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103 votes
35 answers
21k 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 ...
David Ebert's user avatar
  • 3,905
100 votes
20 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, ...
Steven Gubkin's user avatar
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. ...
davidlowryduda's user avatar
87 votes
21 answers
26k 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 ...
Joseph O'Rourke's user avatar
86 votes
19 answers
30k 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?
Brian Rushton's user avatar
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 ...
JDH's user avatar
  • 4,076
81 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}=...
user avatar
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 (...
Mathprof's user avatar
  • 1,205
77 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 ...
Markus Klein's user avatar
  • 9,448
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, "...
Brendan W. Sullivan's user avatar
74 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 ...
Stephen Herschkorn's user avatar
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 ...
Jared's user avatar
  • 2,223
64 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 ...
Geoffrey's user avatar
  • 898
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 ...
MadScientist's user avatar
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 ...
abnry's user avatar
  • 852
59 votes
24 answers
73k 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 ...
Chris Cunningham's user avatar
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&...
Steven Gubkin's user avatar
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 ...
Rijul Gupta's user avatar
  • 1,165
55 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 ...
Mike Shulman's user avatar
  • 6,580
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 ...
user avatar
52 votes
15 answers
13k 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 ...
Chris Cunningham's user avatar
51 votes
3 answers
11k 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 ...
Peter Flom's user avatar
50 votes
21 answers
17k 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 ...
WoJ's user avatar
  • 1,398
49 votes
14 answers
6k views

Should we avoid indefinite integrals?

I am very uncomfortable with indefinite integrals, as I have difficulty giving them a precise sense that matches how they are written and the usual meaning of other symbols. For example, when one ...
Benoît Kloeckner's user avatar
49 votes
10 answers
16k 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, ...
kathleen's user avatar
  • 623
48 votes
39 answers
22k 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 ...
celeriko's user avatar
  • 5,070
48 votes
21 answers
20k 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, ...
QMC's user avatar
  • 779
48 votes
14 answers
5k 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 ...
Steven Gubkin's user avatar
48 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 ...
Mark Meckes's user avatar
  • 1,479
47 votes
24 answers
20k 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. ...
Tutor's user avatar
  • 941
47 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) ...
Brian Rushton's user avatar
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 ...
Joseph O'Rourke's user avatar
46 votes
16 answers
33k 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, ...
Jim Belk's user avatar
  • 8,279
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 ...
Mara's user avatar
  • 888
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-...
alex.jordan's user avatar
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 ...
Nick C's user avatar
  • 9,699
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 ...
Benoît Kloeckner's user avatar
44 votes
28 answers
12k 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 ...
vonbrand's user avatar
  • 12.3k
44 votes
4 answers
3k 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, ...
Brendan W. Sullivan's user avatar
43 votes
15 answers
21k 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 ...
Simply Beautiful Art's user avatar
43 votes
24 answers
13k 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, ...
W. G.'s user avatar
  • 635
42 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, ...
dtldarek's user avatar
  • 8,957
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 ...
Mark Fantini's user avatar
  • 3,040
42 votes
9 answers
10k 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 ...
IchBins's user avatar
  • 429
42 votes
3 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 ...
user avatar
42 votes
5 answers
3k views

How can I help a student who has a "wrong" kind of enthusiasm?

Alice (not real name) is a student in one of my Math 100 (calculus) classes. It's a course offered by my college as a dual credit course at a high school, so the whole class is about 17/18 years old, ...
Torsten Schoeneberg's user avatar
41 votes
23 answers
7k views

How should I answer questions about the purpose of learning math?

What are some good answers to questions e.g. "why do we need to study square roots"? Of course the answer depends highly on who is asking. For the scope of my question, I have a student in ...
BKE's user avatar
  • 1,292
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-...
Brian Rushton's user avatar
41 votes
6 answers
5k 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....
user avatar
41 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 ...
J W's user avatar
  • 4,753

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