Skip to main content
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 ...
Justin Skycak's user avatar
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, ...
PC Luddite's user avatar
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 ...
Steve's user avatar
  • 1,594
15 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 ...
Daniel R. Collins's user avatar
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 ...
kcrisman's user avatar
  • 5,976
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 ...
Daniel R. Collins's user avatar
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 ...
Dirk's user avatar
  • 2,991
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 ...
Marian Minar's user avatar
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 ...
Steven Gubkin's user avatar
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 ...
Scott Eberle's user avatar
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 ...
Henry Towsner's user avatar
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 ...
Opal E's user avatar
  • 4,043
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 ...
guest's user avatar
  • 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 ...
Steven Gubkin's user avatar
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 ...
user52817's user avatar
  • 11k
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 ...
G. Allen's user avatar
  • 1,163
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 ...
mweiss's user avatar
  • 17.4k
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 ...
Nate Bade's user avatar
  • 1,941
8 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 ...
Joseph O'Rourke's user avatar
8 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, ...
dbmag9's user avatar
  • 660
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 ...
Rusty Core's user avatar
  • 1,317
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 ...
fedja's user avatar
  • 3,889
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 ...
Opal E's user avatar
  • 4,043
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 ...
Steven Gubkin's user avatar
6 votes

Against introducing precise definitions first

Teaching undergrads and graduate students, by this point I do not like "precise definitions" at the outset, for the sort of reasons given by W. Thurston, and also for reasons given by I.M. Gelfand. ...
paul garrett's user avatar
  • 14.7k
6 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? ...
Steven Gubkin's user avatar
6 votes

Can a science educator teach math?

Is there something a math teacher can do that a science teacher cannot? The essence of the mathematical discipline is rigorous deductive proof. Feel free to read that as "correct and ...
Daniel R. Collins's user avatar
6 votes

How to explain the concept "Without loss of generality" (through examples)?

I disagree with your definition of WLOG. In my opinion, WLOG is synonymous to "[Obviously, ]the general case can be reduced to the following particular case." Usually the reduction is done ...
Kostya_I's user avatar
  • 1,411
5 votes

Bloom's taxonomy

Bloom's taxonomy is not very helpful for maths, as many of the verbs don't make much sense, and ones that do have meanings occur in the wrong order. There are a couple of people (at least) who have ...
Jessica B's user avatar
  • 5,822

Only top scored, non community-wiki answers of a minimum length are eligible