Chapter 5

CHAPTER 5

DISCUSSION

Introduction

This chapter provides summarized solutions to the questions posed in this constructivist investigation (Guba & Lincoln, 1994). Certain data described the genesis of the Advanced Placement (AP) Statistics course, the initial offering of this course, and the role of the instructor in teaching as recommended by the AP Statistics Test Development Committee. Other data collected addressed students’ understanding in concept-oriented Advanced Placement Statistics classes. Concept-oriented components recommended by the AP Statistics Test Development Committee, published in the Advanced Placement Course Description: Statistics (1997) and the Teacher’s Guide: AP Statistics (1997), were given special attention. Each of the five research questions, delineated in chapter 4, are discussed separately.
At every stage of data collection, this study focused on student learning. I consistently questioned which components of concept-oriented instruction, as defined by the Test Development Committee, affected students’ understanding of statistics. Prolonged engagement and persistent observation at the research site, both addressing trustworthiness (Lincoln & Guba, 1985), provided the opportunity to observe which components may have affected student learning. I gathered student artifacts, various information from Lee, and materials from the College Board to describe these components and their effect on student learning. Ongoing data analysis (Creswell, 1994; Guba & Lincoln, 1994) led to member checking, follow-up interviews, further analysis, and informal conversations with students. Throughout the academic year 1997-1998, Lee satisfied member checking (Creswell, 1994; Guba & Lincoln, 1994) by confirming or denying my observations. Although the focus of the study began as student-centered, two questions, not directly related to student learning, emerged from the data. The first question emerged as a result of examining the AP Statistics course holistically. Another research question emerged from conversations between Lee and myself regarding his teaching philosophy and techniques.

Limitations and Transferability

    Purposive sampling affected the feasibility of generalizing to other environments (Creswell, 1994). Data gathered from the research site regarding the initial offering of AP Statistics represented students’ learning behaviors and patterns from a similar environment. Lincoln and Guba state, "It is not the naturalist’s task to provide an index of transferability, but it is his or her responsibility to provide the data base that makes transferability judgments possible on the part of potential appliers" (Lincoln & Guba, 1985, p. 316). Students at this site referred to as "below average" are likely to be average, or even above average, in many other school settings. In addition, the junior class at this school was above average. To illustrate, students from the two observed classes have been accepted into the following colleges and universities: Brown, Columbia, Cornell, Dartmouth, Duke, Emory, Georgetown, Georgia Tech, Harvard, Johns Hopkins, MIT, Northwestern, Princeton, Rice, Stanford, Vanderbilt, Virginia, Wake Forest, and William and Mary.
    While this learning environment is atypical of secondary schools, this site was chosen because of the characteristics and experiences of the instructor. The primary purpose of this research focused on student learning in a concept-oriented course. To accomplish this, it was necessary to observe an instructor who would competently teach according to the Test Development Committee’s recommended format. After my initial meeting with Lee in May 1996, I was confident he satisfied these criteria.
    However, as this past year (1997-1998) evolved, Lee participated in the data analysis process in a manner I did not predict. As issues emerged from the data regarding classroom discussions, structure, and other relevant issues, I probed his recollections by asking additional questions. As our conversations became more detailed, I became more interested in his reflections and explanations. Unbeknownst to me, simultaneously his interest in this study about his students, also increased. As a result of these conversations, an unexpected relationship developed between Lee, as the practitioner, and me, as the researcher. Completely unsolicited, Lee commented one day that "you’ve really made me think about what I do and why." We have since discussed this idea further. He has realized that while it is still important for him to reflect on his overall goals, and consider if these goals are being accomplished, and it is also important that he collaborate about these goals with colleagues. Even though he is experienced pedagogically and knowledgeable about the content, he has realized that reflection can be a productive and valuable process. From my perspective, this relationship influenced this study. While the purpose of my research was to focus on the students’ learning, the most detailed and informative results were related to Lee’s philosophy and how it affected his pedagogy. Given this evolution of how Lee and I collaborated to describe and understand the learning dynamics in these classes, we both believe that the students’ responses are valid and reliable for this environment.

