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.
376
questions
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13 views
Teaching aid for online mathematics course
Crossposting from the math.stackexchange (Question)
Online classes will start again as the semester will start, I bought an XP-Pen deco 03 to help me with online teaching. I will be teaching ...
6
votes
1answer
102 views
Literature related to Fear of notation and hazily-appeared writing in Mathematics
I am looking for literature related to fear of notation in mathematics.
It is even heard that the font size and font type make a reader reluctant to study mathematical literature, often lecture notes,...
5
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2answers
214 views
Appealing thinking games, that are easy to make; easy to learn, and easy to play
$\color{Green}{\text{My Question in short}}$:
Unprovable claim: Someone who is familiar with 100 thinking-games, and plays 30 of them reasonably well, is more prepared to go to math than the average ...
23
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7answers
7k views
If you warn of common mistakes, how do you prevent putting the idea into someone's mind
For example, if you're teaching integration of $\int \frac{dx}{1+x^2}$, would you mention the common wrong answer of $\ln\left(1+x^2\right)+C$?
--
For myself, I very rarely mention common mistakes ...
5
votes
2answers
196 views
What is “mastery” in a mathematical topic?
This question was prompted by looking at Khan Academy's website to see how a comprehensive lecture series could be done and often I see the word, "mastery". To me, I'd think mastery is ...
7
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2answers
411 views
Logic and proofs in secondary school
Inspired by the question When do college students learn rigorous proofs?, I became curious when pupils in secondary schools learn about proofs, what kinds of proofs they are, how rigorously they are ...
8
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2answers
214 views
Math Education for Students who use Right-to-Left Written Languages
Does anyone know of any studies or have personal experience dealing with difficulties (if any) faced by students studying mathematics if they come from countries which use languages written from right-...
6
votes
5answers
198 views
Concrete way to teach addition and subtraction of fractions
I am teaching 4th-grade kids. The topic is Fraction. Basic understanding of a fraction as a part of the whole and as part of the collection is clear to the kids. Several concrete ways exist to teach ...
5
votes
3answers
305 views
Looking for a HIERARCHY of math subjects
If you were to "map" mathematics onto a tree structure where the top is "Mathematics", and then below it the different branches, then sub-branches, etc.
What do you suggest is a good structure, for ...
18
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6answers
5k views
How rigorous should high school calculus be?
In the UK, calculus taught in secondary school focuses mainly on computation of derivatives and integrals and solving simple differential equations. There is a small amount of discussion about limits ...
3
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2answers
166 views
Has a List of Fundamental Mathematical Skills been compiled?
... in the literature.
I an wondering is there a (considered) list of "fundamental mathematical skills".
I am not sure can I give a solid definition of "fundamental mathematical skill". What I mean ...
4
votes
1answer
140 views
Are there any online question bank of mathematics questions?
I know Dr. Martin Greenhow and his team of Brunel University London have developed online questions and I have used some of these at the following url: http://maths-for-all.co.uk/engineering-...
3
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1answer
157 views
The spatial thinking course for primary school - what to use?
We're planning to run the project for first two grades of the elementary school kids, in which we want to facilitate the spatial thinking development along with the regular arithmetic course and make ...
2
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2answers
193 views
How actually are prime numbers taught in elementary school in United States and how easily do students learn what they're being taught about them?
I read the question https://math.stackexchange.com/questions/1593091/how-to-explain-why-study-prime-numbers-to-5th-graders and according to the body of the question, some students sigh. Also according ...
4
votes
2answers
186 views
What would you recommend for the math thinking course for school?
We're going to make a new math course for kids as intermediary between middle and high school with math profile (for preparation to entrance exams to high school), and before the main part (arithmetic,...
7
votes
1answer
188 views
Let P be a polygon
I've encountered the following misunderstanding.
I pose a question (to undergraduates in the U.S.), for example:
Let $P$ be a polygon of $n$ vertices.
Is it true that every triangulation of $P$
...
20
votes
1answer
310 views
Taxonomy of bad proofs
I am interested in finding examples of poorly written proofs that exemplify the types of mistakes made by undergraduate students in their first year or two of writing proofs. I am interested both in ...
