All Questions
3,686
questions
102
votes
35
answers
20k
views
What female mathematician can I introduce to my High School students?
I enjoy talking about Pythagoras when I teach the Pythagorean theorem. I sometimes mention Descartes when introducing Cartesian coordinates. And Leibniz and Newton are mentioned in many calculus ...
- 3,875
95
votes
18
answers
19k
views
Unique candidate that fails
In the comments to David Speyer's answer here, he points out that "the distinction between 'if there is a formula, it is this one' and 'this formula works' is subtle."
Does anyone have any simple, ...
- 24.3k
88
votes
13
answers
11k
views
How to assign homework when answers are freely available or attainable online?
I find that making homework meaningful is becoming increasingly challenging. Let us suppose that I am planning for next semester's first-semester or second-semester calculus course at my university.
...
- 2,165
86
votes
21
answers
25k
views
Why are induction proofs so challenging for students?
This forum already has many
good, simple examples of induction proofs, a great resource.
As I am soon to teach induction for the $n^\textrm{th}$ time—this time to some perhaps under-prepared ...
- 29.5k
86
votes
19
answers
29k
views
What is a good handwriting font for mathematics?
My students frequently mix up my $t$'s with my $+$'s and my $y$'s with my $4$'s.
What is a good handwriting font for distinguishing these and other easily confused symbols?
- 11.7k
86
votes
15
answers
16k
views
Should I design my exams to have time-pressure or not?
Is it better to design an exam with fewer questions and relaxed timing or with more questions and a resulting time-pressure?
One the one hand, it seems that students who really know the stuff will ...
- 4,086
80
votes
6
answers
8k
views
Issues with "equals", where does this come from and how do I combat it?
An issue I see with students a lot is abuse of the equals sign. For example, one problem asked "what is the degree of the polynomial: $\text{polynomial}$?", and I got answers like "$\text{polynomial}=...
user5108
79
votes
17
answers
20k
views
What's a replacement for "married couples" in combinatorics problems?
Many counting problems start with the assumption that we have a certain number of men and women or a certain number of couples, with the assumption (often unstated) being that that gender is binary (...
- 1,063
76
votes
20
answers
19k
views
Impressive common misleading interpretations in statistics to make students aware of
Statistics are used everywhere; politicians, companies, etc. argue with the help of statistics. Since calculations are needed for the interpretation of statistics, such things should be taught in ...
- 9,388
76
votes
11
answers
12k
views
Whence the "everything is linear" phenomenon, and what can we do about it?
$$ \color{red}{(a+b)^2 = a^2+b^2}$$
$$ \color{red}{\sqrt{x^4+y^4} = x^2+y^2} $$
$$ \color{red}{e^{t^2+C} = e^{t^2}+e^C}$$
I've observed this phenomenon -- wherein, implicitly, students say, "...
- 10.7k
73
votes
17
answers
10k
views
How shall we teach math online?
Many universities, including mine, are now requiring we teach our courses online because corona. How shall we do this? Let’s brainstorm here.
Some challenges:
My school provides limited online ...
65
votes
14
answers
3k
views
Encouraging class participation
I teach calculus to college students, and find it very difficult to get them to speak up in class when I ask questions, or when I'm trying to get a pulse for how much they understand. I think ...
- 2,163
64
votes
13
answers
9k
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 ...
- 921
63
votes
17
answers
9k
views
Is there a virtue to learning how to compute by hand?
I have been professionally tutoring a wide range of students (from elementary school through graduate school) for many years. Most of them are from the United States. I generally focus on helping my ...
- 880
61
votes
4
answers
6k
views
Is it worth grading calculus homework?
I am a young math educator. I've TAed four semesters of calculus for various instructors. Some instructors have required me to grade selected problems in homework sets. Another required me simply to ...
- 852
58
votes
24
answers
70k
views
Optimization problems that today's students might actually encounter?
Our students are not fencing in farm fields, cutting wires and folding them, or designing windows, so they are often uninspired by the optimization problems we give them. They seem like something that ...
- 21.2k
58
votes
4
answers
6k
views
Future educators writing nonsense questions
I teach future elementary educators mathematics content courses.
We play a lot in class with tasks like "Write a variety of word problems which would require the student to multiply 2.3 by 1.4&...