Discussion

From 1996-1997 to 1997-1998

    Information regarding changes from the initial offering to the second offering emerged via the listserve. Although the test format was the same for the first two years, in 1999 the number of multiple choice questions will increase from 35 to 40. According to J. Haberstroh of the Educational Testing Service (ETS; personal correspondence, April 17, 1998), the 1996-1997 test was "under speeded." Students finished the multiple choice section early so there seemed to be time available for more questions. Haberstroh explained that more questions will be added so they can obtain better information in terms of what students do and do not understand about specific content topics (personal correspondence, April 17, 1998).
    About a week before the exam in 1998, a teacher posted to the listserve the distribution of test questions from the previous year. The information supplied to him by ETS follows: Data Analysis: 20-30%; Conducting a Study: 10-15%; Probability: 20-30%; and Statistical Inference: 30-40%. This teacher inquired about the format of the 1998 test and was told the distribution would be approximately the same. No information was requested or released regarding the 1999 exam.
    In 1998 as in 1997, prior to the exam, teachers expressed overwhelming concern about their students’ success on the exam. As May 15, 1998 approached, conversations on the listserve increased regarding techniques to prepare students for the exam. Overall, of those who contributed to the list, most teachers had completed the course syllabus by early May. They used the last few weeks to review. Comments and suggestions addressed questions from the (few) published review books, hints to boost students’ confidence, and scoring information from last year’s exam.
    After the 1998 examination, teachers posted students’ impressions to the listserve. Most students indicated the 35 multiple choice (MC) questions were straightforward and relatively easy. Students’ opinions on the Free Response (FR) and Investigative Task (IT) questions (see Appendix L) were mixed. Some reported these questions were more difficult than the previous year. Others stated the wording was ambiguous or confusing. A few students remarked that it was long, but not too difficult. Teachers wrote comments similar to last year. More than one teacher suggested that there was enough variety to distinguish the students’ scores. Like last year, there was one FR problem, question 3 or the butterfly problem, that generated discussion and debate among teachers. Some commented the problem was difficult while others stated it was confusing. Many indicated concern about how it would be graded. A well-respected statistician, teacher, and author, Paul Velleman, stated, "as a question designed to separate the 5s from the 4s, it is quite good" (APStat listserve archives, May 20, 1998). In general, comments about the test from the initial year and the second year were remarkably similar. Overall, teachers concluded that the Test Development Committee did a remarkable job writing a test that reflected the goals and philosophy of the AP Statistics course.
    Another topic on the listserve that was briefly discussed last year, but more frequently this year, was various college’s policies on granting course credit for AP Statistics. High school teachers wanted to know which colleges accept this course, how many quarter/semester hours would be credited, and what course would they be given credit for. This conversation led some college professors to indicate concern that students who used a graphing calculator in AP Statistics and enrolled in a second statistics course in college would be unprepared for extensive computer applications at the collegiate level. Lee and I discussed their concerns. First, not all colleges and all departments use technology to teach statistical concepts. Second, Lee believed that his students (and others who complete a rigorous AP course) could easily adapt to the statistical software packages most commonly used (Minitab, SPSS, Systat, Data Desk) in college courses. We observed his students as they transitioned from calculator functions to software options. They had no difficulties making this transition.

