48 votes
Accepted

How to handle the situation where a student insists I am wrong during the class?

It depends on how much time I can afford to spend on the problem. I check, as you did, whether I see a mistake. If not, I try to explain the math in a different way: a different conceptual approach, ...
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  • 4,569
29 votes

How to handle the situation where a student insists I am wrong during the class?

I agree with @kathleen, that being a young (and female) instructor can lead some students to be less respectful. In this case, we can use that to our advantage... Long ago, when I was less secure as ...
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  • 16.9k
21 votes

How to handle the situation where a student insists I am wrong during the class?

I have had this problem before with students who always think they're right. If a student continues to insist you made a mistake, when you know that you haven't, then tell the student to hold the ...
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  • 1,178
20 votes

How to answer a three-year-old the question "Why is $2+6$ the same as $4+4$"?

I'm nearly sure I did this with my child when she was young. First, establish that she understands that a number, like three, is equal to $1+1+1$. Hold three fingers up and ask her "how many is this"?...
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  • 7,686
19 votes
Accepted

How to advise students who want to do a "Bourbaki"-style study?

I've run into a few students like this. I usually try to convey a few messages. It is great that you are so interested in foundations and there is absolutely a place in math for people with this ...
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18 votes
Accepted

How to deal with fast students without neglecting weaker ones

I don't think it's fair to tell the students to not read ahead. In fact, I'd encourage it. What you should make clear is that the material in the current section takes precedence, and if somebody else ...
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  • 986
17 votes

Effects of early study of advanced books

I have a bit of anecdotal evidence. I was unfortunately not homeschooled, nor did I have a technical childhood; I spent my childhood painting and writing short stories. I was in gifted classes, but I ...
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15 votes

How to handle the situation where a student insists I am wrong during the class?

Your student reminds me of me in my first algebra class, in 8th grade. I insisted that my answer was a 'better' solution to a homework problem. The teacher was an ex-Marine, who took the time to step ...
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  • 258
15 votes

Effects of early study of advanced books

You asked for anecdotal evidence. I was a "gifted student". The school told me to teach myself 11th grade math (Trigonometry and Algebra 2) in 9th grade. I never formally learned algebra 1, but I ...
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  • 6,735
14 votes

Students who know high-level math before going to college

The question you are asking has little to do with the particular subject in which the student excels and everything to do with student motivation. The students have not developed the skills needed to ...
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  • 871
14 votes

How to handle the situation where a student insists I am wrong during the class?

Taking some extra care to verify the details of a confusing bit of material (preferably with class involvement, intuition-building examples, etc.) is usually an excellent use of class time. Offering ...
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13 votes

How to advise students who want to do a "Bourbaki"-style study?

I would discuss with these students the rather healthy point of view of Terry Tao on the subject. Summary One can roughly divide mathematical education into three stages: The "pre-rigorous" ...
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  • 5,887
13 votes

How to nurture a good student?

I don't see my thoughts expressed by anyone here so perhaps I can chip in! I'm currently a graduate student but I was once that kind of bright bored student you are talking about. I had my fair share ...
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12 votes

Presenting a solution with a stroke of genius

I think it helps to make it abundantly clear whether or not you would expect an average student in your course to come up with such a "stroke of genius". If you're presenting something that might ...
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12 votes

Students who know high-level math before going to college

Apart from quite general issues about smart kids' study skills or lack thereof, my observations over many years gives me the impression that mathematics and computer science offer special hazards/...
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12 votes

How can I teach Mathematics to genius students?

The key with students like this is to allow them to dictate the pace of teaching, while providing interesting and challenging material. Now, that is very easy to say, but here are a couple of pointers:...
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12 votes

Teaching arithmetic operations ($+ - \times \div$) to a 3 year old

My immediate response is 'wait a few years'. I've spent a fair amount of time with 3 year olds, and most of them are busy learning how to be a person in their own right, how to have a conversation, ...
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  • 5,540
12 votes

How to deal with a talented 11-year-old pupil?

Here in the U.S. there's been a rise in the last decade of "math circles"; extracurricular math clubs with students of the same age, with some amount of play/competitiveness to hone their interest. ...
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11 votes

How to advise students who want to do a "Bourbaki"-style study?

I was a bit like that in my first three years if study, then I read the first volume of Schwartz' Analysis, where he introduces the ZFC axioms. This is the point when I understood that one simply ...
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11 votes

Effects of early study of advanced books

To supplement the other U.S.-centric answer: yes, the U.S. standard curriculum through high school is not now and has not been in recent years comparable to several western European or former-easter-...
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  • 13.3k
11 votes

Challenge questions for extremely bright kids

Here are some suggestions for problem sources in English. Some of them are appropriate for very bright students studying geometry or Algebra II, but might nonetheless prove too difficult for students ...
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  • 587
11 votes

How to deal with a talented 11-year-old pupil?

I might disagree with several implicit hypotheses: that mathematics is only a school subject; that the there is a single linear course through it; that the main option is just the speed with which one ...
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  • 13.3k
10 votes
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How does an advisor effectively motivate progress on an independent project?

I've mentored roughly a dozen year-long undergraduate senior research projects, and I've always used a mix of the following techiques to keep students motivated. Set clear goals, both short and long ...
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  • 7,930
10 votes

How to deal with fast students without neglecting weaker ones

I use a technique I learned from my pilates teacher: in class activities, have different options for different ability levels. I have worksheets in almost all of my lessons. I almost never cover all ...
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8 votes

Presenting a solution with a stroke of genius

Solutions that could not have been concieved by the average student It is important to realise that many more solutions can't be concieved by the average student than we usually realise. Even ...
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8 votes
Accepted

Splitting the students by abilities

As per the comments above, I'm going to tackle this explicitly for discrete math and set theory being a shared course. What follows is some strategies I've tried and how well they worked (or didn't ...
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  • 1,950
8 votes

How to deal with fast students without neglecting weaker ones

My experience is that students that are ahead, and most importantly, asking questions too - are more likely to be in the position to be both independent learners, and able to take on peer-to-peer ...
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  • 189
7 votes

How to handle the situation where a student insists I am wrong during the class?

Humbly accept that you could be wrong, and be open to feedback. Turn it into a teaching moment when possible by inviting the student to come up and show their solution. If they are wrong, don't tell ...
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  • 71
7 votes

Presenting a solution with a stroke of genius

Yes, I think most arguments are "routine" in the sense of being very similar to others in the relevant context, while now-and-then there is something "out of the blue". The latter can be ...
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  • 13.3k

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