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<ul><li><p>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</p><p>Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp</p><p> .JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact support@jstor.org.</p><p> .</p><p>National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extendaccess to The Mathematics Teacher.</p><p>http://www.jstor.org </p><p>This content downloaded from 86.15.116.87 on Fri, 2 May 2014 12:38:15 PMAll use subject to JSTOR Terms and Conditions</p>http://www.jstor.org/action/showPublisher?publisherCode=nctmhttp://www.jstor.org/stable/20871523?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp</li><li><p>Randall E. Groth and Nancy N. Powell </p><p>Using Research Projects to Help Develop </p><p>High School Students' Statistical Thinking </p><p>s </p><p>Vf e need to engage </p><p>students in all phases </p><p>of the </p><p>investigative cycle of </p><p>statistics </p><p>tatistics plays a key role in shaping policy in a </p><p>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 </p><p>mately need to engage students in all phases of the </p><p>investigative cycle of statistics, including data gath ering, data analysis, and inference. </p><p>This article describes two projects in which we </p><p>attempted to help Advanced Placement (AP) statis tics students become proficient at moving through the investigative cycle. Although the projects were </p><p>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 </p><p>projects, we also discuss some of our reflections on </p><p>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 </p><p>cycle. </p><p>PROJECT 1 : ANALYZING AND DRAWING CONCLUSIONS FROM EXISTING DATA FILES </p><p>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 </p><p>powerful tool for helping formulate and investigate statistical conjectures, since it allows users to </p><p>quickly import data, calculate summary statistics, test hypotheses, and build graphs and tables. Stu dents had some freedom to choose the problem that </p><p>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 </p><p>were able to move the focus of the project away from the planning and data-collection parts of the </p><p>investigative cycle and toward the analysis and conclusion parts of the cycle. </p><p>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. </p><p>Perhaps partially because of the stated require ments of the project, students attempted to force </p><p>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 </p><p>meaning on intercepts, or any points, that lie well outside the cluster of points used to produce the </p><p>regression line. After identifying these gaps in stu dents' understanding, we were able to address them in future instruction. </p><p>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 </p><p>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 </p><p>tionship between the two variables. Finally, we </p><p>noticed that some students struggled with the idea </p><p>Randall Groth, regroth@salisbury.edu, 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, powelln@district87.org, 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 </p><p>enjoys giving workshops for teachers of grades K-12. </p><p>Photograph by Nancy Powell; all rights reserved </p><p>106 MATHEMATICS TEACHER </p><p>This content downloaded from 86.15.116.87 on Fri, 2 May 2014 12:38:15 PMAll use subject to JSTOR Terms and Conditions</p>http://www.jstor.org/page/info/about/policies/terms.jsp</li><li><p>that two variables can have a correlation close to 1 or -1, yet not cause each other. Identifying these </p><p>problems in thinking proved to be an important first step in dispelling them. </p><p>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 </p><p>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 </p><p>importance of being careful in using formal terms when reporting statistical results. We also noticed that students tended to say in their reports that </p><p>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. </p><p>PROJECT 2: EXPERIENCING ALL PHASES OF THE INVESTIGATIVE CYCLE </p><p>As a final project for our AP statistics course, stu dents designed their own statistical projects and </p><p>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 </p><p>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 </p><p>gating it, gather data, analyze the data, and draw conclusions. </p><p>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 </p><p>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 </p><p>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: </p><p>Introduction (10 pts.) Why would someone be interested in investigating the relationship between the two variables that you have chosen? </p><p>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. </p><p>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 variables. You will answer these questions in the "Results" section. </p><p>Method (20 pts.) What kinds of technology did you use to investigate the relationship between the two variables (for example, Fathom, -83, other)? What did the technology do for you (or what did you make it do for you)? What are some other tools or methods (if any) that you decided to use to investi gate the