- 24.3k
57
votes
15
answers
17k
views
Student: Why not use a calculator?
The kid I am teaching math (subtraction for large numbers right now) just said this is all too easily done by a calculator, why don't we use it?
Well, I did tell him that you can only learn more ...
- 1,165
54
votes
13
answers
12k
views
How do I motivate my students to go to office hours?
I'm currently TAing a Linear Algebra class where a significant portion of the class is struggling, oftentimes getting marked down on homeworks or tests because they misunderstand some concept (rather ...
user37
54
votes
14
answers
6k
views
Should we say that fractions "are" or "represent" numbers?
I never gave this a second thought until a friend who works in education brought it up the other day. Should we say that a fraction like $\frac{1}{2}$ "is" a number, or "represents" a number? In ...
- 6,520
52
votes
15
answers
12k
views
How can we help students learn how to read their textbook?
In most secondary and early undergraduate courses, students purchase expensive and carefully-written textbooks. These textbooks contain, roughly, three things:
Exercises and Answers
Reference ...
- 21.2k
51
votes
3
answers
10k
views
How do blind people learn mathematics?
I am interested in how blind people learn mathematics at any level, but particularly before college. Math is often taught using a lot of visualization; how does this work with blind people?
My ...
- 797
50
votes
21
answers
16k
views
How to explain that winning the lottery is not a 50/50 distribution?
When casually discussing with my 13 yo child about probabilities, he told me
there is a 50% chance to win at the lottery
To what I said
no, there is a 1 chance over 90 million
(I roughly estimated ...
- 1,388
49
votes
14
answers
6k
views
Should we avoid indefinite integrals?
I am very uncomfortable with indefinite integrals, as I have a hard time giving them a precise sense that matches the way they are written and the usual meaning of other symbols.
For example, when ...
- 9,079
49
votes
10
answers
15k
views
How to handle the situation where a student insists I am wrong during the class?
I had one very vocal student in my Calculus recitation last year. Sometimes she would point out if I made a mistake in the lecture.
However, sometimes she would insist that I had made a mistake, ...
- 623
48
votes
39
answers
21k
views
Real-world examples of more "obscure" geometric figures
As part of my secondary geometry class I like to hook students by presenting real-world examples (usually images I find online or have taken myself) of different geometric shapes from real life. For ...
- 5,030
48
votes
21
answers
19k
views
The concept of infinity for a 5 year old
My son, who just turned 5, has been interested in the concept of infinity since long. He asks me a lot of questions regarding infinity. For example, not accepting my infinity + any number = infinity, ...
- 779
47
votes
24
answers
19k
views
How to explain Monty Hall problem when they just don't get it
Talking to some friends, I was asked to explain the answer to the Monty Hall problem (see also here;) .... they were having some trouble because whoever explained it to them didn't do a very good job. ...
- 941
47
votes
8
answers
13k
views
What do math majors (actually) do after graduation?
It's the time of year for prospective college freshman in the US to make campus visits, and I'm once again confronted with my lamentable ignorance when the students and their parents ask, "So what do ...
- 1,469
46
votes
18
answers
12k
views
How to explain the flipping of division by a fraction?
This question is inspired by @DavidButlerUofA's discussion of
"$\div \frac{2}{3}$ as $\times \frac{3}{2}$" in
"Are fractions hard because they are like algebra?"
Q. How can one best convey to ...
- 29.5k
46
votes
16
answers
32k
views
How is calculus helpful for biology majors?
It's common for majors in biology to take calculus courses, and many calculus textbooks (and calculus professors) try to cater to these students by including applications to biology.
My question is, ...
- 8,189
46
votes
9
answers
3k
views
Knowing mathematics does not translate to knowing to teach mathematics. Why?
Many brilliant mathematicians seem to make average or even poor classroom teachers. Is this an accurate assessment? Has there been any research to explain the phenomena?
What is the difference ...
- 888
46
votes
12
answers
31k
views
What should be included in a freshman 'Mathematics for computer programmers' course?
Many universities are changing up the way that they teach math service courses. 1-3 semesters of calculus and maybe a course in linear algebra are often included in majors (such as computer science) ...
