Questions tagged [general-pedagogy]

For questions touching upon pedagogical considerations and problems of a general nature, i.e., not specific to mathematics. Please note that some aspect of the question should still be related to mathematics.

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49
votes
14answers
11k views

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

In most secondary and early undergraduate courses, students purchase expensive and carefully-written textbooks. These textbooks contain, roughly, three things: Exercises and Answers Reference ...
31
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13answers
4k views

Lecturers “(intentional) mistakes” as a teaching tool

I have heard the story (may be an urban legend?) of a top professor who occasionally wanted to teach freshman analysis. He believed in the method of letting students see how a mathematician's mind ...
28
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8answers
2k views

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

I'm working in the field of applied mathematics (optimization and numerics) and I meet a lot of students saying that they are allergic to applied mathematics or that they hate it or some quotes like "...
25
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3answers
971 views

What do you do when you realize mid-lecture that your lesson plan is not working?

I had this happen today, and several times before. I had had difficulty preparing the material, because I knew my students strengths and it didn't seem suited to them. However, it seemed the right ...
22
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3answers
454 views

How to teach perseverance?

I have found that when I give problems that require multiple steps or ideas to solve, students often give up quickly and come to office hours begging for hints. Sometimes I break up such problems ...
20
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5answers
6k views

What is a method you use to handle the students who thinks they “know it all”?

This is a typical problem in my undergraduate Calculus I class. Many of these freshmen come in having made an A in their High-School Calculus class, and believe they know everything they need to ...
19
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11answers
1k views

Books that every aspirant mathematician should read

I am a student and I would love to become a research mathematician one day. So I would like to ask you---experts in mathematics but also in education---what are some influential ($\star$) books ...
19
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4answers
2k views

Students' Messy Sheets: The Big Problem of Exams and Homeworks

Students' messy exam and homework sheets (which are messy because of a bad handwriting or an irregular logical argument in proofs) cause many serious problems. e.g. Reading their arguments takes ...
18
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3answers
329 views

What should I do if I have a student 'hiding' their working out?

I recall in one of my classes earlier this year that I had a student who always 'hid' their working out from me when I walked around to see how well they're going with the question. The usual practice ...
18
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3answers
390 views

When is it appropriate to lecture?

I take it that lecture is rarely the most effective way for a student to learn. Lecture is a case where, I believe, research on learning firmly backs up the common experience that lecture rarely helps ...
18
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1answer
1k views

How much time to spend on a single question?

When I was self-studying as an undergraduate, I would spend up to two weeks working on a single problem or trying to understand a proof in Rudin's Principles of Mathematical Analysis. I realize now ...
18
votes
2answers
243 views

Pressure vs. Laissez-faire: Literature dealing with balance in university-classes

I am seeking for some pedagogical literature dealing with the following question: Imaging you have an average class in college/university: What is a good balance between Laissez-faire and pressure? ...
17
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7answers
7k views

How to deal with fast students without neglecting weaker ones

In my class, what often happens is that some smart students do problems faster than other students. And they are actually going well ahead of my course plan. While I am teaching to other students a ...
17
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5answers
418 views

Against introducing precise definitions first

After introducing eight different ways of viewing the derivative of a function (infinitesimal, symbolic, logical, geometric, rate, approximation, microscopic), Thurston, in his famous essay, ...
16
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3answers
2k views

“But I copied that from a book-reference you gave! How can that be wrong?”, or how can you grade homework which is solved poorly in some book?

Sometimes when assigning homework, it is possible that the homework can be found in some books or lecture notes, sometimes even referenced by yourself. As long as the proofs and arguments there are ...
14
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4answers
2k views

What is a wise reaction to a silly question?

I like students' nice questions too much (sometimes much more than their nice answers). It shows that they are thinking on what I am teaching and I am successful to make them curious about the subject....
14
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2answers
203 views

How can you determine the quality of your teaching, or someone else's?