2
votes
0answers
76 views
Is There Book on Collection of Theorems? [closed]
For example, there is a book titled "Synopsis of Elementary Results in Pure and Applied Mathematics: Containing Propositions, Formulae, And Methods Of Analysis, With Abridged Demonstrations" (...
2
votes
3answers
129 views
How to teach integrals motivated by the work done in moving an object?
I am now teaching Calculus of several variables this semester. In apllications of integrals, the problem of finding the work done in moving an object under a force $F$ is one of the most common ...
6
votes
3answers
344 views
Is there a numerical base that is in any way “better” for simple mathematical calculations than others?
I want to know if there are any numerical bases that are notably well-suited for humans to learn and use at an elementary or grade-school level.
I know that different numerical bases (i.e. decimal/...
5
votes
1answer
174 views
Misdirected, Side-Tracked, and Distorted Ramanujan: Problems in Basic Math Education?
I read that-
“The tragedy of Ramanujan was not that he died young, but that his
genius was misdirected, side-tracked, and to a certain extent :
distorted.
The years between 18 and 25 are ...
5
votes
4answers
223 views
How to convince parents that Mathematical puzzles/games help students in their academics too
I write content and conduct workshops for an education firm and also in schools where I try to make them realise how beautifully mathematics and rational thinking complement each other (on elementary ...
6
votes
3answers
341 views
How do I convince my teachers that a book on maths must focus on conceptual understanding?
I am a senior teacher at this school. We have to select the textbooks for the upcoming session. I am proposing that we have to select books (in maths) that focus more on conceptual understanding and ...
14
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8answers
3k views
Should high school teachers say “real numbers” before teaching complex numbers?
Before complex numbers are introduced in senior high school courses, should we emphasise that solutions (e.g. to quadratic equations) are real solutions?
If we do, then when non-real numbers finally ...
2
votes
2answers
198 views
How should one approach the concept of “plus or minus”, such as in the numerator of the quadratic formula?
The numerator is structured like:
$$(-b)\pm\sqrt{b^2- 4ac}.$$
Is it confusing or acceptable to distinguish between the following two things?
An idiom; and
What is or seems to be a compositionally ...
20
votes
14answers
7k views
Why is it possible to teach real numbers before even rigorously defining them?
In mathematics, one can hardly study any mathematical concept unless it is clearly and rigorously defined. For example, without the definition the fundamental group, it is almost impossible to teach ...
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2answers
104 views
Should the limits of one system of elementary set theory be the limits of a student's mathematical world? [closed]
In teaching elementary set theory, suppose we refrain from emphasizing historical decisions that were made in theory construction.
Is there a danger that students may see the mathematical language ...
7
votes
5answers
2k views
Teaching asymptotic notations at the beginning of calculus [duplicate]
I'm thinking about teaching calculus by firstly introducing the asymptotic notations (big-Oh, little-oh, and $\sim$), secondly explaining their "arithmetic" (things like how to sum little-oh's and ...
6
votes
1answer
849 views
Why is it popular to teach modulus via the example of mod 12 and analogue clocks?
Why is it popular to teach modulus via the example of mod 12 and analogue clocks rather than rectangles or tables that have a finite number of columns in each row, and infinitely many rows?
It's ...
6
votes
3answers
159 views
(Riemann integrability) How do you explain this to a high school student?
The following question was in a high school teacher's guide:
Let $f\colon\mathbb{R}\rightarrow\mathbb{R}$ defined by
$$f(x)=\begin{cases} x & x\in\mathbb{R}\setminus\mathbb{Q}\\
2x & x\...
10
votes
5answers
265 views
Pedagogical considerations behind current order of presentation of trigonometry
A pre-calculus book (Precalculus ed 1 By Miller and Gerken), presents trigonometry in the following order:
1- Angles
2- Trigonometric functions defined on the unit circle
3- Right triangle ...
1
vote
2answers
76 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 ...
