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.
361
questions
5
votes
0answers
86 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 $P$
...
14
votes
1answer
163 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
70 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
126 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 ...
2
votes
1answer
185 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
161 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
217 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
325 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 ...
13
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 ...
1
vote
2answers
180 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
101 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
845 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
155 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
247 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
73 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
141 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
422 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
215 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
371 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
328 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 ...
6
votes
1answer
258 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
103 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
337 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
288 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
146 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
224 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
178 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
220 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
198 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
237 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
102 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
145 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
217 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 ...
8
votes
4answers
419 views
A more rigorous approach to Precalculus
I am a pure mathematics PhD student and graduate teaching assistant at a major state university. During the summers here, teaching assistants are typically appointed to teach an entire course, rather ...
0
votes
3answers
315 views
Could students learn a lot more from school if they're only taught number theory until way later?
According to https://www.inc.com/bill-murphy-jr/science-says-were-sending-our-kids-to-school-much-too-early-and-that-can-hurt-th.html, when students get taught a concept when they're so young, they're ...
6
votes
0answers
71 views
Long-form, multi-step, skills-integrating applied mathematics problems in calculus I, II, III
When recently teaching Calculus II to college students, I instructed my students to read and be ready to work through the first 8 or so questions of James Walsh's climate modeling differential ...
0
votes
3answers
114 views
How can I measure the mathematical computation skills of high school students through a test?
How to analyze the level of difficulty of mathematical computation of a problem on a standard mathematical test designed for high school students? I mean how to choose some indices that can reflect ...
0
votes
1answer
181 views
Grades in a university course on category theory, curving, and how they reflect on the students and/or teacher [closed]
I originally posted this on the Mathematics Stack Exchange, thinking that the best place to post it, but the question quickly accumulated a bunch of close votes since it was not quite within the scope ...
4
votes
2answers
83 views
A Markov chain demonstration that doesn't require computers
I have a large probability class and would like to do some memorable demonstrations of Markov chains for them. Does anyone have any recommendations for a "low-tech" demo that doesn't involve ...
4
votes
6answers
319 views
How to make a student not overlook easy mistakes such as the wrong sign
I am teaching entry calculus to a bunch of students outside class (more like complementary to their math classes, without making much connections) and I can teach on a much more individual level than ...
6
votes
2answers
281 views
Mainstreaming math student
I'm working one-on-one with a student who is part of a sponsored refugee family. He's bright and a good learner, but has had a lot of interruptions to his education. No indication of any learning ...
0
votes
2answers
105 views
Returning Student for STEM - Brush-Up Resources? [closed]
All,
I am hoping to wade into an Electrical Engineering or Mechanical Engineering degree, but I have been out of college for almost 10 years. My last major exposure to math was good grades in ...
4
votes
2answers
846 views
Should young math students be taught an abstract concept of form?
Should a more general concept of the "form" of an equation or expression, be taught to math students as young as elementary school? I'm a fairly new tutor--do more experienced teachers think this ...
6
votes
0answers
125 views
Flow diagrams and summarizing strategies in proof-computation courses: good or bad for learning? Unsuitable for Inquiry-based learning?
For concreteness lets keep our discussion to calculus courses where there is a balance of proof and computations (computing limits but also doing epsilon-delta proofs)
I can understand that in more ...
5
votes
2answers
163 views
What are some suggestions fo teaching statistics concepts to struggling college students?
I'm a private math tutor. I'm fairly new at this, and this semester is the first time I've been tutoring for a statistics class at a community college. I enjoy experimenting and learning about ways to ...
1
vote
1answer
109 views
Verifying Simple Expression Equivalence in a Spreadsheet
For simple expressions with easily derived canonical forms (eg polynomials and simple rational expressions), is there a way to leverage existing tools to verify that two expressions are equal when ...
4
votes
1answer
166 views
Is it feasible to expose undergraduates to a “map”-centric point of view early on?
Question: Would it be feasible to teach undergraduate math students a "map"-centric view early on? If so, how early on?
Now that I'm preparing for a phd program, I'm also reflecting on my ...
3
votes
1answer
138 views
Existing Tools for Math Expression Equivalence Logic
Note - this question was posted here and garnered some decent replies before it was closed as off-topic in Stack Overflow.
Online systems, such as ALEKS, Cengage's WebAssign, and even Khan Academy ...
