I’ve written about the differences between the AP and IB programs. In a nutshell, the IB is an entire comprehensive curriculum leading to a diploma whereas the AP program is a series of subject-specific examinations where students are free to pick and choose which exams they write.

Recently, the Thomas B. Fordham foundation sponsored a study “Advanced Placement and International Baccalaureate: Do they deserve Gold Star Status?” to compare the academic merits of the two programs, specifically comparing the Biology, English, Mathematics and History offerings of each.

The very act of comparing the two, however, requires some judgement calls: since the IB program requires all students to take a senior math course, there can be as many as six different “levels” of math courses offered by Ontario IB schools. Obviously, the content and goals of these courses will vary widely. Certainly, taking the highest of the “Higher Level” (HL) offerings provides a very different foundation than the lowest of the “Standard Level” (SL) courses. Similarly, there are two AP Calculus exams: AB is meant to cover a half-year college course, while AB is meant to cover the material found in a full-year, first year, American college calculus course. The study chose to compare the SL curriculum to the AB exam, citing the justification that both programs are for students not continuing in a heavily math-based university program.

The first problem I have with the comparison is that students who are not intending to study math (or math-related fields) in university have the option of avoiding AP Calculus altogether. Yet, every IB student must take at least SL level math to graduate with the IB diploma. It’s perhaps a little unfair to compare a voluntary, advanced credit course with a required, high school mathematics program, but the point of the study was to establish whether one or both programs really deserved the reputation as a stellar academic program. So, we’ll go with it for now. ðŸ™‚

Given that comparison, I couldn’t comprehend how the IB math program scored higher (B-) than the AP calculus (C+). One of my beefs after several years of tutoring students in the IB program is how students are “pushed through” advanced math topics. This is because senior math is required of all students, and quite frankly, not all students are suited to senior level studies in math. And, given that your final IB “score” is dependent solely on the mark from the IB exit exams, an IB SL program *really* lends itself to teaching to the test.

When you know, for example, that there will be only one exam question concerning derivatives, probably based on throwing something into the air, it’s not too difficult to teach the least talented of students a pattern-based answer that requires no real understanding of the math concepts. There are few 12 year olds who aren’t capable of mimicking these steps.

Today’s update to the story comes via Jay Matthews at the Washington Post in Professor Says Editors Altered Review of AP, IB Courses:

David Klein of California State University at Northridge posted on his university’s Web site his original assessments of AP Calculus AB and IB Mathematics SL, which showed he would have given a C+ to the AP course and a C- to the IB course. The final version of the report, released Nov. 14, raised the IB grade to a B-, contradicting Klein’s view that the AP course was better

. . .

Klein says he does not consider either the AP or IB courses the gold standard for high school math, although in his original report he said they had some strengths not found in mainstream high school programs.

. . .

Klein also says that many of what he considered his strongest points were deleted by the editors, particularly his view that overuse of calculators could interfere with students’ mastery of analytical skills and conceptual understanding. (The report can be seen at http://www.edexcellence.net.)

This, I get. I’ve long taken issue with how both of these programs overuse calculators and minimize manual calculations. The standard argument in favour of using calculators to remove computational barriers is this: the kids can then focus on *analyzing* and higher level thinking skills.

The problem is, as any good math student knows, **our real understanding of mathematical concepts comes from using the underlying math, not avoiding it.**

If you don’t know what dance the numbers are doing, you can’t possibly make meaningful sense of the result.

This is one reason why the MDM4U course (Data Management) is so hard for so many kids. I remember studying statistics at university before computer programs were used for the number crunching. I needed to know, by hand and with no formula cheat sheet, how to compute things like standard deviations and correlation coefficients.

You couldn’t get through that course without *seeing* all the nitty gritty steps involved in arriving at your stats. More importantly, **since you knew exactly what you did with all the numbers, you understood what they meant.** In the Data Management course, however, many students are using calculators and computers to avoid the “trivial” act of actually calculating the statistics — as if that somehow weren’t part of the point.

Granted, arithmetic isn’t mathematics, but arithmetic is how most of us come to understand numbers. Take that away from students, and they’re making a whole bunch of advanced conclusions, based on very little understanding.

I’m not arguing that it’s perhaps more interesting for lower-ability math students to be able to answer questions about whether given data shows a particular trend or correlation. **But, without the ability to do all the work by hand, or at the very least understand it, these students are never going to be in positions where they’ll get to do that kind of higher level mathematical analysis anyway.** So, what exactly is this really preparing them for?

It would be one thing if these programs made it very clear that they are shielding the kids from a lot of the real work. I’m all for a full-disclosure statement that informs the students there is a *lot* more involved in doing this stuff for real, and that they should use their interest/success in these courses to decide whether they want to actually study these concepts (properly!) in university.

But the problem, and the point of this study, is that these programs are often heralded as models of excellence in education. That’s not exactly consistent with the “warning — we’re taking out the ‘hard stuff’ so you can work at a higher conceptual level” disclaimer that *should* accompany these courses, at least as far as mathematics is concerned.

Public misunderstanding of mathematics and mathematical literacy (I guess the educrats want us to use the phrase *numeracy* now) have created a real problem in mathematics education. Because so many people think that math is “hard to do” they don’t realize how easy it actually is to teach and learn math through memorization of procedures and ignore understanding altogether. Therefore, to look at the “hard” questions on an AP Calculus or IB math exam and to see kids answer them looks *impressive*. Memorizing the encyclopaedia sounds impressive, too. And it is, but it’s a feat of memory and not of understanding or appreciation of knowledge.

For homeschoolers, the choice between the two programs is simple. It’s simply not possible to participate in IB offerings without regular enrollment at a local high schools, so AP is your only option.

Is AP worth taking at all? Yes, for many reasons. But, do so with the understanding that the act of preparing for the exam is separate from the act of learning calculus.