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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5
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4answers
1k views

Acceptability of creative questions in assessments

I am a math teacher and I have been for a decade now. One of the foundations of my philosophical approach to teaching has to do with Synthesis. For the purposes of this query, I consider Synthesis to ...
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6answers
2k views

What is the quantitative data on effectiveness of “modern” teaching methods?

What research has been done on how much and in what circumstances various non-lecture types of teching are effective with regards to student knowledge and performance? Meta/review studies preferred ...
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2answers
74 views

Retain problems and combat regression in learning

Regressive Learning It's a really stressful situation. I can achieve but not retain expertise in maths problems. History 6 months back, I studied integration in Calculus at college. I learnt it all ...
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2answers
225 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....
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2answers
201 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 ...
3
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1answer
67 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 ...
4
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0answers
131 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
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6answers
928 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
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4answers
293 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
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1answer
124 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
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0answers
94 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
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2answers
288 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
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1answer
165 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
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1answer
185 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 ...
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3answers
305 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
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2answers
556 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
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3answers
163 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) ...
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2answers
224 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 ...
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5answers
422 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
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3answers
180 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
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2answers
131 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
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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
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3answers
920 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 ...
4
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0answers
226 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
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3answers
467 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
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1answer
287 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, ...
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0answers
53 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
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1answer
176 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
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2answers
205 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
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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
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2answers
909 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
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3answers
337 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
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1answer
172 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
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3answers
492 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
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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 ...
12
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3answers
254 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
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0answers
250 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
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2answers
223 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
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2answers
788 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. ...
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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
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2answers
813 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
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1answer
104 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 ...
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3answers
3k 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
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5answers
449 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
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1answer
235 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 ...
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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 ...
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7answers
8k 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
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1answer
227 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 ...
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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 ...
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2answers
268 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 ...