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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How do you teach the order of a series of events?

I’m looking for research-backed methods for teaching which order a series of events are in. Notably, ordinality in my case is far more important than cardinality. Even better if the technique allows ...
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3 votes
0 answers
137 views

Worldwide standard textbooks vs textbooks from one's home country vs lecture notes by various people - pros and cons

So far I've had three types of professors in my undergrad studies when it comes to choosing the main text for the course: Type A: these are the professors who pick some standard textbook(s) in English ...
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4 votes
1 answer
287 views

is it beneficial to encourage high school students to conduct their own 'research' in mathematics?

Is it good idea to encourage students to look up more about particular topics that interest them? The idea is that I don't think they will understand how to read math literature. for example, if a ...
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2 votes
0 answers
156 views

Peter Liljedahl "Thinking Classroom" pedagogy: what is evidence for its effectiveness?

Peter Liljedahl discusses a lot about "thinking classrooms". There is research and books, which show, that his methods transform classes from "non-thinking" to "thinking"....
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6 votes
2 answers
220 views

Measuring the effectiveness of one-on-one instruction?

I've been recently thinking a lot about what would be the "best possible instruction method", and in regards to that, I've been drawn the question of what would be possible if a student had ...
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  • 684
4 votes
2 answers
605 views

Advice: How to cite literature for high-school students?

Suppose one were writing a book aimed at high-school students (and their teachers), where "high-school" in the US means grades 9,10,11,12 (where college/university starts at 13). The book is ...
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7 votes
4 answers
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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26 votes
6 answers
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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  • 687
1 vote
2 answers
98 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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10 votes
2 answers
278 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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  • 845
6 votes
2 answers
224 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 ...
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3 votes
1 answer
72 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 ...
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4 votes
0 answers
141 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 ...
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7 votes
6 answers
975 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 ...
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  • 769
13 votes
4 answers
316 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 ...
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  • 4,362
2 votes
1 answer
138 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 ...
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  • 593
4 votes
0 answers
113 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 ...
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  • 141
6 votes
2 answers
354 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 ...
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  • 161
5 votes
1 answer
186 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 ...
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  • 526
5 votes
1 answer
260 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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9 votes
3 answers
452 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 ...
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5 votes
2 answers
669 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 ...
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  • 151
2 votes
3 answers
292 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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  • 121
7 votes
2 answers
258 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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  • 173
17 votes
5 answers
492 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, ...
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12 votes
3 answers
190 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 ...
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4 votes
2 answers
140 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 ...
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12 votes
2 answers
213 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 ...
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12 votes
3 answers
1k 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 ...
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4 votes
0 answers
246 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. ...
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23 votes
3 answers
534 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 ...
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14 votes
1 answer
336 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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  • 2,671
2 votes
0 answers
55 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 ...
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  • 4,820
13 votes
1 answer
189 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 ...
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15 votes
2 answers
235 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 ...
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3 votes
3 answers
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 ...
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6 votes
2 answers
1k 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, ...
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  • 163
18 votes
3 answers
397 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 ...
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  • 1,076
6 votes
1 answer
362 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 ...
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12 votes
3 answers
561 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 ...
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  • 335
19 votes
11 answers
2k 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 that ...
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  • 1,093
12 votes
3 answers
273 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 ...
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  • 3,765
3 votes
0 answers
275 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 (...
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  • 905
3 votes
2 answers
272 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 ...
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3 votes
2 answers
844 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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7 votes
3 answers
309 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 ...
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6 votes
2 answers
839 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 ...
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4 votes
1 answer
108 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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13 votes
3 answers
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 ...
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  • 921
9 votes
5 answers
484 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 ...
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