TJ Shales Wrote:
> The Anti-IB stuff I'm hearing -- and now I'm
> hearing it at the school board hearings -- is
> being used by people who clearly have no clue what
> they're talking about. I will bet $1,100 that most
> of those speaking tonight couldn't tell you the
> first difference between an AP and IB syllabus.
> It's crazy and the "divisions" these people talk
> about were created by themselves and fanned by
> fearmongers in their own communities. Talk about a
Hey Shales, I think you are wrong. But in case people are uniformed, here is some data to help them. I start with MIT data (which is arguably a gold standard for math and engineering teaching), and then turn to AP & IB curricula.
Calculus I and II at MIT uses Calculus with Analytic Geometry, 2nd edit, Simmons, 0070576424. Please look at this text book.
From the MIT Calculus I website
Week 1 (2/5-2/8): Limits, derivatives, differentiation rules.
Read Notes G and C, 2.1-2.5, 3.1-3.3.
Week 2 (2/11-2/15): Implicit differentiation, higher order derivatives, exp/log/trigonometric functions.
Read 3.4-3.6, 8.1-8.2, 8.3 (skip Examples 2 and 3), 8.4 (through Example 1), Notes X, 9.1, 9.2, 9.4 (through Example 2), 3.4.
Week 3 (2/18-2/22): Linear approximation, curve sketching, max-min problems.
Read Notes A, 5.2, 4.1-4.4.
Week 4 (2/25-2/28): Mean value theorem, L'Hospital's rule.
Read Notes MVT, 2.6, 12.1-12.3.
Friday 2/29: Midterm 1
Week 5 (3/3-3/7): Definite integrals, numerical integration.
Read 5.3, 6.1-6.4.
Week 6 (3/10-3/14): Fundamental theorem of calculus, properties of integrals.
Read 6.5-6.7, Notes FT, PI.
Week 7 (3/17-3/21): Differential equations, separation of variables, area between curves, surfaces of revolution, length of curves.
Read 5.4, 8.5, 7.1-7.6.
Week 7.5 (3/24-3/28): Spring break
Week 8 (3/31-4/4): Trigonometric integrals and substitution, hyperbolic functions, completing the square, intro to partial fractions.
Read 9.5, 9.7, 10.1-10.6.
Week 9 (4/7-4/11): Partial fractions, integration by parts.
Read 10.7-10.8, Notes F.
Friday 4/11: Midterm 2
Week 10 (4/14-4/18): Parametric equations, arc-length, surface area, polar coordinates.
Read 7.5-7.6, 17.1, 16.1-16.3.
Week 11 (4/21-4/25): Area and arc-length in polar coordinates, average value of a function. Read 16.4-16.5, Notes AV.
Week 12 (4/28-5/2): Improper integrals, infinite series.
Read 12.4, 13.1-13.4.
Week 13 (5/5-5/9): Comparison tests, integral test, absolute and conditional convergence.
Read 13.5-13.6, 13.8.
Week 14 (5/12-5/16): Introduction to power series and Taylor series.
Read 13.7, 14.1-14.4.
From the the MIT Calculus II website
See also http://www.core.org.cn/OcwWeb/Mathematics/index.htm
which lists the homework assignments and other material. Calculus I and II are course #s 18.01 and 18.02. The above approach is embraced in every university I know of. I know of not a single university who teaches math in a different fashion. So why would we want our kids to learn math in high school in a different manner. Is there something about their pubescent brains that requires an approach that is different from what they will see in college. And this is just calculus. For a math/science major, it does not get easier. The math gets much much more specialized. Here is a link to sophomore Calculus for Engineers http://www.core.org.cn/OcwWeb/Mathematics/18-075Fall-2004/LectureNotes/index.htm
. Anyone who wants to be a EE will take this one http://www.core.org.cn/OcwWeb/Mathematics/18-103Spring2004/LectureNotes/index.htm
. And then there are the engineering classes. And this is not unique to MIT…any engineering undergrad will have the same material.
With that as background, look at a comparison of IB and AP math shown at http://www.nap.edu/catalog.php?record_id=10380
. The appendices on this site for AP look like what I have cut-and-pasted from MIT. The IB appendix does not.
So, what to make of this fact that the AP curriculum is organized in a manner similar to the MIT curriculum (and the fact that TJ uses AP and not IB). I think it means that educators in math believe a linear approach to math (e.g., like the AP approach) is the best approach.
But don't believe me....do your own analysis of the AP, IB and MIT data at the links included in this post.