The question in the title is immensely subjective and broad, and so I would like to narrow it to an answerable question: What measures are in common use by administrators and researchers in ...
14
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1answer
274 views

Spiral learning in real analysis

Has there been any attempts at developing a curriculum for teaching analysis (here let us be narrow and say real analysis in the sense of rigorous integral and differential calculus) in a multipass, ...
13
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4answers
288 views

Pedagogical advice/articles for graduate student teaching assistants

Are there any good pedagogical resources or articles that you would recommend to math graduate student teaching assistants (TAs)? Is there any sweeping advice that you would give a TA to improve their ...
12
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5answers
412 views

Use of mathematical humor suitable for motivation/explaination?

There are some intelligent jokes also explaining (in a very extreme way) how mathamticas works, for exameple A mathematician and a physicist are sitting in the teachers lounge. Suddenly the ...
12
votes
3answers
908 views

Mathematical education slang

Amir Asghari recently asked a question about mathematical slang. He was "looking for "non-mathematical" terms or phrases that are used to refer to mathematical objects (of any kind) mainly for ...
12
votes
3answers
171 views

What is the correlation between students' contentment and educational quality?

In order to evaluate new educational material the contentment of students with this material is often measured. However, just because a student is contented doesn't mean that he/she has actually ...
12
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3answers
2k views

What to do about a student's poor handwriting

Related but different: What is a good handwriting font for mathematics? A (former) student of mine (no longer! Thankfully passed his Trigonometry regents last week:) had a problem with his ...
12
votes
2answers
199 views

Do “overview” sections increase learning outcome?

I write a math textbook for which I want to make an overview chapter for each part of the textbook. In those overview chapters I want to motivate and introduce the new mathematical concepts. I also ...
12
votes
3answers
474 views

How to embed English into Calculus lessons

I am teaching abroad to non-native English speakers with a large variance of language skills. I teach both pre-calculus and AP calculus (AB & BC). For both of those classes I define the new ...
12
votes
1answer
170 views

How to choose the school for practising teaching?

I have worked with mathematics and physics in a university and I have taught on several courses. I recently applied to a teacher education program to get formal qualifications for teaching at ...
12
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3answers
245 views

Coaching Students to Use the Back of the Book Correctly

My high school students' textbooks have a full answer key in the back. Nearly all of my students make at least one of these mistakes: Not knowing that the answers are in the back of the book. Hence ...
11
votes
3answers
277 views

Teaching somebody else's class

How do you approach a class taught by somebody else? There are multiple reasons why one could find him/herself in such a situation: an instructor is sick, there is a scheduled rotation of teachers, ...
11
votes
2answers
266 views

Encourage students to strive for understanding despite looming exams

I am teaching an exercice section for a group of students who have (rather difficult and long) exams every two weeks. The students are focussed on the exams and barely willing to take the time to ...
11
votes
1answer
223 views

How can we help students learn to effectively take notes?

All students seem to accept that they should take notes during a lecture. However, they don't think about why they are doing this. Most students think that the reason to take notes is to have a ...
11
votes
1answer
234 views

Effective use of Moodle (or similar)

Currently we are using Moodle to manage our courses here. It has meant structuring the publication and turn in of homework, and has helped in distributing lecture notes and shorter documents to the ...
11
votes
3answers
230 views

How to balance short-term learning outcomes with long-term goals and ethical considerations

Most discussions about teaching often assume that the learning outcome is the important variable (compare evaluations, discussions about clickers, discussions about syllabi, etc.). However, I find ...
10
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3answers
337 views

Experiences with online courses, specially MOOC?

Online courses, particularly massive open online courses (MOOC) are the current rage. I can see that having students going through the material presented at their own pace, whenever they have time, ...
9
votes
5answers
445 views

What to do if there is a disagreement on fundamentals, e.g. axioms or inference rules?

