a grain of salt. But, if this is your job then:
YES.
Why? First, some practical reasons ...
- 5,970
13
votes
Accepted
is it appropriate or beneficial to mention weird results in math?
I would be careful with the type of result for which one needs a lot of new math to digest the explanation.
For example, I would avoid talking about $ 1 + 2+3+.. = -1/12$ because there is basically ...
- 2,982
11
votes
Mathematical education slang
There is the constructivist "guide on the side", contrasted with the traditional "sage on the stage".
These phrases have been popular in secondary and primary education in recent years, but they ...
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11
votes
Mathematical education slang
Similar to 'drill-and-kill', a common one is 'plug-and-chug'. I guess this refers not so much to the method of teaching (drilling students) as to the method of completing the exercises (running the ...
- 5,762
11
votes
is it appropriate or beneficial to mention weird results in math?
If it's the right amount of "weird", then YES (see Zone of Proximal Development). For example, I often try to show students how $0.\bar{3} = \frac{1}{3}$ implies $0.\bar{9} = 1$. This example alone ...
- 549
11
votes
Accepted
Acceptability of creative questions in assessments
I think the given example is highly appropriate. You cannot cover every possible combination of ideas in class. Students display understanding of a concept (rather than "recipe following") by ...
- 24.3k
10
votes
Against introducing precise definitions first
At the secondary level, students have not yet mastered formal mathematics and most will need to continue learning concepts before definitions in many cases. The van Hieles (the Dutch educators who ...
- 421
10
votes
Acceptability of creative questions in assessments
I would frame this issue a little differently than you have. I think it's unreasonable, at least in the context of courses which aren't well into a math major, to ask students to do something they ...
- 11.6k
10
votes
Accepted
The Interleaving Effect: How widely is this used?
In an answer to question 2, a few references I am familiar with are brought up at https://www.learningscientists.org/blog/2016/8/11-1. I was made aware of interleaving through this website. I will ...
- 3,996
9
votes
What is the quantitative data on effectiveness of "modern" teaching methods?
A supplement to @Ben's PNAS article citation:
Hodges, Linda C. "Contemporary Issues in Group Learning in Undergraduate Science Classrooms: A Perspective from Student Engagement." CBE—Life Sciences ...
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9
votes
What is the quantitative data on effectiveness of "modern" teaching methods?
The Education Endowment Foundation has a 'Teaching and Learning Toolkit' which aims to assess the effectiveness of various teaching methods or types of intervention, including collaborative learning, ...
- 670
9
votes
Acceptability of creative questions in assessments
My advice is to minimize the amount of such synthesis required. Don't make it a large fraction of your tests, if at all. Teach the students the methods you expect them to display on the exam. Not ...
- 129
9
votes
Pedagogical insights to be gleaned from AI attempts to ‘learn’ mathematics
In intro proof classes I often wish that I had a large collection of "bullshit student work" for my students to pick apart. ChatGPT is basically a bullshit generator, so it seems well ...
- 24.3k
9
votes
What benefit is there to obfuscate the geometry with algebra?
I have been on committees that write questions for standardized tests and placement tests. In this role, I have reviewed results of many trigonometry questions that were piloted and then revised for ...
- 10.2k
8
votes
Against introducing precise definitions first
One of my most vivid memories of graduate school was working on a problem concerning the Gelfand-Kirillov dimension of certain rings. I had been puzzling over the definition (which was rather new to ...
- 17.3k
8
votes
How can I improve my problem solving/critical thinking skills and learn higher math?
"For example, I can do whatever is on my homework or tests. But, if I'm given a more difficult problem than usual concerning a topic I learned (say logarithms or something), I can't solve it."
Did ...
- 1,163
8
votes
Accepted
Pedagogical advice/articles for graduate student teaching assistants
The MAA has quite a long guide for new TA's, it's a little too much to take in at once but as a supplement it's very good, it's got a section on everything you could hope for:
I agree with Brendan ...
- 1,941
8
votes
Advice: How to cite literature for high-school students?
Research papers require references to verify where your data comes from. Schoolkids don't care where you get your data, extra references or footnotes just irritate them. If the presented information ...
- 1,309
8
votes
Can a science educator teach math?
That depends on the level. In general the rule is that to teach a subject coherently, one needs to know roughly speaking five times more than one is going to present to the students. If this condition ...
- 3,599
7
votes
How to deal with fast students without neglecting weaker ones
When I taught high school, I offered each students a choice between doing two different worksheets, making it clear that one worksheet had many problems at a low level for lots of practice and only a ...
- 3,996
7
votes
What is the quantitative data on effectiveness of "modern" teaching methods?
I would like to echo Peter Saveliev's point in the comments: You are asking about "higher results" but you do not specify what qualities you are interested in measuring.
Do you care about grades? ...
- 24.3k
6
votes
How can we help students learn how to read their textbook?
I have been making mathematical reading skills a large part of my abstract algebra class this semester.
A full 20 percent of their grade comes from writing reflections on the reading the text.
I ...
- 24.3k
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