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.
391
questions
7
votes
2answers
152 views
How to teach the Pythagorean theorem in a satisfying way to high school students?
I've been pretty dissatisfied with the way the Pythagorean theorem is usually taught, mainly for two reasons:
The chosen proof feels like magic and I don't feel like I have a better understanding of ...
13
votes
3answers
2k views
Finding the Balance in a Math Question (Teaching)
As we try to work and teach in the midst of this pandemic, some problems arise when making online math exams. My question is simple: What could be an interesting basic differentiation question such ...
3
votes
2answers
184 views
How do we explain to a little child that a date in 2020 and a date in 2021 are not necessarily a year apart?
I talked with my friend on December 29 2020. Then I talked with him again on January 03, 2021.
Q: What was the year when you last talked with your friend?
A: 2021.
Q: And what was the year the ...
6
votes
1answer
234 views
Do my students know elementary algebra; do they just use online calculators or external help; and is this ok?
Background
I know the question in the title is very broad so I will try to explain it as succinctly as I can. Half my time is spent on as a researcher on didactics, while the other half is devoted to ...
8
votes
7answers
1k views
Advice on teaching abstract algebra and logic to high-school students
NOTE:
This question will soon be duplicated, as I didn't make clear that I was a high school sophmore in the beginning. At first I thought it didn't matter, and somewhat arrogant to mention, but in ...
11
votes
4answers
414 views
How do you teach students about the concept of a proof?
I get this question a lot from new students who are taking their first proof-based math class. They are struggling because they don't have that fluency with proofs, to begin with. They don't know ...
1
vote
1answer
68 views
Resources for Unit Rates
I am currently mentoring my little brother in mathematics. There is an issue with the pedagogy of unit rates. For example when given the following concept " 11.00 U.S. Dollars to 20 Planet X ...
1
vote
0answers
180 views
Do you avoid examples or test questions that showcase an algorithmic plug'n'chug approach?
If we accept that there's not much learning from doing the "same" questions, like find the derivative of $x^2$, and $x^3$, and $x^4$ due to the algorithmic way of how it's done, then what ...
2
votes
2answers
536 views
Teaching Mathematics to a Younger Sibling
I always wanted to teach my siblings mathematics, and one, ten years of age, is particularly eager. For the purposes of specializing recommendations, I will add he can use arithmetic up to ...
0
votes
0answers
89 views
Prerequisites to study Laplace Transform completely?
Hello to all the professors who read this. I'm an electrical engineering undergrad student. I wanted to ask for advice on what I should learn beforehand to fully grasp the Laplace transform. I also ...
-2
votes
1answer
58 views
Relational understanding for a specific topic
I want to aproach the undertanding of the trigonometric function based on the concept of relacional undertanding, but I have problems to came up with and problemic situation for it. I mean I don´t ...
1
vote
2answers
213 views
How can I teach $\frac{300}{200}$ to 10 years old students while s\he knows canceling the zeroes rule?
I am teaching math to a 10 year old student. He learned that
$$\frac{300}{100}=\require{cancel}\frac{3\cancel{00}}{1\cancel{00}}=3$$
and
$$\frac{6000}{300}=\require{cancel}\frac{60\cancel{00}}{3\...
2
votes
0answers
69 views
Math websites/apps for high school students
I am undergraduate math student who is interested in being a high school math teacher. I have been given an assignment to present to my class (for a total of about 20 minutes) a teaching tool or a ...
9
votes
1answer
259 views
If a computer could be programmed to do a math test, then should those tests be changed?
Not only do calculators have solving capabilities, but some computer programs or websites also provide step-by-step solutions to questions (here is WolframAlpha's). Although I understand a logical ...
8
votes
3answers
301 views
Transitioning proof based math courses online
I'd love to learn from anyone's recent experiences teaching online proof based math courses, especially those that have a large group of students who will be working asynchronously. My usual proof ...
1
vote
0answers
64 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 ...
9
votes
2answers
490 views
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
votes
2answers
248 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 ...
32
votes
7answers
9k views
How can teachers warn students about common mistakes without causing the student to make the mistake?
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
213 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 ...
8
votes
2answers
485 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
votes
2answers
220 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
257 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 ...
6
votes
3answers
457 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
votes
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
votes
2answers
170 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
145 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
votes
1answer
165 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 ...
1
vote
2answers
235 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
190 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,...
8
votes
1answer
323 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$
...
22
votes
1answer
387 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
88 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
131 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
388 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
191 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
231 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 ...
7
votes
3answers
357 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 ...
16
votes
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
208 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}.$$
Is it confusing or acceptable to distinguish between the following two things?
An idiom; and
What is or seems to be a compositionally ...
20
votes
14answers
7k views
Why is it possible to teach real numbers before even rigorously defining them?
In mathematics, one can hardly study any mathematical concept unless it is clearly and rigorously defined. For example, without the definition the fundamental group, it is almost impossible to teach ...
-2
votes
2answers
113 views
Should the limits of one system of elementary set theory be the limits of a student's mathematical world? [closed]
In teaching elementary set theory, suppose we refrain from emphasizing historical decisions that were made in theory construction.
Is there a danger that students may see the mathematical language ...
7
votes
5answers
2k views
Teaching asymptotic notations at the beginning of calculus [duplicate]
I'm thinking about teaching calculus by firstly introducing the asymptotic notations (big-Oh, little-oh, and $\sim$), secondly explaining their "arithmetic" (things like how to sum little-oh's and ...
6
votes
1answer
857 views
Why is it popular to teach modulus via the example of mod 12 and analogue clocks?
Why is it popular to teach modulus via the example of mod 12 and analogue clocks rather than rectangles or tables that have a finite number of columns in each row, and infinitely many rows?
It's ...
6
votes
3answers
162 views
(Riemann integrability) How do you explain this to a high school student?
The following question was in a high school teacher's guide:
Let $f\colon\mathbb{R}\rightarrow\mathbb{R}$ defined by
$$f(x)=\begin{cases} x & x\in\mathbb{R}\setminus\mathbb{Q}\\
2x & x\...
11
votes
5answers
287 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
84 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
151 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
430 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
232 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 ...
