The first Advanced Placement Calculus exams were administered in 1955.  Back then a total of 285 students sat for the test.  In the ensuing years, the numbers have steadily increase, passing the 100,000 (AB and BC exams) mark in 1993, the 200,000 mark in 2003, and the 300,000 mark in 2009.  At the current growth rate, it is expected that more than 400,000 students will sit for the exam in 2013.  The exam consists of four main parts:  two multiple choice sections, one with a calculator and one without; and two free response sections, 2-3 questions with a calculator and 3-4 questions without.  The multiple choice sections are graded electronically.  Each June, more than 800 high school and university calculus teachers descend on Kansas City, Missouri to grade the free response sections of these exams.  These graders, who are called exam readers, attend briefings to learn the intricacies of the grading rubrics to ensure that all readers grade the same way.  There is no question that each reader would grade the questions differently if left to our own judgments.  These briefings, which include numerous examples, help to ensure uniformity of grading.  There is no intention or attempt to justify, persuade or reach agreement on the rubrics.  In fact, among the readers, there is always some disagreement with grading rubrics, some trivial some more substantial.  Although the readers have seven long days of reading, there are also social and professional events in the evenings.  The week-long reading experiences have been touted as high quality professional development as well as an opportunity to discuss classroom practices and ideas with colleagues. 

Discussion

 After teaching AP Calculus for a few years, I was invited to participate in the AP Calculus reading.  I have continued to participate in these readings each June for six years.  The College Board © touts the benefits of reading the AP exams as:

• Exchange ideas with faculty, teachers and AP Development Committee members
• Establish friendships within a worldwide network of faculty members
• Become familiar with AP scoring standards, which provide valuable knowledge for scoring your own students' essays.

In my own experience, after my first reading, I felt that I had gained in three separate areas:  (1) I had a better understanding of the grading design and could pass that on to my students; (2) I developed a better sense of verbal precision (refer to f(x) as f(x) not as “it” or “the function;” refer to f’(x) as f’(x), not “the derivative,” or “the function’s derivative;” and, (3) I had seen the importance of using units in context.  I have stressed all of these in my AP Calculus classes ever since. 

While the AP reading is a valuable experience, readers do have differences of opinion on the way in which student responses are graded.  However, the grading standards are clear and all readers grade to the same standard, whether we agree with it or not.  For example, the first question on both the AB and BC 2013 exams read as follows:

On a certain workday, the rate, in tons per hour, at which unprocessed gravel arrives at a gravel processing plant is modeled by a cosine function, G(t)=90+45cos(t²/18), where t  is measured in hours on the closed interval [0, 8].  At the beginning of the workday, when t = 0, the plant has 500 tons of unprocessed gravel.  During the hours of operation, the plant processes gravel at a constant rate of 100 tons per hour.

(a) Find G'(5).  Using correct units, interpret your answer in the context of the problem.

 Part (a) of the question was worth two (out of nine) points.  The first point was earned for supplying the correct answer to three decimal places, G'(5) = 24.588 or 24.587.  The second point was earned for correctly explaining that G'(5) is the rate at which the rate of gravel arrival is changing at t = 5 in tons per hour squared.  In other words, G'(5) is the rate of change of the rate of change.  Most students did not earn the second point.  However, a good number of students gave a correct explanation, including the units, in tons per hour squared, but did not reiterate that this was at t = 5.  For this omission, the second point was lost.  Some readers thought that the inclusion of a correct explanation, and the inclusion of the correct units was convincing evidence that the student should get the second point. 

There are several blogs available in which disgruntled former AP Calculus readers complain in great detail about the unfair or capricious application of standards.  One example is titled, “The AP Calculus Grading System is Badly Broken” and is available at http://www.lehigh.edu/~shw2/ap2001.html.  I acknowledge that I also disagree with some of the grading standards.  I believe that some students are unfairly docked points for trivial reasons and I believe other students are given points for responses that require little or no evidence of actual mathematical thinking.  I want to acknowledge this; however, this is not the focus of my research.  I do, however, expect that the topic will arise in my research.  I will be asking the teachers if they have given their students “pointers” based on the nit-picky grading standards sometimes applied to the grading.

I noticed that at the readings, other participants told me that they believed they were much better teachers because they had attended the AP reading.  Throughout the reading, readers are heard saying that they are learning so much and that they will be changing the way they teach.  I wonder if that is really true. My students have asked me if I thought they had an advantage because I was an exam reader.  My answer is always, “of course!” I know that my reading experiences have affected my classroom practice and my student’s average AP exam scores have increased in the past several years.  So, I am wondering if there is a causal connection in general. 

 Potential Research Questions

Because of my involvement in GMU summer institutes the past several summers, I have become increasingly fascinated and interested in teacher professional development.  I want to know what impact on their professional development is made by participation in the AP Calculus reading.  Do these teachers improve their own understanding of calculus?  Do they really change their practice; and, if so, what impact does it have on their students’ content knowledge and performance on the annual AP Calculus exam.  