4
votes
2answers
145 views
Finland's performance on international competitions
Why it is said that Finland has a particularly good education system, but Finland's performance on international mathematics competitions is quite often at relatively intermediate level?
9
votes
1answer
426 views
Is there research on the efficacy of taking good notes in math class?
I teach at community college, and have often encountered others talking about helping students learn to take good notes. I have never felt that I took good notes as a student. I was too busy thinking ...
8
votes
4answers
223 views
Should school syllabus include chapters partially?
In my locality, many schools have this tendency to partially include this and that chapter in the syllabus (for almost every subject). For example, (most of the chapters are subdivided in two or more ...
3
votes
2answers
376 views
Enlighten younger students about the concept of “procedural justice” in mathematics?
I am tutoring a 16-year-old student from my home country (in Asia) in, roughly speaking, precalculus. I would like to give him a feeling of procedural justice, so to speak, in modern mathematics, ...
6
votes
4answers
346 views
Ideas for the introduction of the derivative?
I want to introduce to my class to the derivative, but I am still searching for a good, realistic context that isn't too hard to understand, without seeming to be contrived. Do you have an ideas for ...
5
votes
1answer
286 views
Propositional and predicate logic, with quantifiers: Is there any research when it is ideal to explicitly teach in mathematics education?
In terms of helping students to understand propositional and predicate logic, with quantifiers, is there any research regarding when it is most advantageous for students studying mathematics, to first ...
2
votes
0answers
107 views
A compelling example of what complex numbers are for, before teaching them [duplicate]
When talking to kids before they are taught complex numbers, I would really like to give some examples of why it will be exciting to learn them. I am comfortable explaining the intellectual ...
4
votes
7answers
346 views
Category mistakes regarding symbols and their impact on math (mis) understanding. ( Object symbol/ sentence symbol confusion)
A friend of mine that teaches math has made many times the following experiment :
drawing two circles on the blackboard representing two sets A and B such that A and B are disjoint
writing on the ...
8
votes
3answers
291 views
Solutions to exercises
I am teaching the exercise sessions for a 3rd year algebra course (intro to field theory, Galois theory and Algebraic geometry). The format of the course is as follows: for every 2 hour lecture by the ...
3
votes
1answer
148 views
Naming arbitrary constants: subscripts, primes, or just more letters?
When choosing names for arbitrary constants either during a lesson or while working with a single student, should one use$\{n_1,n_2,n_3,\dotsc\}$ or $\{n, n', n'', \dotsc\}$ or $\{a,b,c,\dotsc\}$? Is ...
9
votes
2answers
233 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....
2
votes
0answers
182 views
why don't we do labs in/for math?
(this is in the US and at a high school level)
why don't we dedicate a day of the week each week to do a lab for math for exploration? I mean we already do that for Earth Science, Physics, Chemistry ...
5
votes
1answer
240 views
How is math taught in elementry school in Finland?
I read on the internet that Finland has the best education system in the world at that in Finland, students are taught to love mistakes and that's how they learn and become smarter. I could not find ...
6
votes
2answers
207 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 ...
5
votes
0answers
243 views
Mimic lecturing on blackboard, but facing audience [closed]
I teach mathematics at MSc and PhD levels. My preferred method of teaching is old-fashioned: talking and writing on the blackboard at the same time.
Why? Because it has many advantages:
Handwriting: ...
2
votes
2answers
107 views
Are questions on overlapping solids of revolutions without prior definitions and instructions fair given that there are divided interpretations?
If words of command are not clear and distinct, if orders are not thoroughly understood, the general is to blame. But if his orders are clear, and the soldiers nevertheless disobey, then it is the ...
8
votes
2answers
147 views
Math Lessons with Two Parts and a Combination
This is fairly open ended, so I understand if people consider this to be off-topic.
I'm interested in creating math lessons where two groups each learn how to use a different simple math skill, and ...
4
votes
3answers
234 views
How to explain the motivation of parentheses in addition, subtraction and multiplication?
My kid, 5 years old, knows addition, subtraction and multiplication now, of course, in a basic level.
Also he understands that parentheses means "whichever inside shall be computed first".
When I ...
