51 votes
Accepted

Should students be told they're wrong

All four of your options lead with "They are told..." Consider asking the student questions instead. At the very least, this shows interest, and they may end up catching their own mistakes as they try ...
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  • 606
41 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 ...
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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 ...
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  • 1,834
40 votes
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Examples why university education is important for future high school teachers

I'm not completely sure how well this addresses the question, but here is my best response. A few years ago I was teaching a Methods course for preservice secondary math teachers. Over the course of ...
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  • 16.1k
38 votes
Accepted

How do I motivate my students to go to office hours?

When I'm the instructor for the course, I remind them of the time and location of my office hours by writing it on the board at the beginning of every lecture (if you're not the instructor, you can ...
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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 ...
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  • 4,306
37 votes
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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 ...
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  • 1,834
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 ...
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31 votes

Examples of Innumeracy

A recent Times article titled Americans Are Bad at Math, but It’s Not Too Late to Fix offered an example - A&W's "Third Pounder hamburger failed to catch on because During focus groups, the ...
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29 votes
Accepted

How is education in mathematics relevant to law?

A 16 year old once told me that he has no need for mathematics since he wanted to become a lawyer. I told him that he wouldn't make a good lawyer if he jumps to such conclusions without first ...
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  • 526
28 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 ...
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  • 297
27 votes

What to do with students who think they "already know it," but actually don't?

Allow me to contribute from the student perspective. I've taken College Algebra classes three times at three different levels and schools due to unusual circumstances. To make things even more ...
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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 ...
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  • 5,887
26 votes

Examples of Innumeracy

Re-Re-Edit (May 2019): Found in a selection of tweets here but pasted as images to preserve. Credit for the first one goes to @lizardbill and to the rest to @GeneticJen: Re-Edit (Jan 2016): Perhaps ...
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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 ...
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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 ...
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25 votes

Examples why university education is important for future high school teachers

Here is some text from the paper "Teacher Characteristics and Student Achievement Gains: A Review" (Wayne and Youngs, 2003): Three analyses take advantage of the detailed teacher data in NELS:88 ...
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25 votes

Interacting with high school teachers (US)

Talk to math teachers as you would talk to any other professional with whom you share a common interest (the education of your son). Note, I have addressed this to respond to you specifically in ...
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  • 7,375
25 votes

Justifications for: Why learn mathematics?

Most of what you learn in school isn't directly useful. When I was in primary school I was taught the difference between warm and cold-blooded animals. I've never used that information; should I not ...
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25 votes

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 ...
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23 votes

Examples of Innumeracy

There's the Verizon "0.002 cents versus 0.002 dollars" mishap, wherein an unhappy customer calls to complain that he was billed 0.002 $/kB after being told the rate is 0.002 cents/kB. The confusion is ...
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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 ...
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21 votes
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Motivating the study of matrices

Even without explicitly introducing the language of "linear maps", "vectors", and so on, you can still develop matrices as a shorthand for such maps, thought of as exchange rates. Example: Machine A ...
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20 votes
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What arguments can I give a high school student why mathematics is important?

I really like this answer given by John Green: https://www.youtube.com/watch?v=x78PnPd-V-A "School is not about you! School does not exist for your benefit or for the benefit of your parents. ...
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20 votes

What to do with students who think they "already know it," but actually don't?

I was unofficially advising a student the other day who told me "I am struggling, but I know more than my friends in the class." This was the excuse she used for not attending meetings of a popular ...
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  • 7,375
19 votes

How can we help students who are very anxious about math?

There are a few strategies that are supported by experimental research which I will share here, but they all have to do with stereotype threat. I am sure there are other types of anxiety related to ...
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  • 1,950
19 votes
Accepted

How to deal with very motivated students having "off-topic" interests?

Some possible approaches: Challenge the student. A possible reason why the student is having "off-topic" interests is that the student doesn't find the "on-topic" things interesting (he "thinks" it ...
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  • 2,671
19 votes

Examples of Innumeracy

Let me offer a different type of response, a student's answer to a problem. The question offered the height of a building, the equation for distance of a falling object, and asked to calculate the ...
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19 votes
Accepted

How to justify teaching students to rationalize denominators?

My thinking is that it is just so damn useful for students to be aware of these tricks. The examples/exercise should allow them to develop a sense of when and how it is helpful to simplify an ...
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