39 votes

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

One thing you might do is contrast reading mathematics textbooks with reading novels. I have seen this done at the start of a textbook draft for a course on the Kuratowski closure operators (MESE ...
user avatar
18 votes
Accepted

How to deal with fast students without neglecting weaker ones

I don't think it's fair to tell the students to not read ahead. In fact, I'd encourage it. What you should make clear is that the material in the current section takes precedence, and if somebody else ...
user avatar
  • 986
18 votes
Accepted

How much time to spend on a single question?

The key is not just that you spend time on a problem - it is normal to struggle with problems at the level you have described - but that you do so in a productive way. In fact, the notion of ...
user avatar
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 ...
user avatar
  • 1,076
16 votes

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

For reading individual proofs, my colleagues and I have had some success in research studies with self-explanation training adapted for mathematics students. We haven't extended this work to whole ...
user avatar
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 ...
user avatar
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 ...
user avatar
  • 860
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 ...
user avatar
13 votes

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

When I've taught mathematics, getting students to even attempt to read the textbook has always been a challenge. One of the things that I always start with is having students type sentences into ...
user avatar
  • 1,016
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 ...
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 ...
user avatar
  • 5,752
12 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 ...
user avatar
  • 2,932
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 ...
user avatar
  • 2,932
11 votes
Accepted

How can we help students learn to effectively take notes?

It's a skill you can teach fairly explicitly I teach 16-18 year old students A-level maths in classes (not lectures) in the UK. Over the course of two years I gradually switch from telling them ...
user avatar
  • 1,912
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 ...
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 ...
user avatar
10 votes

When is it appropriate to lecture?

This is a bit tongue-in-cheek, but it is good to lecture after students think they have mastered something via an active learning experience, provided the lecture is the result of long effort to find ...
user avatar
  • 5,877
10 votes

Encourage students to strive for understanding despite looming exams

Part of the problem is simply that you're trying to combat rationality. Regardless of what level you're teaching, grades are important. They control scholarships and school admissions (be they ...
user avatar
  • 986
10 votes

How to deal with fast students without neglecting weaker ones

I use a technique I learned from my pilates teacher: in class activities, have different options for different ability levels. I have worksheets in almost all of my lessons. I almost never cover all ...
user avatar
10 votes
Accepted

What to do about a student's poor handwriting

There are many reasons for handwriting problems, and many of these reasons may not be remedied with mathematics education methods and approaches. For example, Asperger's Syndrome has been associated ...
user avatar
  • 7,385
10 votes

Examples of cultural limitations on math education

A quintessential example of a cultural clash over math education in US schools, I would say, is the entire Math Wars, an ongoing struggle over standards and pedagogy in K-12 schools. It is a struggle ...
user avatar
  • 7,385
10 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 ...
user avatar
  • 5,540
10 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 ...
user avatar
  • 663
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 ...
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 ...
user avatar
9 votes

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

I do something at least mildly annoying: I make 10% of their class grade be showing up each week with the examples from the sections of the book we will cover that week written out by hand. That is, ...
user avatar
  • 1,102
9 votes

How to react to students saying that they are allergic to applied mathematics?

Perhaps the experience of just such a student may help you? As a student, when I chose my second-year maths courses, I compared the list of topics that were in second-year courses to the topics I ...
user avatar
9 votes
Accepted

Books that every aspirant mathematician should read

Here goes nothing. I have many other suggestions that are not listed; there is always one more example of a great math book: "The enjoyment of Mathematics" H. Rademacher, O. Toeplitz. You can't beat ...
user avatar

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