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.

7
votes
2answers
182 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....
4
votes
2answers
155 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 ...
2
votes
1answer
62 views

Practical Implication for Correlation (Lay individual vs Scholarly Group)

Can you please explain or provide resources that explain this issue (esp. to a lay audience): How to understand the significance of a co-relation number that studies (esp. meta-analyses) produce. The ...
3
votes
0answers
115 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 ...
7
votes
6answers
902 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 ...
13
votes
4answers
275 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 ...
2
votes
1answer
117 views

Reference or term for connected sage-on-the-stage?

I heard that there is evidence that a "connected sage-on-the-stage" teaching style is at least as effective as guide-on-the-side / flipped classrooms. I have been unable to find significant references ...
4
votes
0answers
74 views

Research on how to teach math to children - what proven approaches are there to teaching math effectively? [closed]

I posted a related question on the Math.SE, but was directed here where I'm asking an similar but different question. I've been tasked with helping to redesign a math curriculum for an enrichment ...
6
votes
2answers
260 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 ...
4
votes
1answer
144 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 ...
5
votes
1answer
149 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 ...
8
votes
3answers
254 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 ...
5
votes
2answers
453 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 ...
2
votes
3answers
143 views

Free, open-source, customizable, interactive math books with gaming elements

Free, open-source, customizable, interactive books games. Most kids find computer games much more fun than learning math. Many programmers (including some programmers with 5-6 digit monthly salaries) ...
7
votes
2answers
221 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 ...
17
votes
5answers
404 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, ...
12
votes
3answers
169 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 ...
4
votes
2answers
128 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 ...
12
votes
2answers
197 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
900 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 ...
3
votes
0answers
222 views

And the joke was NOT a joke [closed]

This is not a question; so I perfectly understand that it could be deleted almost immediately. Yesterday, I was attending a New Year eve party and I was introduced to a young and brilliant lawyer. ...
22
votes
3answers
445 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 ...
14
votes
1answer
263 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, ...
2
votes
0answers
50 views

Lancasterian/Monitorial system at a secondary level?

While getting stuff ready for the soon-to-be-here school year, I came across Joe Lancaster and the Monitorial system, where older students who have mastered certain content areas are charged with ...
12
votes
1answer
166 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 ...
14
votes
2answers
196 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 ...
3
votes
3answers
2k views

Funny things students say when learning mathematics [closed]

I apologize for the "softness" of this enquiry, but as mathematics educators I believe these are some of the most rewarding moments of teaching our discipline. Having said that, may I share with you a ...
6
votes
2answers
730 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, ...
18
votes
3answers
321 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 ...
6
votes
1answer
141 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 ...
12
votes
3answers
470 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 ...
19
votes
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 ...
12
votes
3answers
240 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 ...
3
votes
0answers
238 views

Learning a topic deeply [closed]

I am currently a "self-studier", so the manner in which I learn is I have a textbook and I work through it in a relatively linear fashion. As I am introduced to new concepts I ask questions (...
3
votes
2answers
213 views

What is the true generalization of a notion?

In mathematics we usually can generalize a particular notion in many different ways. Some of these generalizations could be contradictory. When I teach maths/logic to my students I usually encourage ...
3
votes
2answers
769 views

Examples of cultural limitations on math education

Based on Maggie Koerth-Baker's article, "What do Christian fundamentalists have against set theory?", it seems there are some parts of culture which put some restrictions on math education. ...
7
votes
3answers
293 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
804 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 ...
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 ...
12
votes
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 ...
9
votes
5answers
442 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 ...
11
votes
1answer
229 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 ...
18
votes
1answer
935 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 ...
17
votes
7answers
6k 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 ...
11
votes
1answer
215 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 ...
47
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 ...
11
votes
2answers
258 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
3answers
224 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 ...
31
votes
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 ...
16
votes
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 ...