Sunday, June 1, 2014

AP Calculus and the Common Core

In February, 2013, Trevor Packer, Senior Vice-President for the Advanced Placement Program and Instruction at The College Board, appeared before the American Association of School Administrators (AASA), the professional society for school superintendents, to provide information about the Advanced Placement Program. Following that session, he had a short video interview in which he was asked to comment on the relationship between the Common Core State Standards (CCSS) and the College Board’s Advanced Placement Program. What he said about CCSS and AP Calculus has, unfortunately, been misreported. With Trevor Packer’s encouragement, I would like to attempt a clarification: There is no conflict between the Common Core and AP Calculus. In fact, it is just the opposite. If faithfully implemented, the Common Core can improve the preparation of students for AP Calculus or any college-level calculus.

In the AASA summary of the conference proceedings, “College Board: Reconciling AP Exams With Common Core,” Packer’s comment on AP Calculus was reported as follows:
“Despite these measures, there are still difficulties in reconciling many AP courses with the Common Core. In particular, AP Calculus is in conflict with the Common Core, Packer said, and it lies outside the sequence of the Common Core because of the fear that it may unnecessarily rush students into advanced math classes for which they are not prepared. 
“The College Board suggests a solution to the problem of AP Calculus ‘If you’re worried about AP Calculus and fidelity to the Common Core, we recommend AP Statistics and AP Computer Science,’ he told conference attendees.”
This article, written by a high school junior serving as an intern at the meeting, is not in line with the video of Packer’s remarks, “College Board’s Trevor Packer on Common Core and AP Curriculum,” where he says that
“AP Calculus sits outside of the Common Core. The Calculus is not part of the Common Core sequence, and in fact the Common Core asks that educators slow down the progressions for math so that students learn college-ready math very, very well. So that can involve a sequence that does not culminate in AP Calculus. There may still be a track toward AP Calculus for students who are interested in majoring in Engineering or other STEM disciplines, but by and large, the Common Core math sequence is best suited to prepare students for AP Statistics or AP Computer Science, which have dependencies on the math requirements of the Common Core.”
The assertion of a conflict between the Common Core and AP Calculus was a misinterpretation on the part of the student. Nevertheless, this lack of clear articulation between Common Core and AP Calculus is easy to misinterpret.

Packer’s remarks arose from concerns that I and others have expressed about the headlong rush to calculus in high school (see, in particular, MAA/NCTM Joint Position on Calculus). As I pointed out in last month’s column (FDWK+B, May, 2014), almost 700,000 students begin the study of calculus while in high school each year. Not all of them are in AP programs. Not all in an AP program take or even intend to take an AP Calculus exam. But we are now closing in on 400,000 students who take either the AB or BC Calculus exam each year, a number that is still growing at roughly 6% per year with no sign that we have reached an inflection point. Over half the students in Calculus I in our colleges and universities have already completed a calculus course while in high school. At our leading universities, the fraction is over three-quarters. Unfortunately, merely studying calculus in high school does not mean that these students are ready for college-level calculus and the subsequent mathematics courses required for engineering or the mathematical or physical sciences.

The problem for many students who enter with the aspiration of a STEM degree is inadequate proficiency at the level of precalculus: facility with algebra; understanding of trigonometric, exponential, and logarithmic functions; and comprehension of the varied and interconnected ways of viewing functions. Packer speaks of slowing down the progressions through mathematics. This is in response to a shared concern that the rush to get to calculus while in high school can interfere with the development of a solid foundation on which to build mathematical proficiency. Much of the impetus for the Common Core State Standards in Mathematics comes from the recognition that there are clear benchmarks consisting of skills and understandings that must be mastered before students are ready to move on to the next level of abstraction and sophistication. Failure to achieve those benchmarks at the appropriate point in a student’s mathematical development risks seriously handicapping future mathematical achievement.

