Henry Towsner
  • Member for 7 years, 10 months
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Why is learning mathematics compulsory?
87 votes

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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How to respond to “solve this equation” in a basic algebra class
69 votes

This is a really interesting question, because similar issues---the question of how demanding to be about formatting of answers---come up a lot, at all levels, and the answers aren't always ...

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Why are percentages part of the curriculum?
Accepted answer
55 votes

Percentages are widely used throughout society - in news, scientific publications, and so on. Learning to understand them is a necessary literacy skill. Percentages don't have a particular ...

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How rigorous should high school calculus be?
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52 votes

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, ...

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Adding irrelevant humorous questions to a quiz exam
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36 votes

I think there's room for differences of opinion on this, and the answer might depend on the ages of the students or who the specific students are. When I was a student I enjoyed questions like this, ...

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Should I be teaching point-slope formula to high school algebra students?
36 votes

As someone who teaches calculus to college students, I expect my students to have seen point-slope form. We just start using it (because it's the right way to talk about tangent lines and ...

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Why are induction proofs so challenging for students?
35 votes

In my experience, the biggest issue is that students don't have a clear grasp of quantifiers, so they don't see the distinction between "for all n P(n)" and "consider an n such that P(n)". This leads ...

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Difference between high school and college calculus courses
33 votes

Assuming we're talking about mostly US students, most American high schools teach calculus in a way that's very focused on the AP test. The pressure to get students through that with an adequate ...

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Why don't textbooks foreground marginally generalized theorems?
24 votes

Spivak proves $\sqrt{2}$'s irrationality fully, but banishes $a^{1/b}$'s to the exercises. Isn't proving (only) the latter more efficient? Yes, it's certainly more efficient. So what? Efficiency is ...

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I'm worried that my struggles with calc 2 mean I won't be able to become a professor later
22 votes

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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Why so many single-variable calculus textbooks? But still no equivalents to Visual Group Theory or Complex Analysis for other subjects?
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22 votes

Single variable calculus is in a very different situation from the other topics you mention. The number of students in the US who take single variable calculus is at least two orders of magnitude up ...

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Don't these word problems seem designed to be confusing?
21 votes

I think there's a countervailing issue that the book you're describing is trying to deal with. I teach college students, so I don't know what the particular approach it's taking is age appropriate ...

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Teaching indefinite integrals that require special-casing
20 votes

I'd avoid giving problems like that to students first learning indefinite integrals (either by not asking it at all, or specifying the range x>1 in the question). It's a subtle algebraic trap, and if ...

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Should students be given partial scores when they gave an incomplete proof by contradiction?
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20 votes

There's no abstract reason that an imperfect proof by contradiction should categorically fail to get credit. A proof should generally get partial credit based on how much knowledge of the relevant ...

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Rationale for not dividing both sides of an equation by $x$ (ex: $6x^2 = 12x$)
19 votes

I think your student pointed out the key issue: "Well, obviously I didn't know that zero was an answer when I was doing the problem". That's exactly right: at the time the student was dividing, they ...

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Intergration by differentiating will get you $0$ marks - but how to explain why?
18 votes

I agree with the other post that you should give full credit unless there were clear directions saying what would and wouldn't be acceptable approaches. I think it would be very, very hard to convey ...

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The concept of infinity for a 5 year old
17 votes

I'm not sure why the two basic things adults seem to say about infinity are "infinity is not a number" and "∞+1=∞", both of which are at best misleading. (Infinity doesn't name a number, but it does ...

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Is the current education system as bad as most critics and famous pure mathematicians try to convey?
15 votes

I think this question is, probably accidentally, responding to a strawman argument. It presumes that the criticism of math education coming from pure mathematicians is some combination of "students ...

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What holds your students back in Calculus?
14 votes

Here's one I haven't seen mentioned so far: students coming into calculus are very uncomfortable with the idea that there might be more than one way to do something, and especially that they might ...

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It is good to have old exams (with solutions) published?
14 votes

Other people have given other good reasons to have old exams be public, but I want to emphasize the one Andrew Stacey points out in comments: old exams often are public, and pretending they're not ...

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The term "unique" for functions and operations
13 votes

I don't think there's a lot of educational value to fixating on trying to word definitions in exactly the perfect way. Students have trouble with the notion of a function because it's hard. The way ...

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Enlighten younger students about the concept of "procedural justice" in mathematics?
12 votes

On the contrary, many seem surprisingly impatient when being asked to prove 1+1=4/2, whose proof (with properly delimited deepness) involves nothing beyond and possibly well below most people's ...

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Mindless use of "antisimplifications" such as $1/x+1/y=(x+y)/xy$ and $1/\sqrt{2}=\sqrt{2}/2$
12 votes

For students at that level, routine algebraic calculations are an easy step, while thinking about what steps to take is quite difficult. So they'll often prefer to do familiar calculations - even long ...

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What are non-math majors supposed to get out of an undergraduate calculus class?
11 votes

I'll address one piece of your question: how to think about proofs in a class for non-majors. I've tried to approach this by assuming that, whether or not a proof is good for the students, they haven'...

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Acceptability of creative questions in assessments
10 votes

I would frame this issue a little differently than you have. I think it's unreasonable, at least in the context of courses which aren't well into a math major, to ask students to do something they ...

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How to explain what's wrong with this application of the chain rule?
10 votes

f is not a function of (only) z - f here is a function of x as well as z. I think this explanation is intelligible to a calc 1 student, and gets at the heart of the matter.

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Are there any negative consequences in applying operations/functions to a whole equality?
10 votes

The notation your students are using isn't wrong. It's perfectly clear - anyone who knows algebra instantly knows what they mean - it's not particularly confusing, and it isn't going to quickly lead ...

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Convincing a high schooler that $i$ is a number
10 votes

One of the historically compelling arguments for complex numbers was that they can be used to find real valued solutions to polynomials. There's a nice discussion on this site. For example, the ...

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Should tests given after the drop date be made less difficult in order to help the remaining students raise their grades?
10 votes

Fairness suggests that the grade a student gets shouldn't depend on the semester they happen to take a course in. So the first question I'd ask is what sorts of grades have students typically gotten ...

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How to teach logical implication?
10 votes

When I've taught propositional logic I acknowledge that this is a formalism that doesn't perfectly match the English usage, and use it as an opportunity to point out The evaluation of $\rightarrow$ ...

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