All Questions
Tagged with curriculum calculus
14 questions
6
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2
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Topics covered in Calculus I and II (university level) that aren't covered in the AP Curriculum
I teach AP Calculus BC at my high school and we have AP Calculus AB as a pre-req for taking BC. So most of my students are coming in with a strong calculus foundation, and I can spend less time on the ...
- 2,129
5
votes
1
answer
358
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How does the average level of expected mathematical sophistication at high school level increase?
I remember reading an old calculus book (years 1920-1930) and in the preface it was portrayed as revolutionary because it was for high school students. Nowadays, that is not revolutionary, because ...
- 615
9
votes
6
answers
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Can we skip Newton's Method?
I am teaching an introductory calculus course for high school juniors and seniors. It is not formally described as an AP Calculus course, but it is supposed to map roughly onto Calculus AB.
The ...
- 361
15
votes
8
answers
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How should I introduce the Chain Rule
I'm halfway through my first year of teaching AP Calculus to high school seniors. It's been going generally well, but I'm feeling like I really could have done better getting them into the Chain Rule....
- 5,697
2
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6
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Is there a more telling name for "Calculus 2"?
I see a lot of places where "Calculus 1" is referred to as "Introduction to Calculus", or "Single-variable Calculus." "Calculus 3" is referred to as "Multiple-variable calculus."
Is there an ...
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10
votes
3
answers
437
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The royal road to calculus
In the early 1900s Felix Klein lay out his vision for secondary mathematics curriculum. He wanted schools to teach calculus, so that universities would not be burdened by it. And at the core of the ...
- 201
13
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4
answers
1k
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Is Calculus Necessary?
That title is a quote from Fred Roberts:
Fred Roberts. "Is Calculus Necessary?"
Proceedings of the Fourth International Congress on Mathematical Education.
1980. p.52ff.
"Calculus is not ...
- 30.2k
10
votes
4
answers
509
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Surrounding a subject and strangling it to death versus concentrating on the main point
Standard calculus textbooks begin by introducing limits, including
limits of a fraction as the numerator and denominator approach $0,$
limits of a fraction as the numerator and denominator approach $\...
- 1,933
3
votes
1
answer
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Why is the convergence of infinite series covered in Calculus II?
I'm teaching AP Calculus BC for the first time this year. The AP curriculum is an attempt to cover most of the material in a two-semester university freshman calculus series, and so I am reminded of ...
- 1,796
13
votes
4
answers
4k
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Why do we teach calculus in high school rather than a different math course?
In most high schools (in America), I think it is safe to say that the highest math subject offered is calculus.
But why is it calculus rather than number theory or some other branch of mathematics?
...
- 1,602
10
votes
8
answers
606
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What topics should be included in a course matching these specifications?
I posted this question on m.s.e., where I upvoted the two answers, both of which said rather little by comparison to what the question asks. Hence this present posting.
Say you have a calculus ...
- 1,933
23
votes
8
answers
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Should we teach trigonometric substitution?
This is the question that was not asked here. Also related is this question, but both presuppose that it will be taught and ask about how best to do it. My question here is, suppose we are designing ...
- 6,680
15
votes
2
answers
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Introducing the Lebesgue integral before Riemann's
Has anyone attempted to introduce, or has data on such endeavor, Lebesgue integration before Riemann? I've seen many discussions about how the Riemann integral is obsolete and that it is presented ...
- 3,060
18
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4
answers
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Emphasizing Statistics instead of Calculus
In a 3 minute talk on ted.com, mathematician Arthur Benjamin made the argument that it makes sense to give emphasis on statistics instead of on calculus in school, after students have been given a ...
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