The AP Statistics Course

Data to answer Research Question 1, focused on the salient features of the AP Statistics course and the genesis of these features by addressing the development of the AP Statistics course and the initial offering. This course emerged from concern that many high school students were not enrolling in mathematics courses in their senior year. Dedication and extensive efforts by members of the College Board, ETS, and prominent statistics educators were realized this past year with the successful administration of the first AP Statistics exam. Informal interviews with committee members revealed the Reading (see chapter 4) was successful and informative. As reported in chapter 4, their impressions of the first Reading included relief at the overall success of the first year and the examination; support of holistic grading and rubrics; a consensus that students stated assumptions poorly; students written responses were weak; and that some students used the calculator inappropriately in the Free Response questions. Other salient features of the course and the initial offering of the AP exam included the AP Statistics listserv and printed resources for teachers (see Appendix E). The listserv provided a forum for teachers to obtain assistance with the subject matter. Conversations on the listserv revolved around AP Statistics curriculum topics, specific homework problems in a book, use of projects in the course, technology tips and applications, and finding information on the Internet. Printed resources included materials published by the College Board and texts written by leaders in statistics and education.

The Instructor

Lee explores a variety of resources to stay current in his teaching practice. He collaborates with other teachers by attending conferences, conducting workshops, hosting workshops and participating in the listserv. He teaches adjunct at a local community college that utilizes laptop computers and a CD-ROM in the introductory statistics course. He is currently working with one major publisher to have his school serve as a beta test site for an interactive statistical software package. He is coauthoring a test bank of statistics questions and reviews textbooks for different publishers. He frequently searches the Internet for interesting data sources and websites containing thought provoking multiple choice questions.
As the 1998 AP Statistics exam approached, I asked Lee to describe the overall differences between what he did the first year and the second year. His initial response involved choice of the textbook. In academic year 1997-1998, he used a text that was completely activity driven (Rossman, 1997). He stated that these students did not respond well to this nontraditional text.

This year’s class was not nearly as self-motivated or self-reliant as last year. Last year, I could say, ‘here’s today’s activity’ and sit down and wait for the occasional question/comment/aha. This year, it would immediately be ‘How do I do this?’ or ‘I don’t understand’ or ‘I don’t know where to start.’ They relied on me more and on themselves less. (personal correspondence, May 15, 1998)

I asked Lee if this information would impact how he approached his classes next year. He replied that while he enjoyed the activity-driven text, he thought the students responded better when he incorporated ideas and activities from a variety of sources (personal correspondence, May 15, 1998). As to 1998-1999, he is changing to a new text written for the AP course (Yates, Moore and McCabe, in press).
When I asked what he did differently the second year, he also described curricular issues.

Topic wise, I went into more depth about things like types of error and power of a test, non-parametric statistics, a little ANOVA, much less probability (but still more than is expected on the AP syllabus). I think the students who were with the program, ended up with a better understanding of the big picture. (personal correspondence, May 15, 1998)

He assigned major projects both years. In his opinion, the self-motivated students (from the first year) worked harder throughout the four months, submitted more thoughtful weekly project reports, and presented better projects overall. He chose to defer any major decision about projects until he works with next year’s students and has an idea of their abilities and attitudes. In his final remark, he stated that he stressed conceptual understanding both years and will not change that. He explained that they have to understand the reasoning behind what they are doing and why. He would continue to require that they provide clear explanations that reveal their level of conceptual understanding.

