Skip to main content
46 votes

How do I show students the Beauty of Mathematics?

Imagine you are put in jail. You are forced to paint a painting every day for 10 years. You have no choice in the subject: one month you paint dogs, another month you paint horses, another month ...
Steven Gubkin's user avatar
43 votes

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

I found that my former students (low achieving ninth graders in the U.S.) always responded best when I answered with this: You enjoy watching sports right? Whether it's Football, Basketball, the ...
ruferd's user avatar
  • 2,081
38 votes
Accepted

How to solve the problem of Wolfram Alpha?

First of all, I believe this question is quite similar to the question "How to give homework for integration technique?". I avoid the temptation of repeating my answer for that question. Instead, I ...
Amir Asghari's user avatar
  • 4,438
37 votes
Accepted

How do I show students the Beauty of Mathematics?

To expand on my comment, I found that high school kids like watching YouTube videos. (I mean, they don't have to do any work right? Just sit and listen.) These are a few of my go to channels to pull ...
ruferd's user avatar
  • 2,081
35 votes
Accepted

Explaining Sigma-Notation

I've experienced positive results by first having students spend some time writing out sums in full (or using ellipsis notation if there are many terms). That way, it gets annoying to spend so much ...
Justin Skycak's user avatar
34 votes

How to get past the "mystique" of Maths

This is indeed a challenge, especially for adults. Three suggestions, none of which is a panacea. (1) Emphasize a growth mindset. Make it clear to them that learning math is a skill accessible to ...
Joseph O'Rourke's user avatar
31 votes

When is it appropriate to warn about the difficulty of a subject?

I know this is generally accepted as normal behavior by teachers, but personally, if I ever find myself tempted to attach disclaimers like "don't worry if you feel overwhelmed by this", then ...
Justin Skycak's user avatar
29 votes

Combative students in proofs classes

You don't say in the question what kind of school this is. It must be a four-year school rather than a community college, but there is no indication of what its admissions standards are like. If this ...
user18014's user avatar
  • 307
29 votes

What are some research-level opportunities in mathematics that do not focus on proofs?

I think a more correct view is that proof is the LAST of several stages involved in researching something in math. What follows is a quickly sketched out scenario of what is often the case. Before ...
Dave L Renfro's user avatar
27 votes

How to solve the problem of Wolfram Alpha?

Imagine you had to look up every word you wanted to use, because you had a poor vocabulary. This would get old, very quickly. The trouble is, many people don't have a genuine need to internalize ...
Jon Bannon's user avatar
  • 6,173
27 votes

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

The closest I came to getting fired for something I said to a student. The student asked "When will I ever use this math in the future?" I responded, "Well, you won't, but the smart ...
JTP - Apologise to Monica's user avatar
26 votes

What are some recent, interesting, accessible pieces of mathematics

Perhaps: The discovery a year ago in 2015 of a new tiling of the plane by a convex polygonal tile, found by Mann, McLoud, and Von Derau (the latter of whom was an undergraduate at the time of the ...
Joseph O'Rourke's user avatar
25 votes
Accepted

Combative students in proofs classes

There's probably no silver bullet. But one tool I use is in these situations (e.g., I teach discrete mathematics etc. at a U.S. community college) is to very closely align with a good textbook. In ...
Daniel R. Collins's user avatar
22 votes

I'm worried that my struggles with calc 2 mean I won't be able to become a professor later

A lot of students seem to make it through high school and well into college with the idea that school is supposed to be easy, and that having to work hard, or being confused at times, or struggling ...
Henry Towsner's user avatar
17 votes

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

My answer is maybe a little bit off. Still, I have had some luck in the past with two separate similar students to yours by communicating roughly the following concept using the outline below. An ...
Chris Cunningham's user avatar
17 votes

How to get past the "mystique" of Maths

I think it's something you have to tackle head on on the first day of class. Some materials I pull from are: Jo Boaler's work on mathematical myths, such as: Some people are math people and some are ...
Matthew Leingang's user avatar
17 votes

Combative students in proofs classes

EDIT: I would like to clarify that my response below is not intended to be definitive. This is an extremely difficult problem to have. It is perhaps the most difficult problem one can have as a ...
Steven Gubkin's user avatar
16 votes

What are some of the open problems that can be suitably introduced in a calculus course?

It's still not known whether $$\zeta(5) = \sum_{n=1}^\infty \frac{1}{n^5}$$ is a rational number.
Alexander Woo's user avatar
16 votes

How can I give feedback that is not demotivating?

Here are some rhetorical devices I use to deliver corrections in class that are very gentle to students' egos: "You have a slice of something correct there, but maybe we should look more closely ...
Daniel R. Collins's user avatar
15 votes

Mnemonics for some properties in mathematics

Recently, a student in my beginning algebra course offered the following to the class, regarding signed number multiplication: Assuming positivity is like love, and negativity is like hate, then... "...
Nick C's user avatar
  • 9,639
15 votes

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

Money Most people will not need to compute the trajectory of a ballistic projectile, but everyone will need to deal with money to live in any advanced society. Furthermore, while many people can get ...
Lawnmower Man's user avatar
15 votes

When is it appropriate to warn about the difficulty of a subject?

I can remember two teachers warning us about the difficulty of a subject. The first warning was by a teacher of measure theory and probabilities. In the first half of the semester we'll study ...
Stef's user avatar
  • 556
14 votes

Examples why university education is important for future high school teachers

While teaching polynomials to future high-school teachers, I realized one example of pretty advanced mathematics that is needed to understand why a certain important (but often kept implicit) result ...
Benoît Kloeckner's user avatar
14 votes

Teaching a student who refuses to learn

This is not an answer, but an assertion that what you are experiencing is not something new. Here are some quotes from a 1993 article of an Estonian math prof, who moved to the U.S. in the early 1990s,...
Rusty Core's user avatar
  • 1,317
14 votes
Accepted

Creating an Engaging Class Atmosphere

I agree with @Tommi that creating community is bigger than one activity. I do a number of things at the start of semester, but building community is also in the way I teach, every day of class. (I ...
Sue VanHattum's user avatar
  • 20.8k
14 votes

What are some research-level opportunities in mathematics that do not focus on proofs?

I have taught Discrete & Computational Geometry to US undergraduates project-based, as opposed to assignment- and test-based. Some of the projects do involve proofs, but others are more ...
Joseph O'Rourke's user avatar
14 votes

What are some research-level opportunities in mathematics that do not focus on proofs?

With the technological advances of the past couple decades, computational mathematics is now somewhat accessible to undergraduates. The wikipedia entry for computational mathematics lists out the ...
Aeryk's user avatar
  • 8,021
13 votes

Motivation in School

I will try to give a research-related answer. There are several suggestions from the literature and you may have to take a deeper look at them. First, a decrease in motivation is also observed in ...
Anschewski's user avatar
  • 4,811
13 votes
Accepted

Teaching new stats students confidence intervals, hypothesis testing, and other general techniques for inference

I've been teaching introductory statistics for the same amount of time at a large urban community college. I have never had this response from a class in toto. Last semester I did have one student say ...
Daniel R. Collins's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible