Questions tagged [mathematical-pedagogy]

for questions on general considerations and problems of teaching mathematics, i.e., issues specific to teaching mathematics yet relevant to various contexts and courses.

Filter by
Sorted by
Tagged with
8
votes
3answers
581 views

Changing students' approach to math

It's been quite a while since I was tutoring a high school student and even longer since not a gifted one. However, this time, something was amiss. I have asked him to show me how he does some ...
9
votes
5answers
453 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 ...
5
votes
3answers
252 views

The values of trigonometric ratios

Today I explained to my students how the value of $\sin(90°)$ is 1 by first drawing a right angled triangle and taking $90°$ as a reference angle, and told them that now $\sin(\theta)=\frac{\text{...
19
votes
3answers
1k views

What to do when a majority of students have insufficient mastery of the prerequisite material?

I'm currently teaching a second-semester calculus course in which a significant percentage of my students (over half) either tested into the course just out of high school, took a much easier first ...
13
votes
6answers
2k views

How do I Introduce Converse Theorems in Class?

I'm teaching geometry to grade 8 and 9 students, and I find that they often mistake theorems with their converses. For example, when I give them a 3, 4, 5 triangle and ask them to decide whether or ...
29
votes
7answers
961 views

How can we help students learn to write about their mathematics?

As a guiding example, imagine an undergraduate Calculus II course where students have to complete a guided "research project" and write a "paper" about their work. This can be a shockingly new ...
18
votes
2answers
3k views

Example “bad proofs”?

As a sidetrack in this question it came up that it is important to have students read texts (in particular proofs) critically. As examples it is nice to have correct proofs at hand (presumably in the ...
6
votes
2answers
637 views

Puzzles for Logic Courses featuring propositional logic and set theory?

Puzzles are interesting form of exercises. They help students to learn the teaching material in a funny way. Particularly in logic, puzzles could be very useful to show the complexity of the subject. ...
18
votes
5answers
3k views

Why use the word Quadratic?

While talking about different types of equations, a student in my class asked: Why we use the word quadratic to refer to second-degree equations? Here is some context: 1) Linear ($x^1$) equations ...
20
votes
2answers
802 views

Adult Mathematical Literacy

In short, my question is: What percentage of American adults know what a prime number is? Since this question is very specific, and my interests are a bit broader, I'd also be happy with: Is ...
7
votes
4answers
289 views

Multivariable limits

Multivariable limits are harder than their one-variable counterparts, and textbooks examples usually focus on limits that don't exist when approaching from different straight lines. This gives the ...
8
votes
1answer
184 views

Surfaces and volumes for vector calculus

We'll reach vector calculus very soon and the following problem presents itself: how can I help students distinguish curves, surfaces and volumes as separated entities? I've seen they hold the ...
12
votes
2answers
786 views

Definitions/proofs that allow “useless” cases?

I often see students confused/mystified by definitions (and proofs) that allow/consider "useless" cases. A case in point is the definition of a DFA (deterministic finite automaton), which allows ...
6
votes
4answers
468 views

Are puzzles a good way to interest pre-college students?

Nothing more quickly disspitates the myth that most people aren't interested in math than hitting them with a good puzzle and watching the instinctive human urge to solve it get to work. To be fair, ...
9
votes
5answers
486 views

Inspiration for Learning Math Pedagogy

I attended a really great university with excellent math professors, engaged and intelligent classmates, and great community. However, my education classes were horrendous to say the least. While I ...
7
votes
3answers
300 views

Writings about mathematics education by famous mathematicians [closed]

I'm interested to read writings about mathematics education written by famous mathematicians. By famous mathematicians, I mean roughly anybody with a result or object named after them. I'm not sure ...
18
votes
3answers
844 views

How to deal with very motivated students having “off-topic” interests?

There are some very motivated students who are very interested in math (in general), where the interest takes over most of their time. The problem is that they don't put enough time in the lecture ...
34
votes
2answers
2k views

What does math education research know about difficulty vs. effectiveness?