Group Projects

    Watkins et al. (1997) recommended that "statistics should be taught through the examination of real data prompted by real questions" (p. 4). Group projects can be structured to accomplish this. In considering the research question regarding students’ projects, the evidence suggested a relationship between the projects’ effectiveness and students’ mathematical abilities. The strongest student in each of the two classes indicated the project did not help them understand the concepts. Neither student, Carter nor Fran, suggested the project was directly linked to the course content. They both expressed difficulties in perceiving project activities, such as writing survey items or collecting data, as mathematical tasks. However, the weaker students directly commented that at least one part of the project provided a learning experience that helped them understand concepts in general. Hiebert & Carpenter (1992) explained prior knowledge by stating "students interpret and respond to new situations in terms of what they know" (p. 80). Consistent with this prior knowledge theory, the weaker students provided specific examples that connected their project experience to their current understanding. In addition, these students consistently stated the project was more difficult than they had anticipated.
    Examination of project data also revealed gender trends. All five girls provided favorable impressions of the overall group process. Even the female student, Fran, who said the project did not help with concepts, indicated the project was a worthwhile activity. On the other hand, no patterns emerged among the boys. Their opinions about the effectiveness of the project on learning ranged from no relationship to strong connections.
    Statisticians recommended that content presented in statistics courses be more closely aligned with the statistical techniques that statisticians use to conduct data analysis (College Entrance Examination Board, 1997). In an interview, one student referred directly to this recommendation. Ethan said, "I felt like we were doing what a real statistician would do" (EB, Interview). This comment suggests that data collection and analysis directly provides the type of learning experience recommended by the Test Development Committee.
    Hiebert & Carpenter (1992) described the relationship between understanding and prior knowledge. He suggested that "understanding can be viewed as a process of making connections, or establishing relationships, either between knowledge already internally represented or between existing networks and new information" (p. 80). This idea was expressed as one student explained her techniques of data analysis. Fran, in group FMN, completed AP Calculus BC, AP Physics, and AP Economics the previous year. She conducted most of the statistical analysis for their project. (She said the other members of her group did not understand what she was doing during several stages of analysis.) During their presentation, she explained that they investigated how the slopes changed. In our interview I asked her how she knew to do that. She directly referred to her knowledge of slopes from calculus. At a different stage of analysis, she noticed the similarity in curves. In an interview, she revealed that it was her knowledge from economics and physics that led them to investigate this similarity with respect to time.
    As presented in chapter 4, students during one project presentation did something that surprised and excited me. BDL compared fat grams in items from different fast food restaurants. To begin their presentation, they handed out biscuits from one particular fast food restaurant and let everyone eat one. Then, they went around the room and asked everyone how many grams of fat were in each biscuit. They recorded the data on the board and talked briefly about the distribution of this data. Lee and I observed this activity with no initial reaction. Midway through their presentation, I realized that they had modeled his behavior. Lee had gathered data from students numerous times this way. At the end of the class, I approached Lee and asked him if he noticed what they had done with the biscuits and the data. He had not noticed that their behavior reflected his pedagogy. The student who suggested that they bring biscuits and then collect data also had no idea they had modeled Lee’s technique.
    Overall, the students who excelled in prior mathematical experiences indicated the project was not helpful in developing statistical understanding. These students did not see that active involvement with data and the analysis techniques provided an overall framework to connect statistical concepts. On the other hand, the students who had weaker backgrounds said the project provided a comprehensive, positive learning experience. These same students enjoyed the project and indicated it was a worthwhile endeavor.

Students Gathering Data

The second research question probed one specific aspect of the project, data collection. Results from the second research question are similar to findings from the first question. Research findings revealed that students’ active involvement contributed to their learning of statistical concepts. However, the degree that students attributed their learning to these activities varied depending on their mathematical abilities. This varying degree of learning was, again, accentuated in the weaker students and not as definite for those with stronger mathematical backgrounds. Most students indicated writing survey questions or conducting a random sample was more difficult than the traditional classroom experience would suggest.

The First AP Statistics Exam

Each AP course culminates with the corresponding exam. Although some students nationwide opt not to take the exam, the exam is the year-long goal for most students. At the research site, students who enrolled in AP classes were required to take the corresponding exam. The third research question addressed the effect of concept-oriented instruction on students’ performance on the exam. Components recommended by the Test Development Committee are described individually: the project, group setting, use of technology, and teacher effect.

The Projects’ Effect on the Exam

Statistics educators suggested that students experience collection and analysis of data in order to appreciate the intricate details of realistic statistical studies (Moore, 1996; Roberts, 1992; Watkins et al., 1997). In Lee’s classes, the project provided an opportunity for students to experience a comprehensive statistical process. Based on test scores and conversations with students prior to the project, Lee believed that students did not see connections between classroom content and real world scenarios (personal correspondence, March 17, 1998). Data revealed that the project helped weaker students prepare for the exam. Several students commented that the project made the subject matter more concrete, helped them recall and apply earlier concepts, and provided an overall framework that helped them connect concepts. Students stated that experiencing the process was more meaningful than reading the text or studying in class. In addition, students who gathered their own data or had experimental design issues within their project, referred directly to the Free Response experimental design problem (see Appendix C). Some students said they expected a more difficult experiment to design while others simply stated the FR experimental design question was easy. Overall, data gathered in this environment suggested that group projects helped students, especially the weaker ones, prepare for the AP exam.

