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25
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7 answers
How do you coach students who often make small errors?
Some students are prone to making small calculation errors. Not errors in understanding, but errors like adding or multiplying integers incorrectly, or dropping a negative sign. Unsystematic errors in the terminology referenced here. Sometimes…
Mike Pierce
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25
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Why do we still teach the determinant formula for cross product? And is it as bad as I think it is?
The cross product is an important vector operation in in any serious multivariable calculus course. In most textbooks that I'm aware of, right after the definition, we always introduce the determinant formula
$$
\mathbf{u} \times \mathbf{v} =
…
user13395
25
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23 answers
How can I explain why we need proofs to someone who has no experience in mathematical thinking?
I know someone I really like, but sadly, that person has absolutely no experience in math or mathematical thinking above third grade mathematics (+, - are fine, but division already makes problems). This person is an adult and not stupid, but he…
user15257
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Are there disadvantages to teaching complex numbers as purely geometrical objects?
Complex numbers are, or at least were to me, generally introduced like this:
There's no number whose square is negative. That's a shame! Well, whatever - we'll make one up! Set $i^2=-1$ and declare that all the usual rules of the real numbers…
Jack M
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The impact of dyslexia on learning mathematics, and available resources
I have always loved the beauty of mathematics and physics. However I'm severely dyslexic and find it hard to keep numbers in my head, any more than 4 numbers at a time and they melt together and lose their meaning. (You know that feeling when you…
Project-404
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8 answers
Counterintuitive consequences of standard definitions
Let me motivate my question with the following situation. While teaching the concept of continuity, I usually start with motivating the concept. Then, when we see that there is an important and intuitive concept here, we start formalizing it. After…
András Bátkai
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25
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Redundant zeros
How to convince a middle school student that $0.50=0.5=0.500=\cdots$?
I used the fact that $0.50=\frac{5}{10}+\frac{0}{100}=\frac{5}{10}=0.5$ but that far from intuitive.
Then I tried to explain that $50$ apples to $100$ apples is the same as $5$…
user5402
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7 answers
Why do we care about multiple proofs of the same theorem?
I am teaching a math appreciation course to high school students who are approximately 17 years old, in their last year of high school, and who do not believe they will choose a STEM major in university. We will be doing a lesson on visual proofs…
Amanda
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"Function" vs "Function of ...": how much does it contribute to students difficulties?
Most textbooks I've seen (and teachers I've met, myself included) are rather careless about the distinction between variables and functions.
For example, when we write $y=f(x)$ we all know that $f$ is the function, while $x$ and $y$ are variables.…
Michael Bächtold
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A Series of Unfortunate Examples!
All of us know, when teaching, the "right" choice of examples is important. Though, making the "right" choice is one of those things that are easier said than done. Here is the story of a series of unfortunate examples I used in my class yesterday.…
Amir Asghari
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13 answers
Ideas for high school pure maths projects
I am thinking of giving my high school students some pure maths projects to do. It is a lot easier to think of some interesting stats projects but not in pure maths. The students' maths background are weak, they might not really understand the…
user71346
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1 answer
Tutoring elementary student who reverses left and right
I am a volunteer math tutor. My student is in fifth grade. He was evaluated in August and found to be at the first grade level in math. (His reading is very close to grade level.)
He has epilepsy, memory problems and ADD, and has made slow but…
aparente001
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24
votes
7 answers
Repeated addition: standard notation?
My daughter showed me the picture below, which came from 9GAG. It shows a question on an exam asking the student to "use the repeated addition strategy to solve: 5 x 3." The student answered "5+5+5" and the teacher gave the answer a one-point…
JRN
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5 answers
Any support for mathematical "learning types?"
Back when I was an undergrad calculus TA, I participated in a general TA training class. We were taught to be mindful of different "learning types," such as visual learners, audio learners, and kinesthetic learners.
It wasn't until recently that I…
davidlowryduda
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6 answers
What are some good rules for handling student questions during exams?
For example, I gave an exam earlier today with a problem that ended in the sentence
Use the chain rule to find $(f\circ g)'(3)$.
During the exam, one of the students asked me what the circle between the $f$ and $g$ means, and I answered that it…
Jim Belk
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