# 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.

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### 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 ...
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 ...
252 views

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 $\sin(\theta)=\frac{\text{... 3answers 1k views ### What to do when a majority of students have insufficient mastery of the prerequisite material? I'm currently teaching a second-semester calculus course in which a significant percentage of my students (over half) either tested into the course just out of high school, took a much easier first ... 6answers 2k views ### How do I Introduce Converse Theorems in Class? I'm teaching geometry to grade 8 and 9 students, and I find that they often mistake theorems with their converses. For example, when I give them a 3, 4, 5 triangle and ask them to decide whether or ... 7answers 961 views ### How can we help students learn to write about their mathematics? As a guiding example, imagine an undergraduate Calculus II course where students have to complete a guided "research project" and write a "paper" about their work. This can be a shockingly new ... 2answers 3k views ### Example “bad proofs”? As a sidetrack in this question it came up that it is important to have students read texts (in particular proofs) critically. As examples it is nice to have correct proofs at hand (presumably in the ... 2answers 637 views ### Puzzles for Logic Courses featuring propositional logic and set theory? Puzzles are interesting form of exercises. They help students to learn the teaching material in a funny way. Particularly in logic, puzzles could be very useful to show the complexity of the subject. ... 5answers 3k views ### Why use the word Quadratic? While talking about different types of equations, a student in my class asked: Why we use the word quadratic to refer to second-degree equations? Here is some context: 1) Linear ($x^1\$) equations ...
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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 ...
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### 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 ...
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 ...
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 ...
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, ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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. ...
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 ...
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 (...
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### 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 ...
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 ...
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, ...
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 ...