The Classroom Setting

    Research indicated cooperative group work can encourage activity among students and this facilitates student learning (Borasi, 1995; Brush, 1996; Ganter, 1997; Good, McCaslin, & Reys, 1995; Good et al., 1992; Hoek, 1997; Velleman & Moore, 1996). The Test Development Committee recommended the use of "cooperative group problem solving" (College Entrance Examination Board, 1997, p. 10). Lee used round tables to encourage students to discuss ideas freely among themselves during class. Class time usually resembled a discussion, where Lee and students asked and answered questions. Students indicated they always felt comfortable asking each other questions, comparing answers and strategies, and seeking help from Lee. Students frequently engaged in side conversations while Lee was discussing a topic. During interviews, only one student indicated this did not help him learn. Several students gave mixed opinions, stating advantages but also distractions. Every student who mentioned "distracting" was in sixth period. This specific class had a small group of disruptive students and Lee made only small efforts to control their outbursts. Groups at tables removed from these outbursts were more successful at completing problems. Students, who not distracted by the outbursts, would stray from discussing statistics but only after they were satisfied with their procedures and solutions. Overall, students indicated the seating arrangement provided a relaxed, comfortable environment and they perceived this as an advantage.
    Group strategies were particularly effective for girls. All five girls expressed positive ideas about sitting at round tables. They specifically referred to a physically comfortable learning environment, an open and relaxed classroom, and ease of seeking help either from Lee or other students. Some boys echoed these same ideas, but did not make the connection directly to their learning. The one student who said this class arrangement was distracting was male. In addition, the students who engaged in the distracting behavior were male.
    Overall, the use of round tables was effective in facilitating student learning, particularly for girls. All negative comments were directed to a small, specific group of students who were frequently loud and disruptive. These students could have been controlled by more aggressive classroom management techniques. Regardless, all but one student indicated these distractions did not interfere with their learning.

Technology

Technology was considered an essential tool in data analysis and therefore is required in the AP Statistics course (College Entrance Examination Board, 1997; Watkins et al., 1997). Since "the computer is central to what statisticians do" (College Entrance Examination Board, 1997, p. 9), the Test Development Committee recommended that instructors incorporate computers and statistical software packages in the course. However, the Committee acknowledged disparity exists in high school facilities and therefore, recommended the combined use of graphing calculators and computers. A graphing calculator was required for the exam. At the research site, students had extensive experience with the TI-83 in previous classes. Lee was adept and knowledgeable regarding use of the calculator for teaching statistics. Class discussions always utilized this technology. He frequently used the calculator to explore concepts in depth beyond the recommended syllabus. The school also had computer laboratories. Early in the year, Lee reserved the computer lab for classes and students utilized statistical software for descriptive data analysis. As the year progressed and students responded well to the ease and convenience of the TI-83, Lee used the computer lab less frequently.

The Computer Lab. Findings from this study suggest that the computer did not facilitate learning more than the calculator. Students referred to the computer as advantageous only with respect to preparation of their oral project reports. Several students indicated they used the computer to gather data from the Internet, but most groups utilized the computer labs only because of printing capabilities.