- 11.7k
46
votes
4
answers
4k
views
How to respond to “solve this equation” in a basic algebra class
I asked this question once on math.se, but don't follow the link unless you want to risk biasing your own response: https://math.stackexchange.com/questions/444696/how-to-respond-to-solve-this-...
- 901
45
votes
21
answers
7k
views
How to help new students accept function notation
I am struggling to help some of my new precalculus students accept function notation -- something new to them this term. I am looking for strategies to help them adopt this new notation.
Their main ...
- 9,184
45
votes
18
answers
3k
views
How to teach logical implication?
One of the challenges of undergraduate teaching is logical implication. The case by case definition, in particular, is quite disturbing for most students, that have trouble accepting "false implies ...
- 9,079
44
votes
28
answers
11k
views
Good, simple examples of induction?
Many examples of induction are silly, in that there are more natural methods available. Could you please post examples of induction, where it is required, and which are simple enough as examples in a ...
- 12.3k
44
votes
4
answers
2k
views
Teaching undergraduates who expect a high-school-like learning environment
tl;dr: Some students expect to be told "what's on the test", to memorize and then move on. What can be done to change how they learn while teaching them what to learn?
Context: Introductory, ...
- 10.7k
42
votes
12
answers
7k
views
Is it advisable to avoid teaching "multiplication as repeated addition"?
I've had this discussion with a couple of friends. I argued that teaching multiplication as repeated addition isn't a good idea because it doesn't help children differentiate between the two ...
- 3,030
41
votes
22
answers
11k
views
Response to Students Who Say "This Is Not Important"
Lately, my students keep telling me why what we are learning is not important. They ask me when will we use this in the real world?
I explain how math is important in gambling, cooking, finance, ...
- 615
41
votes
11
answers
11k
views
Formula sheets and books during tests and exams
Some teachers make memorizing formulas, definitions and others things obligatory, and forbid "aids" in any form during tests and exams. Other allow for writing down more complicated expressions, ...
- 8,907
41
votes
6
answers
15k
views
How can I estimate the length of an exam?
Background: I am fairly new at teaching, and in every subject I have taught, I have had difficulty estimating the length and difficulty of an exam. I need to write an exam for a university senior-...
- 11.7k
41
votes
8
answers
9k
views
How to teach math to someone who is neither [really] willing nor able to understand it?
I'm not a teacher, I am a student. But in math, I am one of the best ones in my class so sometimes other people will ask me to explain stuff to them. And usually it works quite well: If I understood ...
- 419
41
votes
11
answers
3k
views
Big list of "interesting" abstract vector spaces
When introducing an abstraction it is important (in my opinion) to have a wide variety of examples of this abstraction.
Since finite dimensional real vector spaces are classified up to isomorphism by ...
- 24.3k
41
votes
5
answers
3k
views
Effects of early study of advanced books
Context:
There was recently a question on Math.SE: Inferior to Other Younger and Brighter Kids which starts as follows:
I'm a high school student (Junior/Grade 11) and I'm currently studying ...
- 8,907
41
votes
2
answers
2k
views
What does math education research know about difficulty vs. effectiveness?
I've asked basically the same question previously on on math.SE, then
cogsci.SE without much response, surely here is the place to ask this.
As anecdotal evidence is plentiful, but unfortunately ...
user370
40
votes
14
answers
20k
views
Why is learning mathematics compulsory?
In most education systems, Mathematics is a compulsory subject from primary school all the way to the start of university. A common reason given is that essential concepts like addition and ...
- 863
40
votes
14
answers
20k
views
Why do we teach complex numbers?
In algebra II, USA, we teach our students complex numbers. However, after algebra II, they never use complex numbers until pretty much complex analysis. The whole point of teaching them complex ...
- 1,572
40
votes
6
answers
4k
views
What am I supposed to be learning with long proofs of the main theorems in class?
It seems like this is exclusively how (most) people teach graduate/upper div math classes. They go through the proof of some big theorem, sometimes it might take two lectures. It's obviously important....
user5108
40
votes
4
answers
5k
views
Rings before groups in abstract algebra?
The default approach to teaching abstract algebra seems to be groups first, then rings. However, occasionally a textbook pops up (e.g. Childs' A Concrete Introduction to Higher Algebra, Hodge et al's ...
- 4,625