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 ...
- 24.4k
41
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 ...
- 2,061
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 ...
- 4,428
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 ...
- 2,061
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 ...
- 6,262
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 ...
- 29.5k
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 ...
- 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 ...
- 5,768
29
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 ...
- 6,262
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 ...
- 6,133
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 ...
- 29.5k
26
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 ...
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 ...
- 24.4k
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 ...
- 11.6k
19
votes
What books are like Knuth's Surreal Numbers?
Flatland by Edwin Abbott Abbott
It's a story about a 2-dimensional being's encounter with a three-dimensional being. (Well, there's a class(?) allegory at the beginning, but you can skip that.)
- 3,810
19
votes
What books are like Knuth's Surreal Numbers?
Gödel, Escher, Bach: an Eternal Golden Braid by Douglas Hofstadter is a book about Mathematics, Art, Music, Computer Science and Artificial Intelligence. It alternates story chapters and descriptive ...
- 341
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 ...
- 764
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 ...
- 24.4k
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.
- 2,484
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 ...
- 24.4k
15
votes
How to teach perseverance?
I believe that my students can learn best when they display perseverance (sometimes called grit). I'll discuss how I teach, model, and encourage mathematical perseverance.
Tell a story about ...
- 900
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...
"...
- 9,194
15
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 ...
- 21.2k
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 ...
- 653
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 ...
- 407
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 ...
- 9,079
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,...
- 1,309
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 ...
- 20.1k
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 ...
- 29.5k
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