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 ...
  • 1,076
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 ...
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 ...
  • 890
14 votes

Experiences with online courses, specially MOOC?

A year after this question was asked, the bloom is definitely off the MOOC rose. The primary finding is that the majority of people who finish one already possess a prior bachelor's degree; offering ...
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 ...
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 ...
  • 5,838
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 ...
  • 2,962
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 ...
  • 2,962
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 ...
  • 5,664
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 ...
  • 780
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 ...
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 ...
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 ...
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 ...
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 ...
  • 3,887
9 votes
Accepted

How to choose the school for practising teaching?

First off, I would like to commend your desire to teach at a high school level. It is a very challenging and tiring profession but it is so rewarding and IMHO is one of the most useful settings that ...
  • 4,890
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 ...
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
8 votes

How can we help students learn how to read their textbook?

I had tried a few different strategies in high school with little success. My first attempt was having the students read the textbook and take notes on what they read in a very prescribed way. At the ...
  • 631
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 ...
  • 16.9k
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 ...
  • 1,901
8 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 ...
  • 119
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 ...
  • 1,290
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 ...
  • 1,329
7 votes
Accepted

Funny things students say when learning mathematics

From John Stembridge's web site at http://www.math.lsa.umich.edu/~jrs/plans.html : "Are we going to have to think today, or is it going to be all math?" --a student in Phil Hanlon's Math 115 class
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 ...
  • 3,887
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? ...
7 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 ...

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