relationship? </p><p>Data Analysis (20 pts.) Copy and paste all Fathom output into this section. Once you have your Fathom output pasted into a Word Document, you can move the output around in the docu ment even on a computer that does not have Fathom. You might want to copy and paste your output before writing the other sections of this report. Are there any "unusual" values in the data set? What makes them unusual? Are you choosing to throw out any of the unusual values before you plot a regression line? If so, justify the decision to throw out unusual values. </p><p>What is the equation of the regression line? What is its slope and intercept? What is the correlation coefficient r? What are some of the graphs that you analyzed to investigate the relationship? </p><p>Results (20 pts.) How strong is the relationship between the two variables? How do you know how strong the relationship is? Are they positively or negatively associated? Since you know the strength of the relationship, what are some of the questions that you can answer? What are the answers to these questions, and how did you find them? What valuable information is provided by the slope and intercepts of the regres sion line? What are some questions that you can now answer since you know the slope and intercepts of the regression line? What are the answers to these ques tions, and how did you find them? What valuable information is provided by the regression line? What are some questions that you can answer now that you know the regression line and its equation? What are the answers to these questions, and how did you find them? Discuss the answers to any of the other questions that you wrote in the "Back ground" section. </p><p>Conclusion (10 pts.) What did you learn (for example, about statistics, technology, baseball, cars, build ings) that you did not previously know? Is there anything you would do differently if you were to write the paper again? What are some other interesting studies that could be done that are related to what you did in this paper? </p><p>Fig. 1 </p><p>Project involving the analysis of existing data </p><p>Vol. 97, No. 2 ? February 2004 107 </p><p>This content downloaded from 86.15.116.87 on Fri, 2 May 2014 12:38:15 PMAll use subject to JSTOR Terms and Conditions</p>http://www.jstor.org/page/info/about/policies/terms.jsp</li><li><p>Helping students </p><p>develop statistical thinking is </p><p>extremely </p><p>challenging </p><p>of athletes to those of nonathletes. Still another </p><p>group decided to investigate the relationship between the stock price of a company that produced fatty foods and the amount of obesity in the United States. Even though some groups took one or two </p><p>class periods to settle on a question that interested </p><p>them, allowing the students to identify their own </p><p>problems to investigate helped them develop feelings of ownership of the problems at the outset. </p><p>Because of the diversity of the questions posed by members of our class, students chose a number of different types of plans for completing the proj ects. The students who wanted to examine the rela </p><p>tionship between the types of music and grade point averages for students at the high school decided that a survey would be the most efficient way of </p><p>gathering information for their project. The students who were investigating the number of steps taken in a day, the types of cars driven in town, softball </p><p>throwing, and blood pressure all chose observation al studies as their mode of inquiry. Students inves </p><p>tigating the questions about blood pressure, brain </p><p>size, and stock prices of a company chose to use </p><p>preexisting data to help answer the questions. The </p><p>diversity of modes of inquiry used by our students in answering the questions that they had posed re </p><p>flected some of the methods of data production that </p><p>they had studied during the AP statistics course. </p><p>The students who gathered their own data came </p><p>to appreciate that gathering data for a statistical </p><p>study can be a complex endeavor. The pair using a </p><p>survey to gather information realized that the man ner in which they asked the survey questions could </p><p>easily influence the manner in which people respond ed. The student who investigated the relationship between the number of steps that a student takes in a day and his or her grade level used an electronic device called a Digiwalker, which we provided. However, he quickly discovered that the device </p><p>reported inaccurate data. The group investigating the softball-throwing question needed to learn how to operate a radar gun that they borrowed from a </p><p>policeman. The pair of students gathering informa tion about blood pressure discovered that finding a </p><p>truly random sample of students was impossible, since some teachers would not let students out of class to have their blood pressure taken. The com </p><p>plicated and often imperfect nature of gathering data was conveyed to students in a manner that was far more memorable than conventional text </p><p>book instruction. Once the data had been gathered, many of our </p><p>students used both Fathom and Excel to help ana </p><p>lyze the data....</p></li></ul>