The Graphing Calculator. Findings from this study revealed that using graphing calculators did allow students to emphasize conceptual understanding. Most students interviewed suggested that while they knew how to do calculations by hand, use of the calculator allowed them to concentrate on statistical ideas. This was particularly true for the weaker students. They indicated relief from the pressure of calculating complicated formulas by hand. The calculator provided a sense of security because they knew the mathematics were correct. This allowed them to focus on comprehension and application of the results. On the other hand, the strongest student in each of the two classes said technology was not effective in facilitating learning. One student, Carter, believed most students were capable of learning with or without technology. The other student, Fran, reread the text and stated reading was more beneficial for her. However, these two students were exceptional, even in this environment.
Overall, findings from this study suggested technology was useful in facilitating student learning, especially for "average" to "below average" students. The calculator could promote student learning. The computer had advantages for analyzing large data sets and producing graphics, but students did not need this to learn introductory statistical concepts. However, they did require an experienced user to instruct them in operating a graphing calculator so they can focus on conceptual development.

Impact of the Constructivist Teacher

Lee’s students achieved great success on the initial AP Statistics exam. The results for his three sections of 40 students are shown in Table 2.

Table 2
1997 AP Statistics Exam Results Reported for the Nation and for Lee’s Classes
National Lee’s Classes
AP Score Number Percent Number Percent

5 1204 15.7% 35 87.5%

4 1694 22.1% 5 12.5%

3 1871 24.4% 0 0%

2 1518 19.8% 0 0%

1 1380 18.0% 0 0%

TOTALS 7667 100% 40 100%

Findings from this study revealed important strategies of Lee’s pedagogy. Field notes suggested that the single most important element of his teaching was his philosophy of teaching and learning. Lee was a constructivist and consistently placed the students at the forefront of the learning process. He encouraged them to conjecture and speculate. He then provided a learning environment that supported them as they confronted these ideas and constructed accurate statistical concepts. Students said the structure of the room encouraged them to ask questions of each other and him. Also, his subject matter expertise emerged in the students general responses. In addition, students provided examples of specific pedagogy that assisted in their preparation for the exam. Strategies they cited included: exploration of content in more detail than covered on the AP exam, especially probability, probability distributions, and simulations; tests that included multiple choice and free response questions to prepare them for the AP exam format; and spending the last month reviewing extensively rather than introducing new material not covered on the exam. Other typical techniques I observed included: written, numerical, and graphical interpretations required in class and on assessments; active involvement of students during class via data collection and group problem solving; frequent use of simulations in class and on tests; introduction of topics by means of activities; and facilitating during their projects, forcing students to make decisions and then act on those decisions.
Lee was extremely concerned about his students this year (1997-1998). He mentioned numerous times last year that he believed the initial offering would be the most tentative, and therefore the least strict. He based this on a theory that the committee would be concerned about acceptance of the course and the exam. Also, conversations between us revealed that he felt he reached the pinnacle with his first year’s scores. Therefore, it would be difficult to repeat, especially since this year’s class was not as strong as last year’s students. In addition, he believed his students last year were more self-motivated throughout the entire year. (I believe this is why the lack of discipline in sixth period did not deter students from their goal of learning and doing well on the exam.) They sensed he had high expectations of them and they rose to the challenge. He did not have the same response from this year’s students. I asked him to predict his students’ scores both years. The initial offering, his predictions for all three classes (even though I only observed two classes) were that 11 would score a 5, 21 would score a 4, and 8 would score a 3. His results were 35 students received a 5 and 5 received a 4. It is worth noting that all five students who received a 4 were predicted to score a 3. Academic year 1997-1998, he predicted 22 students would score a 5, 17 would score a 4, and 6 would score a 3. Since exam results for 1997-1998 were not available at this time, I cannot present the actual results.

Implications

The AP Statistics Test Development Committee recommended concept-oriented, activity-based instruction in the classroom. In general, data revealed that students benefitted from active involvement in the class. Students needed to be actively involved with data at all levels of statistical processes. The activity could involve data collection, data analysis, use of technology, or group problem solving. Findings revealed students benefitted from frequent exposure to speculating about data, conducting analysis to test their claims, and discussing their results. This research suggests that use of technology, group projects, and data collection were most beneficial for the weaker (mathematically) students. Overall, each type of activity contributed to their overall development of statistical concepts, especially average and below average mathematics students.

