88
votes
Why is learning mathematics compulsory?
Questions like this, or variants (from students, the notorious "when will I use this in real life") seem to be pretty common, and I'm always a little surprised, because the unstated premise - that ...
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85
votes
What female mathematician can I introduce to my High School students?
Emmy Noether comes first to mind, as one of the most influential mathematicians in abstract algebra, specifically in the development of Noetherian rings (along with many properties of ideals).
One ...
- 11.1k
61
votes
What female mathematician can I introduce to my High School students?
Julia Robinson! I recommend her for a high school audience for a few reasons:
Mathematical reasons: She is best known for her work towards the solution of Hilbert's 10th Problem, regarding an ...
- 10.4k
59
votes
Impressive common misleading interpretations in statistics to make students aware of
Anscombe's quartet is pretty good:
All four of these sets have almost identical mean and variance for both x and y coordinates, correlation, and best-fit linear regression. But they're obviously very ...
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58
votes
Accepted
Impressive common misleading interpretations in statistics to make students aware of
Here are two well known examples:
If someone tests positive for a rare disease (say its prevalence is 1 out of 100,000) with a test that has a 1% false positive rate, it is tempting to say that we ...
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52
votes
Accepted
How rigorous should high school calculus be?
Not very rigorously at all, but that doesn't (and shouldn't) mean just memorizing calculations. (I should add that I'm basing this on my experience teaching calculus to non-major college students, ...
- 11.3k
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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50
votes
What female mathematician can I introduce to my High School students?
Perhaps not strictly a mathematician in the traditional sense, but I think Ada Lovelace might be a great woman to start with in today's digital world. She even has an important programming language ...
- 601
49
votes
Impressive common misleading interpretations in statistics to make students aware of
A book I remember has the title "the egg-laying dog". The titular dog enters a room where we placed 10 sausages and 10 eggs. After a while the dog leaves the room, and we observe, that the ...
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45
votes
Accepted
How do I teach algebra?
As a personal tutor, I’ve been teaching algebra to kids from ages 8 to 16 for many years. Mostly I find myself in the position of picking up the pieces when the kids are failing and fearing more ...
- 1,214
45
votes
Response to Students Who Say "This Is Not Important"
"Lately, my students keep telling me why what we are learning is not important. They ask me when will we use this in the real world?"
There's a quick reply to this that I think people won't ...
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43
votes
Impressive common misleading interpretations in statistics to make students aware of
Sally Clark (http://en.wikipedia.org/wiki/Sally_Clark) was convicted in the UK of murdering both her infant sons, when in fact it is much more likely that they died of natural causes. The case ...
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43
votes
Student asked me if it is necessary to simplify fractions at the end of answering a question. I'm not sure how to respond
The short answer to your question is: everyone is right.
I agree with people here that in many contexts, $0.75$ or $\frac{3}{4}$ would be a more desirable answer than $\frac{45}{60}$. I also agree ...
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42
votes
What female mathematician can I introduce to my High School students?
Sophie Germain and her work on Fermat's Last Theorem.
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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 ...
- 19.4k
41
votes
Accepted
Are there science-backed effective teaching strategies?
In terms of controlled experiments, then, yes. Note that most are opposite or orthogonal to virtually all pedagogical norms in math education.
Active recall. "Put away all your notes and ...
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40
votes
What is the current school of thought concerning accuracy of numeric conversions of measurements?
The product of two numbers should be given with as many significant digits as the least precise of the numbers multiplied (see https://www.nku.edu/~intsci/sci110/worksheets/...
- 1,258
39
votes
How can we help students learn how to read their textbook?
One thing you might do is contrast reading mathematics textbooks with reading novels. I have seen this done at the start of a textbook draft for a course on the Kuratowski closure operators (MESE ...
- 18.1k
39
votes
Accepted
Rationale for not dividing both sides of an equation by $x$ (ex: $6x^2 = 12x$)
Just before dividing, you can reason "Either $x=0$ or I can divide by $x$." This creates two separate cases to be analyzed.
This works for dividing by anything. You want to divide by $\sin(x)$? You ...
- 6,350
38
votes
Pi or Tau? How should the circle constant be taught?
(Disclaimer: I peronally really don't care if one uses $\tau$ or $\pi$, both are just numbers for me.)
But I would strongly recommend to use $\pi$. Why?
In every technical literature, in many ...
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38
votes
How do I nicely tell my coworkers that they are NOT mathematicians?
I do not know if there is an accepted definition of what a mathematician is. There are teachers of mathematics and professors of mathematics, for example, and most people agree that people of the ...
- 2,922
38
votes
Response to Students Who Say "This Is Not Important"
Math is just as useless as almost any other subject
As a math tutor, I've thought about this a lot over the last 15 years or so. Aside from tutoring, I don't use my math education in "the real ...
- 489
37
votes
What female mathematician can I introduce to my High School students?
Any Living One who is friendly enough to come talk with them.
Seriously, learning about "people in books" can sometimes be inspiring. But actual live role models are best. Write a local college, ...
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37
votes
What female mathematician can I introduce to my High School students?
Maryam Mirzakhani, who just won the Fields Medal, and also was the first Iranian student to win a gold medal in the IMO in 1995 with a perfect score.
My colleague Mohammad Javaheri was on Iran's IMO ...
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37
votes
Real-world examples of more "obscure" geometric figures
Trapezoid
Native Peruvian architecture makes heavy use of the trapezoid for stability in earthquakes. (The Spaniards thought they were primitive as they didn't use arches ... but most of the Spanish ...
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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 ...
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