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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6answers
2k views

Is there a good way to explain determinants in an elementary linear algebra class?

Many colleges offer an an elementary linear algebra class for sophomore math, science, and economics majors. Such a class typically covers a chapter on determinants, including the following aspects: ...
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3answers
273 views

Using Several Textbooks in a Course

Sometimes a teacher prefers to use several textbooks in his/her courses because he/she thinks the arguments of each book is better in a part of course material or there is no comprehensive textbook in ...
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1answer
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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 ...
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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 ...
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4answers
880 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. ...
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6answers
963 views

How to present $\Bbb Z/n\Bbb Z$ to highschool level audience

I have the oportunity to talk to a highschool class about mathematics, the topic I got to present are the integers modulo $n$, ie, $\Bbb Z/n\Bbb Z$ , however I don't want to be very heavy and formal, ...
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6answers
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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 ...
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5answers
772 views

Descriptive Thinking vs. Formal Writing

Sometimes I come across some exam answers which describe a proof sketch or a counterexample very well but are not written formally. Such proofs show that a particular student understands the general ...
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3answers
364 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 ...
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3answers
546 views

Is there any math text reader device to help children who cannot see?

I don't teach school math but as a part of my voluntary activities in some NGOs, sometimes I am in this special situation. When I was in a school for special children who cannot see I came across a ...
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6answers
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How to teach math to someone who is neither [really] willing nor able to understand it?

I'm not a teacher, I am a student. But in math, I am one of the best ones in my class so sometimes other people will ask me to explain stuff to them. And usually it works quite well: If I understood ...
8
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1answer
149 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 ...
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Notation Conflict between Teachers and Textbooks

In mathematics notation plays an important role in clarifying the subject. A bad notation could be confusing. Recently I use a logic textbook which has a very nice approach and content but an ...
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11answers
8k views

Whence the “everything is linear” phenomenon, and what can we do about it?

$$ \color{red}{(a+b)^2 = a^2+b^2}$$ $$ \color{red}{\sqrt{x^4+y^4} = x^2+y^2} $$ $$ \color{red}{e^{t^2+C} = e^{t^2}+e^C}$$ I've observed this phenomenon -- wherein, implicitly, students say, "...
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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 ...
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6answers
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Is there any difference between teaching calculus for math and engineering students?

In our university both math and engineering students attend in the same calculus classes. There are arguments in our department about the possible influences of this approach on students. It seems ...
34
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2answers
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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 ...
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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 ...
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12answers
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Mathematical problems for preschoolers

What are some mathematical problems that are feasible for preschool children to stimulate their intellectual development? There are multiple natural laws that are not apparent to them, for example: ...
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1answer
110 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 ...
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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 ...
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5answers
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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, ...
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9answers
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How can mathematics educators encourage innovation and creativity?

Almost by definition, innovation requires that things be done differently than established custom has it, and comes from the young more often than from the old. In a field as old and established as ...
5
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3answers
123 views

Three approaches to regular languages

Disclaimer: This is a theoretical computer-science question to see how the community will react, relevant meta discussion can be found here. I picked the topic to be formal languages, as question ...
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5answers
598 views

Presenting a solution with a stroke of genius

When presenting the $3$-dimensional proof of the Desargues' theorem an average student might have, speaking informally, a "WTF moment". It is an extreme case, but a similar situation could happen in ...
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5answers
1k views

Questions with “round” answers only?

Textbook writers are blessed with only solving problems with neat answers. Numerical coefficients are small integers, many terms cancel, polynomials split into simple factors, angles have ...
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6answers
663 views

Would taking 5 minutes to explain the history behind a mathematical idea help stimulate learning the idea?

I read a paper in my "Research Issues in Mathematical Education" class that I have applied to the Undergraduate Calculus I and Calculus II class that I teach. I take five minutes to explain the ...
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7answers
978 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 ...
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14answers
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Revisiting topics from previous courses

I teach calculus to students who have almost all taken calculus before. (Primarily first-year college students who took calculus in high school but didn't perform well enough to skip the course.) ...
9
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4answers
239 views

Using original texts while introducing new concepts in class

I'm still a undergrad math student, and my experience in education in math is very limited, however I've been lucky enough to meet teachers that encourage students who are interested in teaching, like ...
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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 (...
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11answers
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Looking for simple “interesting” math problems that cannot be easily solved without algebra

I often find students who dislike algebra. They prefer to work with numbers in solving problems. I believe there are many problems that are hard to solve without algebra. For example: Finding the ...
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3answers
7k views

Good examples of proof by contradiction?

In later courses on automata theory, many students just seem incapable of getting a proof that a language isn't regular right, be it using the pumping lemma (see also the many questions on the matter ...
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25answers
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Good, simple examples of induction?

Many examples of induction are silly, in that there are more natural methods available. Could you please post examples of induction, where it is required, and which are simple enough as examples in a ...
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3answers
469 views

Why teach back substitution with row reduction?

Many linear algebra books include two versions of row reduction for solving systems of linear equations: (1) Reduce to echelon form, and then use back substitution. (2) Reduce to reduced echelon ...
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6answers
802 views

How can we help students who are very anxious about math?

In many parts of the world, the majority of the population is uncomfortable with math. In a few countries this is not the case. We would do well to change our education systems to promote a healthier ...
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4answers
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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 ...
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8answers
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Knowing mathematics does not translate to knowing to teach mathematics. Why?

Many brilliant mathematicians seem to make average or even poor classroom teachers. Is this an accurate assessment? Has there been any research to explain the phenomena? What is the difference ...
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5answers
345 views

Is required reading of the text effective, and how can it be assessed?

This will likely depend on the class, of course. But I've asked calculus students in the past if (a) they regularly read the textbook and (b) whether this is helpful for them and (c) whether they like ...
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2answers
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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 ...
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3answers
284 views

Any suggestions on how to approach recursion and induction?

Much mathematics is intimately tied to recursion, be it in definitions (like factorials and integer powers) and proofs by induction. This is also very relevant in computer science and programming. ...
18
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3answers
906 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 ...
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3answers
841 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. ...

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