Recommendations

Recommendations to Future AP Statistics Teachers

Several characteristics of a successful AP Statistics teacher emerged from this study. They include but are not limited to: competency in content knowledge; familiarity with the AP Statistics syllabus; willingness to seek assistance from experienced instructors; take time to explore the variety of resources available; the ability to act as project facilitator allowing students to experience and construct their own knowledge; and accept the idea that statistics is not an exact science and therefore uncertainty exists about the truth of the conclusions. In order to achieve these goals, Lee and I made the following recommendations:

I. Learn Statistics.
a. Enroll in a junior-senior level two-semester introductory statistics sequence.
b. Attend a week-long AP Statistics workshop

II. Order College Board Materials (see Appendix E)
    a. Advanced Placement Course Description: Statistics (The Acorn Book)
    b. Teacher’s Guide: AP Statistics
    c. Free Response Questions

III.Collegiality Support
    a. Subscribe to the AP Statistics Listserv (see Appendix L)
    b. Attend local, regional and national conferences. Statistics sessions are          increasing in number and many are appropriate for high school teachers.
    c. Communicate with other AP Statistics teachers in your area. Team teach if   possible.
    d. Subscribe to at least one of these journals/newsletters (see Appendix L).
        1. AmStat News
        2. Chance Magazine
        3. Journal of Statistics Education
        4. Mathematics Teacher
        5. Statistics Teacher Network Newsletter
        6. Stats Magazine
        7. Teaching Statistics

IV.Include activities and simulations frequently in class

V. Assign group projects
    a. Use ASA guidelines and submit to the national project competition (see Appendix J)
    b. Choose small projects that are manageable for students and instructor
    c. Require students to keep a journal that is read and discussed at routine    intervals

VI. Use a graphing calculator and supplement with computer output

VII. Include writing as part of routine assessment. Emphasize explanations, stating assumptions, and defending their choices.

Statistics educators have recommended pedagogical changes consistent with the current mathematics reform movement. While implementation of activities, technology, projects and cooperative group strategies can be demanding on a new teacher, teaching statistics can be fun and rewarding.

Recommendations for Further Research

This study generated additional research topics. Recommendations for future research include: studying a novice teacher for his or her effectiveness of concept-oriented instruction; research the use of writing to investigate students’ metacognitive processes, particularly on tests and project reports; investigate extended use of computers during class time; examine the effects of smaller projects; compare a traditional text to an activity-based text; investigate learning differences and how weaker students are affected by concept-oriented instruction; and probe simulations and their effect on student learning.

Summary

This constructivist study revealed salient features of the initial offering of the AP Statistics course, including the Test Development Committee, the listserve, College Board materials, the annual Reading, and annual test score results. This study revealed several components recommended for successful teaching of AP Statistics. These included an understanding of statistics, willingness to teach subjective material, collaboration with other statistics teachers, use of calculators and computer output, assign projects, allow students to work on problems in groups, encourage problem solving and discovery learning, cover the AP syllabus thoroughly, and review if possible. It is interesting to note, these results are congruent to teaching strategies recommended by David S. Moore (Moore, 1988, 1990, 1997; Moore & McCabe, 1993). Data gathered from students suggests some aspects of the Test Development Committee’s recommended pedagogy effects students differently, depending primarily on their academic level. Overall, concept-oriented instruction by an experienced, constructivist teacher was successful.
The implications of the research included suggestions for future AP Statistics teachers. Students need to be actively involved with data at all levels of statistical processes. To accomplish this, teachers can include projects, gather data in class, use technology for data analysis, cover the AP course content in detail, and include group activities, particularly for females or weaker students. Students need to conjecture about data, conduct analysis to test their claims, and describe their results either verbally or written. Suggestions for further, or previously stated, research includes the effectiveness of concept-oriented instruction; students’ learning styles, abilities and processes; technology; and teachers’ roles, beliefs and strategies.