I've asked basically the same question previously on on math.SE, then cogsci.SE without much response, surely here is the place to ask this. As anecdotal evidence is plentiful, but unfortunately ...
14
votes
4answers
1k views

When should I say “nothing is as it seems”?

"Intuition" is the best friend and worse enemy of mathematicians! Sometimes using intuitive arguments could be very helpful to understand the nature of a phenomenon. Many of the deepest true ...
9
votes
1answer
355 views

The Lord of the Fields [closed]

In our department, something is growing up into the darkness. A dark power which seduces my colleagues and their students one by one and leads them into the shadow. Those whose hearts are corrupted ...
25
votes
2answers
1k views

Students who know high-level math before going to college

There is a high school in the city I live in which has some high-level math courses in their curriculum. It's a special math class mentored by some university lecturers, and the children basically do ...
7
votes
4answers
2k views

Physics in Linear Algebra

Talking about physical phenomena related to a particular field of mathematics can be interesting for students and might further motivate their study of the subject. For instance, there are ...
7
votes
3answers
351 views

Can music improve math abilities?

This question is inspired by a set of questions at the end of Timothy Gowers' book: Mathematics: A Very Short Introduction, Oxford University Press, 2002. The possible relation between mathematics ...
5
votes
2answers
136 views

How can one deal with classes split up (in terms of previous knowledge)?

Imagine a class which is split completey regarding previous knowledge which is in some way needed for the class. How can you deal with such a class? How can you - without giving too much workload to ...
7
votes
6answers
2k views

Ockham's Razor & Mathematical Proofs

Occam's Razor (also written as Ockham's razor from William of Ockham (c. 1287 – 1347), and in Latin lex parsimoniae) is a principle of parsimony, economy, or succinctness used in problem-solving. It ...
11
votes
1answer
531 views

Ideological Teaching in Logic Courses

Logic and its sub-fields are closely related to philosophy. There is an undeniable mutual interaction between one's philosophical point of view and his/her approach in teaching mathematical logic. In ...
5
votes
4answers
848 views

Mathematics Education in Africa

It seems there are few well-known professional mathematicians in Africa. It is mainly because of the poor quality of elementary/undergraduate mathematics education in African countries. Question 1. ...
6
votes
0answers
130 views

How to nurture an unprepared student [closed]

What and how much scaffolding is necessary for a motivated undergraduate student who doesn't have the ideal prerequesites for work? This could be for a number of reasons: He didn't realize the ...
6
votes
1answer
123 views

Is there a tag/competence classification for mathematics education?

I am looking for both a course hierarchy of mathematics education (for example, Galois theory is part of abstract algebra) and a representation of all competences involved in learning mathematics (...
7
votes
1answer
148 views

Philosophical Subjects in Logic Courses

Many of the notions, methods and theorems of the mathematical logic and its different sub-fields like set theory, model theory, etc. are closely related to some philosophical background. I believe ...
8
votes
1answer
355 views

How formal should I be as a university teacher? [closed]

I try to be not only a good teacher but also a good friend for my students. I tell them that they can call me by my first name even in the formal colloquiums. I give them a personal phone number to ...
15
votes
5answers
1k views

Is Peer Instruction suited to mathematics classroom?

Peer Instruction is a method developed by Eric Mazur in Harvard, designed with a student-centered approach in mind. In a nutshell, the core of the method is that when presented with a problem, ...
4
votes
1answer
109 views

Would chapter mini-projects be more beneficial than weekly homework for large classes n>100

I am trying something new this semester in my Calculus classes. I currently have over 400 students, and there is no way I can find the time to grade and give constructive criticism on all the ...
23
votes
4answers
2k views

Non-answerable questions on exam: What to do?

What is a good strategy when you realize (e.g. while grading the exam) that a question on an exam was incomplete/wrong? More concretely: If it is decided that additional points should be given: How ...
25
votes
3answers
814 views

Counterexamples in first year calculus

Many believe (I think rightly so) that the presentation of counterexamples should play an important role in the teaching upper level mathematics courses such as real analysis and topology. ...

1
4 5 6 7
8