The Common Core was designed as a common core, a set of expectations we intend for all students. There is an intentional gap between where the Common Core in Mathematics ends and where mathematics at the level of calculus begins. This gap is partially filled with the additional topics marked with a “+” in the Common Core State Standards in Mathematics, topics that usually get the required level of attention in a course called Precalculus. As the name suggests, Precalculus is the course that prepares students for calculus. This is the articulation problem to which Packer alludes. Completing the Common Core does not mean one is ready for the study of AP Calculus or any other calculus. It means one is ready for a number of options that include AP Statistics, AP Computer Science, or a Precalculus class.

There is no conflict between AP Calculus and the Common Core. Rather, there is an expectation that if the Common Core is faithfully implemented, then students will be better prepared when they get to AP Calculus and the courses that follow it.

5 comments:

  1. This is beautiful. Thank you. I did this post on it: http://wp.me/p2OKqy-1QY

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  2. Ze'ev WurmanJune 3, 2014 at 2:22 PM

    Thank you for that beautiful re-interpretation of Packer's words that would make the Central Committee of the Communist Party of the Soviet Union proud.

    Just to make sure that Packer's words are correctly interpreted:

    "There may still be a track toward AP Calculus for students who are interested in majoring in Engineering or other STEM disciplines, but by and large, the Common Core math sequence is best suited to prepare students for AP Statistics or AP Computer Science,"

    In other words, Packer acknowledges that Common Core DOES NOT prepare students for STEM disciplines. Yes, schools may try and stitch together a track that will lead towards Calculus and STEM, but "by and large" this is not what Common Core is about.

    So tell me again what was wrong with what that "high school junior serving as an intern" wrote, that calculus "lies outside the sequence of the Common Core"?? I am also sure that Mr. Packer did speak at that event, even if not on that video clip, of "the fear that it may unnecessarily rush students into advanced math classes for which they are not prepared." After all, this is told left and right by all Common Core peddlers to defend the deletion of significant chunks of content from high school mathematics.

    Comrade Bressoud, the Party is proud of you! The blood of young interns is the oil on the wheels of our Glorious Revolution.

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  3. I have taught remedial freshman HS math through Calculus. I have studied CCSS k-12 along with Singapore math k-8 and believe CCSS is better for Calc. The problem in teaching Calculus is not the Calculus; it is weaknesses with Algebra. The problem in teaching Algebra is weaknesses with fractions. All the way through, students have been memorizing, compartmentalizing, and confusing practices.I don't need to take anyone's opinion by faith because the appendix of the CCSS clearly lays out the sequence in high school, leaving the fourth year for pre-calculus or a class better suited for a non-STEM career path. All over the country districts are finding different ways to accelerate students such that they are able to take Calculus in HS just as they always have. If students are taught the traditional way: http://tinyurl.com/fract222 they will not be as prepared for calculus as with CCSS: https://www.illustrativemathematics.org/fractions_progression That is something we can all reason through for ourselves.

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  4. "The problem for many students who enter with the aspiration of a STEM degree is inadequate proficiency at the level of precalculus: facility with algebra; understanding of trigonometric, exponential, and logarithmic functions; and comprehension of the varied and interconnected ways of viewing functions. Packer speaks of slowing down the progressions through mathematics. This is in response to a shared concern that the rush to get to calculus while in high school can interfere with the development of a solid foundation on which to build mathematical proficiency. Much of the impetus for the Common Core State Standards in Mathematics comes from the recognition that there are clear benchmarks consisting of skills and understandings that must be mastered before students are ready to move on to the next level of abstraction and sophistication. Failure to achieve those benchmarks at the appropriate point in a student’s mathematical development risks seriously handicapping future mathematical achievement."


    This is the issue but the problem is that schools (due to the politics) will not enforce this notion anymore. Slowing down isn't an answer. The last part of your paragraph is the answer. Before students move on to higher level classes they must first show reasonable mastery in the previous classes. It isn’t a complicated notion, just politically complicated.

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