If you are a first-year student at my university who shows up to major in engineering, math or physics and you don’t already have credit for the first calculus course – via the first Advanced Placement calculus course or by some other means – then you are already a semester behind, or worse.
The first Advanced Placement Calculus course, called Calculus AB, is the low-hanging fruit in the drive to better prepare students for college majors in engineering and physical science. And a look backward to middle school shows why.
About 35% of the students who took Algebra 1 in Florida last year were 6th, 7th and 8th graders. For a Florida student who takes Algebra 1 in 8th grade, the most reasonable math sequence is Geometry in 9th grade, Algebra 2 in 10th grade, Precalculus in 11th grade, and finally AP Calculus AB in 12th grade.
That is, if 35% of the students who took Algebra 1 (a required course for graduation in Florida) took it in 8th grade or earlier, then 35% of Florida’s high school graduates should be taking AP Calculus AB in 12th grade or earlier. Florida’s passing rate on the AP Calculus AB exam is about 50%. If one assumes that is reasonable (a questionable assumption that can be addressed), then one concludes that about 17% of Florida’s high school graduates should have passed AP Calculus AB.
Yet only 4.1% of Florida’s 2012 high school graduates had passed the AP Calculus AB exam.
To be fair, this is not just a Florida problem. The top-ranked state in the nation for percentage of high school grads passing the AP Calc AB exam, Massachusetts (surprise!), posts a number of only 6.9%. Florida is ranked only 19th in the nation on this parameter (see below), but the Massachusetts number is inexplicably low as well.
How can our production of calculus-trained high school grads be so low?
Those who are familiar with the high school math sequence will immediately ask this question: How many students skip AP Calculus AB to take AP Calculus BC as a first calculus course instead? AP Calculus BC covers all of the material covered by Calculus AB (mostly differential calculus, giving university credit for Calculus 1) and then adds integral calculus and series and sequences (so that those who pass the Calc BC exam earn university Calculus 2 credit as well). Some students skip over AP Calculus AB and just take AP Calculus BC. My eldest child did that; my kids #2 and #3 took AB before BC. Only 1.8% of Florida’s 2012 high school grads had passed the Calc BC exam. Even if every one of them skipped over Calc AB, that would tell us that only 5.9% of grads had AP calculus credit. That is still inexplicably low compared to the 35% who take Algebra 1 in middle school. (The corresponding numbers in Massachusetts: 2.8% of high school grads have Calc BC credit, so that at a maximum 9.7% of high school grads have AP Calculus credit). And it’s worth pointing out again that many students take Calc AB before Calc BC, and the actual percentage of high school grads having AP calculus credit is lower.
So why is the number of high-school-grads-with-AP Calc credit so low? I don’t know. The best I can do is share some anecdotes about what has happened to individual students.
One student I heard about earned a “B” in Precalculus class and on that basis was not allowed to continue on to AP Calculus AB. I can’t tell you why – whether it was because the high school that student attends considers “B” a bad grade or whether the school limits enrollment in AP Calculus AB and they had enough “A” students to fill the available seats. If it’s the latter, then the school has a responsibility to find another teacher who is highly qualified to teach calculus (and every certified math teacher in Florida should be!).
I have had students – engineering majors in fact – who took AP Statistics instead of AP Calculus AB. I ask my students to fill out a survey on the first day of class that asks, among other things, what their highest high school math course was. I specifically tell them that AP Statistics does not qualify as a math course, at least not in my world.
AP Statistics is an excellent course. All three of my kids took it. They took it while they were also taking a real math course (Precalculus, AP Calculus AB or AP Calculus BC). But taking it instead of taking Precalc or an AP Calculus course is a big mistake – and those who advise students to do this are harming their students.
How big a problem is this? The number of 2012 Florida high school grads who had taken AP Statistics was 10,531, approximately the same as the number that had taken AP Calculus AB (11,670). Once again, this isn’t necessarily a problem – but it is if students are taking AP Statistics instead of an AP Calculus class.
Then there are the students who just don’t want to take any more math. This includes some students who want to major in science – the ubiquitous aspiring biology majors. Such students should be reminded that: (a) Even college biology majors have to take calculus; and, (b) their lives will be much better if they choose college majors in biochemistry or something similar, which (surprise!) requires more calculus.
So what can Florida do to improve this situation? I’ll make two suggestions (with no expectation that either will get any traction).
The first has to do with Florida’s new high school graduation scheme, which was signed into law last spring. The law provides for three graduation tracks, one of which is called “Scholar” and presumably provides an incentive for upper quartile high school students to aim high. Does it? In math and science, not so much. The math requirement for the Scholar designation is for Algebra 1, Geometry and Algebra 2, plus an additional “rigorous” math course – which is actually designated as “Statistics or an equally rigorous math course.” It could be Precalculus, of course, but the law’s language shines the spotlight on Statistics. The statistics language should be removed from the law and replaced with Precalculus. Period. To call a high school grad a “Scholar” in 2013 without a Precalculus course is a travesty.
The second suggestion is about math teachers. Perhaps there are not enough seats in AP Calculus AB classes because there are not enough teachers qualified to teach calculus. Perhaps Florida’s 50% pass rate on the AP Calculus AB exam is because some of the classes that do exist are not well taught. If either is true, then the answer is more strong math teachers in our high schools – teachers who have completed an upper division program in mathematics so that elementary calculus is easy.
In Florida, there is at least one teacher education program in math that graduates teachers who are prepared to teach calculus – FSU-Teach, the UTeach clone at FSU. The University of Florida and Florida Institute of Technology also have UTeach clone programs, and they probably do a fine job of producing highly qualified math teachers as well. Nevertheless, there are not nearly enough strong students entering math teaching, and we need to do more to attract such students into the profession. Like pay them more.
There are things that Florida’s universities can do to graduate more engineering and physical science students. But the weak high school preparation of aspiring engineers will continue to be a problem until it is addressed. Steering more high school students in AP Calculus AB is a practical way to start.
% 2012 high school grads with AP Calc AB credit
New York 6.0
New Jersey 5.1
New Hampshire 4.5
South Dakota 4.1
South Carolina 3.7
North Carolina 3.5
Rhode Island 3.1
North Dakota 2.4
West Virginia 1.9
New Mexico 1.6
District of Columbia 0.8