            Possible research questions are:

• How do AP Calculus teachers perceive the professional development at the AP Calculus reading?
• Does participation in an AP Calculus national exam reading affect teachers' classroom practice?  If so, how?
• Are the AP Calculus exam scores for students whose teacher participates in the AP Calculus reading significantly different from the students whose teacher does not participate?

Abbreviated Literature Review

        Ackerman (2013) found that enrollment on AP courses is an indicator of success in college admissions and that performance on AP exams is an indicator of future academic success.  Students who take AP classes in high school are more likely to be graduated from college in four years and more likely to have higher GPAs than their classmates who did not take AP classes (Klein, 2007).  However, one could argue that students who register for AP courses already have the ability and motivation which would lead them to success in college.  On the other hand, students report that their AP Calculus course prepared them well for college mathematics courses (Anonymous, 2008).  But, if we limit AP access to only those who are well-prepared or who we deem have a high probability of success, then some students who could actually do well are being denied access.  Earning a low score on the AP Calculus exam does not indicate that the student did not get anything out of the course; the exposure to college level material can still play a part in preparing the student for college work (Kelleher, 2004). 

            Low scoring does call into question both the readiness of the students and the proficiency of the teacher.  Imig (2008) found that AP teachers who enjoyed higher pass rates on AP exams gave their students more questions which promote critical thinking and problem solving skills and who also spent more time engaging students in peer discussions.  One way for teachers to develop their proficiencies is to participate in AP readings.   Cannon and Wise (2004) advise biologists that becoming a reader for the AP Biology exam will make them better teachers.   Broyles (2008) found that teacher participation in a professional development institute positively impacted the student performance in different Algebra classes.  Likewise, in 2008, a study found that “teacher experience and science subject coursework were not significantly related to students’ achievement” and concludes that other teacher characteristics, which can be acquired through professional development and mentoring, are impacting instructional effectiveness and student achievement (Zuelke, 2008, p. 68).

Proposed Method

I plan to survey high school teachers learn what changes they have made because of their participation in the AP reading and how their students’ understanding has changed and how their average scores have been affected

I have contacted the AP Calculus Chief reader and the College Board; however, for legal reasons, they have declined to provide me with email addresses for readers who are high school teachers.  A list of readers and the schools at which they teach is available on the AP Calculus website.  I have copied the list and eliminated all the university professors; I have a total of about 500 names.  I have been searching the Internet with the teacher names and school names to try to find their email addresses and am having a good amount of success.  At my current rate, I should have over 100 email addresses.  I also placed a message on the AP Calculus listserv and have had 10 high school teachers contact me to volunteer to participate.  I will also be sending a request to the readers who were at my reading table and those whom I know from previous years.  I believe I will be able to get a sample of at least 30, probably more.

After I have a pool of interested readers, I will obtain informed consent and ask them to complete a demographic survey, a Lickert-scale survey and answer some open response questions.   Additionally, I intend to conduct individual interviews, either in person or via telephone, with several experienced readers.  At about the mid-year point, I will conduct a follow-up survey to determine if the teachers have actually implemented the changes which they planned to incorporate.

I plan to use Survey Monkey to conduct the surveys.  I want to make the survey in several chunks so that the participants do not get weary.  The first part is the demographic information.  The second part is a Lickert-scale series of questions.  And, the third part is the open response questions.  My unfinished drafts of these three at the end of this paper.  I have not yet developed the interview questions or the follow-up questionnaire.  I also need to determine if informed consent can be achieved via a short Survey Monkey survey or if that must be done with paper and a physical signature.

My Evolving View and Experiences with Teacher Professional Development

Current Status

I am currently working on my HSRB paperwork and intend to submit it after I have had some discussion with my committee.  I want to ensure that my questions are bias free and that I am collecting all the information which I need.  Links to the three parts to my survey on which I am currently working are:  Demographic Information, Lickert Scale Questionnairre, and Open Response Questionnairre.  I still need to develop the Follow-up Questions and the Interview Questions.

References

Ackerman, P. L., Kanfer, R., & Calderwood, C. (2013). High school advanced placement and student performance in college: STEM majors, non-STEM majors, and gender differences. Teachers College Record, 115(10), 1.

Anonymous.  In praise of AP calculus. (2008). The Chronicle of Higher Education, 54(38), B26.

Cannon, R. E., & Wise, D. (2004). Become a better biologist: Read the advanced placement biology essays. Bioscience, 54(9), 806-807.

Imig, A. (2008). A case study of teacher effectiveness in advanced placement courses. (Order No. 3349287, George Fox University). ProQuest Dissertations and Theses.

Kelleher, M. (2004). Low pass rates on AP exams raise questions about teaching. Catalyst Chicago, XV, 10.

Klein, A. (2007). Researchers see college benefits for students who took AP courses. Education Week, 26(22), 7.