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.
350
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5answers
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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
791 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 ...
5
votes
3answers
144 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\...
8
votes
4answers
166 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
59 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 ...
3
votes
2answers
126 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?
8
votes
1answer
404 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 ...
7
votes
4answers
207 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 ...
2
votes
3answers
339 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
307 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 ...
4
votes
1answer
226 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 ...
1
vote
0answers
96 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 ...
3
votes
7answers
317 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 ...
7
votes
4answers
281 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 ...
2
votes
1answer
140 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 ...
8
votes
2answers
209 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....
1
vote
0answers
174 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 ...
4
votes
1answer
201 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 ...
5
votes
2answers
190 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
228 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: ...
1
vote
2answers
96 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
144 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 ...
3
votes
1answer
127 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
391 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
272 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
70 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
111 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
170 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
80 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
311 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
267 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
842 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
124 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
151 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
107 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
158 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
137 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 ...
7
votes
3answers
294 views
On fractions and the least common multiple
At least in my country, the explanation of the basic operations over rational numbers is done very near to the concept of prime numbers, prime factorization, and the calculation of the least common ...
4
votes
2answers
196 views
Why bother completing the square to find the minimum/maximum of a quadratic function?
Given a question like
Find the coordinates of the minimum point on the curve $y=3x^2+2x+9$.
students are often taught to solve this by completing the square.
The class I am currently teaching ...
12
votes
3answers
210 views
Quizzes (with questions known in advance) instead of homework in a graduate mathematics class. Good Idea or Bad Idea? Pros and Cons?
I'm teaching a graduate course in mathematics next semester. I'm planning to have a midterm and a final exam. But I'm thinking about having weekly (or once-every-two-weeks) in-class quizzes instead of ...
50
votes
13answers
8k views
How to get past the “mystique” of Maths
This question is primarily discussing maths education for adult learners, on courses teaching engineering mathematics at an undergraduate level. These students generally never set out specifically to ...
8
votes
3answers
179 views
Targeted group game for 8 or 9 players
I am a graduate math student and I believe that a nice way to raise the mathematical skills of people(especially students!) is to familiarize them with games and encourage them to use their minds and ...
9
votes
1answer
291 views
How to deal with poor students who don't take notes?
I want to set the context for me asking this question before stating it properly.
I teach at college/university level. This question deals with first-year students, fresh from school. So think ...
4
votes
2answers
112 views
Exposure to Algebra 2/Calculus Under Time Constraints
As part of a free summer enrichment program for highly-motivated high school students, I need to plan eight hour-long lessons for mini-courses titled as "Algebra 2" and "Calculus" separately. Despite ...
3
votes
2answers
130 views
Ideas for high-school proof class?
I have a math degree and have been hired to teach a proof class at a summer program. Our goal is to help the students learn the material they need for school (they take an algebra class separately) ...
15
votes
3answers
387 views
What to do if all students lack prerequisites?
I am teaching a calculus class for business this summer (6 students) and all of them do not have the math background needed for the class. We are supposed to cover derivatives and integrals, but they ...
5
votes
2answers
174 views
How to explain NP-hardness and NP-completeness to students
Computer science is becoming more and more important for mathematicians nowadays. Terms like big data, algorithm, artificial intelligence and others are frequently on the news. Many mathematical ...
13
votes
2answers
346 views
Is higher-math pedagogy responding properly to Wolfram Alpha's existence?
Is the current state of math teaching in undergrad college courses struggling with the availability of easy cheap access to Wolfram Alpha?
The homework problem below, one of 40 assigned from one ...
6
votes
2answers
224 views
Effective Assessment that's Easy to Grade
A colleague of mine will be teaching 3 classes (pre-calculus and two sections of calculus, at the university level) next semester with an additional grader in only one of those classes (pre-calculus). ...