Sometimes it happens that a person doesn't want to accept your argument, because he claims not all the inferences are valid. There's a famous example of Lewis Carroll, namely What the Tortoise Said to ...
9
votes
2answers
215 views

Pros and cons of randomised question generation

I am developing an assessment piece where the content is the same but the particular numbers are different for each student. It involves finding Triangle Centers given points using coordinate geometry....
8
votes
3answers
267 views

Should I teach a subject I don't like?

Recently I was asked to tutor some students individually on a basic course of Linear Programming, centered on all the "typical" introductory subjects like graphical methods, Simplex Algorithm and ...
7
votes
6answers
918 views

is it appropriate or beneficial to mention weird results in math?

Is it appropriate to mention weird/exciting results in math (or use as cautionary tales why one cannot apply mathematics naively) in say high school level? Examples of these results include the ...
7
votes
2answers
222 views

Ethics of looking at other proofs before submitting work

I am in my third year of undergraduate math, and now that classes are becoming more proof-based, many of my homework questions are proofs of relatively basic concepts that can be found with a quick ...
7
votes
3answers
294 views

Students iPads and mobile phones in class: good or distracting?

Nowadays almost everybody uses such devices almost every time! Particularly during my lectures in the class I can see some students who are working with their iPads and mobile phones. In such a ...
6
votes
2answers
279 views

How can I improve my problem solving/critical thinking skills and learn higher math?

I'm a rising sophomore in high school. So far, I've taken Algebra One, Two, and Geometry in school. I want to learn higher math such as precalculus/trigonometry, calculus, linear algebra, and more, so ...
6
votes
2answers
811 views

How can a math teacher manage a class when unprepared?

Sometimes a math teacher becomes sick or depressed like any other human and is not able to be prepared for lecture. Sometimes a math teacher spends too much time on a research project and does not ...
6
votes
2answers
193 views

Collaborative note taking

I have been encouraging my classmates to connect with me on Google Docs to work collaboratively on taking notes. Still, no takers though. I imagine that if I were a professor, I would attempt to get ...
6
votes
2answers
860 views

Disadvantages of working-backwards solutions

Is the 'start with the desired result and work backwards' problem solving method discouraged? I'm now in my 3rd university year and every physics problem has been solved using the 'given values, ...
6
votes
1answer
156 views

How can I make my notes more useful for future reference?

I was looking at this previous question on writing lecture notes he says: Most students think that the reason to take notes is to have a reference for later, but we know that the real reason to ...
5
votes
2answers
513 views

Bloom's taxonomy [closed]

I am starting out as a teacher and I'm confused about the verbs that we use in Bloom's taxonomy. I was looking at a lot of websites that provide verbs for Bloom's level that describe the skill ...
5
votes
1answer
164 views

Which mental model, Webb's DoK, CCSM's Aspects of Rigor, or Bloom's Taxonomy, is most useful?

Different people use different mental models, such as Webb's DoK (depth of knowledge), CCSM (Common Core State Standards) aspects of rigor, and Bloom's Taxonomy. At a high level, here's how I'm ...
4
votes
1answer
102 views

How to design a compact course without loss of main benefits of a usual course?

In some situations one need to design some compact courses for undergraduate/graduate students. I would like to know how to do it without any loss of generality, main ideas and any other important ...
4
votes
1answer
164 views

Erasing students' work - etiquette/guidelines?

What are some guidelines on erasing students' work such as on a chalkboard/whiteboard in a classroom or on paper in a private tutorial class? Usually this is for the parts of maths that involves ...
4
votes
2answers
130 views

suggestion for probability and stats text to suit my learning style.

I am of a mature aged learner and want to learn probability and statistics at a senior high school (k12) and undergraduate level for my own general understanding. I have discovered in the past that I ...
4
votes
0answers
127 views

What effect does giving numerical or written grades have on learning?

When I was in school, pupils were given numerical grades, or the equivalent of numerical grades but disguised as words, on their performance in various school subjects and also behaviour. A key ...