Most Popular
1500 questions
15
votes
4 answers
How would you explain what a PDE is to a very educated layman with no math background?
Is every mathematical concept, even the complex ones, explainable?
As someone who will be needing to explain my line of work for a position to a committee who is very, very, educated, just not in math (I would say over a decade or so years removed…
Wow McWow
- 151
- 2
15
votes
4 answers
Is it better to provide students with guided notes or to have them write their own notes, or both?
When I taught calculus, I posted my notes after the lecture. Then I had the students fill out a mid-quarter evaluation, and a lot of them wanted me to post my notes before class.
What I started doing was printing and handing out the notes to them,…
Felix Y.
- 1,430
- 10
- 23
15
votes
1 answer
Reference request for studies on gender in math examples, homework problems, or math exams
I am looking for a study or reference on gender in math problems given in mathematics.
In math texts or even on math exams, if there is a word problem involving people, these people or "characters" in the problem are given names and pronouns. For…
Felix Y.
- 1,430
- 10
- 23
15
votes
2 answers
How to effectively internalize math?
Terrence Tao commented of internalizing [here: https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/ ]
"It is true that some mathematicians can be vastly more efficient than
others at learning material, but I…
user6330
15
votes
7 answers
Students strictly follow the steps and notations in sample problems without understanding them
It's just an observation, but I'll be highly appreciated if anyone with experience in teaching (or TA-ing) lower-division calculus can explain this phenomenon in detail.
I'm one of a TAs who's responsible to write up a section quiz last week.…
user2139
15
votes
6 answers
Are precise drawings important in geometry?
In Finnish middle school (yläkoulu) the students learn to measure distances and angles, draw geometric figures and do certain calculations (area, volume, surface measure, trigonometry). There are also geometric constructions.
As a teacher, to what…
Tommi
- 7,018
- 2
- 25
- 54
15
votes
3 answers
Should Euclid's algorithm be taught as rigid or flexible?
Euclid's algorithm is a way to find the greatest common divisor of two natural numbers $a$ and $b$.
In the usual version of the algorithm one tries to find $p,q\in\mathbb N$ so that $a=pb+q$ and $0\leq q
Joonas Ilmavirta
- 3,750
- 1
- 18
- 51
15
votes
4 answers
Student converted $\sqrt{x^2}$ and ended up with just $x$ instead of $|x|$
I asked a student I tutor what $\sqrt{x^2}$ was so I could show him why the solution is $|x|$ instead of just $x$. He ended up changing the problem to $(x^2)^{1/2}$ and then multiplied the exponents to get $x^{2/2}=x^1=x$. Now I'm well aware why the…
Brendan
- 253
- 1
- 4
14
votes
4 answers
As a TA, how to reduce imprecise notations/statements in students' exams
I'm not a course instructor, just a TA of the first quarter calculus course who lead discussion sections and grade exams.
When grading the midterm, I found large number of students showed some understanding of the concepts/problem solving…
user2139
14
votes
4 answers
Simpler explanation for finding the vertex of a parabola
I'm tutoring a Grade 11 Math student in BC, Canada, and we're going over parabolas. He's having difficulty with finding the vertex of a parabola - not how to find it, but WHY it works. And I'm having a hard time finding a good way to explain…
Brandon
- 143
- 6
14
votes
1 answer
Spiral learning in real analysis
Has there been any attempts at developing a curriculum for teaching analysis (here let us be narrow and say real analysis in the sense of rigorous integral and differential calculus) in a multipass, spiral approach?
If there is, has there been any…
Willie Wong
- 2,731
- 16
- 32
14
votes
3 answers
Worksheet: Homology in Intro Lin Al
I am about to start grad school and I am trying to think seriously about teaching [you know, before I get swamped with my own coursework]. I wrote a hypothetical worksheet for an introductory linear algebra class which tries to do something a little…
Eric Stucky
- 242
- 1
- 8
14
votes
3 answers
How to measure the understandability of a proof?
Is there a way to measure the understandability of a proof? From a search in the internet I have only found methods for measuring the understandability of software or tests for measuring the readability of a text.
Are there similar tests or methods…
Stephan Kulla
- 2,031
- 1
- 10
- 28
14
votes
4 answers
What is a wise reaction to a silly question?
I like students' nice questions too much (sometimes much more than their nice answers). It shows that they are thinking on what I am teaching and I am successful to make them curious about the subject. Also it allows me to explain on the subject…
user230
14
votes
2 answers
How the real numbers are taught?
I'm interested to know how the real numbers are introduced at beginner level in different countries.
In my (old) experience of teacher in Italy there was some well defined steps:
1) Introduce the field of algebraic numbers, showing that there are…
Emilio Novati
- 261
- 1
- 4