Using Research Projects to Help Develop High School Students' Statistical ThinkingAuthor(s): Randall E. Groth and Nancy N. PowellSource: The Mathematics Teacher, Vol. 97, No. 2 (FEBRUARY 2004), pp. 106-109Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/20871523 .Accessed: 02/05/2014 12:38
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Randall E. Groth and Nancy N. Powell
Using Research Projects to Help Develop
High School Students' Statistical Thinking
Vf e need to engage
students in all phases
investigative cycle of
tatistics plays a key role in shaping policy in a
democratic society, so statistical literacy is essential for all citizens to keep a democratic government strong (Wallman 1993). However, fostering the sta tistical thinking is a complex endeavor We ulti
mately need to engage students in all phases of the
investigative cycle of statistics, including data gath ering, data analysis, and inference.
This article describes two projects in which we
attempted to help Advanced Placement (AP) statis tics students become proficient at moving through the investigative cycle. Although the projects were
implemented in an AP class, they could be included as part of any class in which linear equations and best-fit lines are studied. As we describe the two
projects, we also discuss some of our reflections on
the extent to which the projects helped our stu dents become more proficient. In the first project, the students focused on the data analysis and infer ence phases. In the second project, the students had the opportunity to experience all phases of the
PROJECT 1 : ANALYZING AND DRAWING CONCLUSIONS FROM EXISTING DATA FILES
Project 1, shown in figure 1, was assigned during the first semester of the school year. At the time, students were using their textbook (Yates, Moore, and McCabe 1999) to study concepts related to cor relation. Project 1 helped students develop deeper understandings of some of the concepts that they were studying, and it helped them become comfort able using the computer program Fathom (Finzer, Erickson, and Binker 2001). We saw Fathom as a
powerful tool for helping formulate and investigate statistical conjectures, since it allows users to
quickly import data, calculate summary statistics, test hypotheses, and build graphs and tables. Stu dents had some freedom to choose the problem that
they would study; we encouraged them to explore some of the data files contained in Fathom. Because Fathom comes packaged with existing data files, we
were able to move the focus of the project away from the planning and data-collection parts of the
investigative cycle and toward the analysis and conclusion parts of the cycle.
In assessing students' work on the first project, we gained several important insights about stu dents' thinking while they engaged in analyzing data. These insights were valuable for guiding future instruction. We found that some students tried to make the intercepts of the regression line have meaning even when they did not. Some stu dents tried to make sense of a negative regression line intercept within the context of plotting SAT scores versus grade-point average.
Perhaps partially because of the stated require ments of the project, students attempted to force
meaning on the intercept when it really had no use ful physical interpretation. Some students also did not seem to realize that it was dangerous to force
meaning on intercepts, or any points, that lie well outside the cluster of points used to produce the
regression line. After identifying these gaps in stu dents' understanding, we were able to address them in future instruction.
Although many students identified the slope of the regression line as a rate of change, quite a few had difficulty giving the specific units of the rate of change. In addition, some students confused the
slope of the regression line with the correlation coefficient and stated that the slope of the regres sion line indicated the strength of the linear rela
tionship between the two variables. Finally, we
noticed that some students struggled with the idea
Randall Groth, firstname.lastname@example.org, teaches mathe matics education at Salisbury University in Salisbury, MD 21804. His interests include teaching mathematics methods courses for preservice teachers and researching high school students' statistical thinking. Nancy Powell, email@example.com, is a 1992 Presidential Awardee and the lead teacher for mathematics at Bloomington High School in Bloomington, IL 61701. She is interested in helping students make mafamatical connections and
enjoys giving workshops for teachers of grades K-12.
Photograph by Nancy Powell; all rights reserved
106 MATHEMATICS TEACHER
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that two variables can have a correlation close to 1 or -1, yet not cause each other. Identifying these
problems in thinking proved to be an important first step in dispelling them.
Since the assignment involved completing a writ ten report, we helped students learn to communi cate the results of statistical analysis. In assessing the students' work on the projects, we noticed that several students used the formal term outlier to describe "unusual" data points in a bivariate situa
tion, even though they had only studied formal pro cedures for identifying outliers in univariate situa tions. We then had a class discussion of the
importance of being careful in using formal terms when reporting statistical results. We also noticed that students tended to say in their reports that
they were using the regression line to "find values," when a more precise wording would have stated that the regression line can be used to "predict approximate values." These imperfections in com munication allowed us to emphasize that even if statistical analysis is correctly done and the conclu sions are appropriate, the study is of limited value if the data-analysis process and the conclusions are not communicated properly.
PROJECT 2: EXPERIENCING ALL PHASES OF THE INVESTIGATIVE CYCLE
As a final project for our AP statistics course, stu dents designed their own statistical projects and
posters. We instructed students to follow the guide lines given by the American Statistical Association (ASA) at www.amstat.org/education/posterl.html, and we allowed them to do joint projects with class mates who had common interests. The ASA guide lines helped students experience all phases of the
investigative cycle. We set aside approximately two weeks to allow everyone in class to identify a quan tifiable problem of interest, make a plan for investi
gating it, gather data, analyze the data, and draw conclusions.
As students began to select their problems, sev eral interesting ideas for projects emerged. One student wished to learn whether a relationship existed between a student's grade level and the number of steps that he or she took in a day. A pair of students decided to investigate the relationship between the types of music that students listened to and their grade-point averages. Another pair of students wondered how the distribution of types of cars driven in town compared with the distribution of types of cars driven in the entire United States. Yet another pair became interested in the relation
ship between brain size and intelligence. A larger group of students wanted to determine whether boys could generally throw a softball faster than girls. An other group decided to compare the blood pressures
Project Choose one pair of variables from the "Data in Depth" folder in Fathom that interests you and that seems to be correlated. Write a short paper organized in the following manner:
Introduction (10 pts.) Why would someone be interested in investigating the relationship between the two variables that you have chosen?
Background (20 pts.) Does one of the variables that you have chosen actually influence the other? If you think so, make an argument that one does influence the other. If you do not think so, explain why the variables that you have chosen are correlated but one does not "cause" the other.
What are some interesting questions you have that will be answered when you analyze your data set? Include questions that can be answered by finding the equation of the regression line, the slope and intercepts of the regression line, and the strength of the linear relationship between the v