The Graphing Art Project encourages students to explore functions as they create art. Students
write functions with domain and range restrictions that generate interesting pictures. The project is easily
tailored for different levels of mathematical learners. Algebra 1 students create art using linear functions;
precalculus students include conic sections, exponential, logarithmic, trigonometric functions and the
greatest integer functions in their work. Students may write graphing calculator programs to reproduce
and animate their art

Angel, Nancy

Mathews, Susann M.

Reed, Michelle

KnowledgeBank at OSU

Getting Students Excitedabout Data AnalysisSusann M Mathews,Wright State UniversityMichelle Reed,Wright State UniversityNancy Angel, The Greenmont Elementary SchoolAbstract: The Graphing Art Project encourages students to explore functions as they create art. Studentswrite functions with domain and range restrictions that generate interesting pictures. The project is easilytailored for different levels of mathematical learners. Algebra 1 students create art using linear functions;precalculus students include conic sections, exponential, logarithmic, trigonometric functions and thegreatest integer functions in their work. Students may write graphing calculator programs to reproduceand animate their art.Keywords. Function, art, graphing, multiple representations1 IntroductionThe Guidelines for Assessment and Instruction in Statistics Education (GAISE), written jointly bythe American Statistical Association and the National Council of Teachers of Mathematics,addresses the need for all adults to be statistically literate (Franklin et al, 2007; NCTM, 2000).The report provides guidelines for enabling all students to develop statistical literacy by the timethat they become adults. However, for students to achieve such an end, statistical education mustbegin in elementary school. In the main body of the paper, we refer to the GAISE levels, which aredevelopmental statistical levels. However, as noted in the conclusions, these developmental levelscorrespond roughly to the more specific standards addressed in the Core Curriculum Standards forSchool Mathematics (CCSSI, 2010).Ms. Angel was interested in the statistical learning of her third-grade students and in learningto use technology appropriately in her classroom. She decided to guide her students through astatistical investigation and asked the following questions:1. Why should third-grade students carry out such an investigation?2. With guidance can third-grade students carry out a statistical investigation?3. What does developing and completing a statistical problem involve?The GAISE report, in particular level A, the developmental level for beginning data analysis,addresses the first question: in order to obtain statistical literacy, students must begin in elementaryschool with a gradual introduction to understanding the statistical process. This part of the reporthelped her understand not only how to perform a statistical investigation, but also why her studentsneeded to learn how to ask a question and collect and analyze data to answer it. Furthermore, shecould then guide her students through their statistical problem solving at the right developmentallevel.According to the GAISE, statistical problem solving is an investigative process that involves fourcomponents, though the sophistication of the investigations vary with regard to level of students:Page 26 Ohio Journal of School Mathematics 681. Formulate Questions - formulate one (or more) questions that can be answered with data.2. Collect Data• design a plan to collect appropriate data• employ the plan to collect the data3. Analyze Data• select appropriate graphical or numerical methods• use these methods to analyze the data4. Interpret Results• interpret the analysis• relate the interpretation to the original question (GAISE, p. 9)TinkerPlots R© is a data analysis software allowing students to enter data in a table and to create dotplots and bar graphs from the data. Using the GAISE investigative process, Ms. Angel worked withher 20 third graders to consider the weight of elementary students’ book bags and to collect andinterpret data regarding book bag weights of first through fifth grade students at their school.2 Formulate QuestionsMs Angel asked her third-grade class to think about typical student book bag weights and com-parisons of weight between grade levels and genders. Note that the teacher posed a question ofinterest to the students and the question was not restricted to their own classroom. Furthermore, theteacher asked students to consider variability of the data by asking them to think about comparisonsbetween grade levels and genders. She placed the students into five small groups to think aboutthe answer. The groups reported that they thought book bags would weigh: 13 lbs, 105 lbs, 5 lbs, 2lbs, and 12 lbs. All groups hypothesized that fifth graders would have heavier book bags becausethey have more work and carry more “stuff” around. They believed boys had heavier book bags forvarious reasons: boys have a lot of stuff, boys put CDs in their book bags, boys usually have morethings, and boys are stronger. To expand the number of participants in the study, the third gradersincluded students outside their own classroom.To solve the problem of who had the heaviest book bags, the class broke down the question intosubquestions that they would be able to answer from the data they could gather. The studentsdecided they wanted answers to the following questions:1. How much do students’ book bags weigh?2. Which students, first through fifth graders, carry the heaviest book bags?3. Are girls’ book bags heavier than boys’ bags or vice-versa?3 Collect DataThe five groups were excited to visit each classroom in grades 1 through 5 in their school to find outif their conjectures were true. Each group was assigned one grade level for collecting data. Theyread letters to the classes to introduce themselves and to explain the project.Students were taken one by one into the hall to gather data. The following data were recordedin a table provided by their teacher: a number for each student instead of an actual name, gender,grade, body weight, and weight of the child wearing their book bag. After collecting data, studentsOhio Journal of School Mathematics 68 Page 27Hi, we are , , , and from Ms. Angel’s third grade class. We are doing anexperiment on the weight of book bags. We want to find out how much book bags weigh, whichgrade has the heaviest book bags, and do girls or boys have the heaviest book bags. We would liketo weigh each of you and then weigh you with your book bag to find out the weight of the bookbag. Thank you for helping us with our experiment.Fig. 1: Letter for collecting data.needed to take one more step and compute the weight of the book bag by subtracting studentweight from the weight of the same student wearing a book bag. As appropriate for GAISE level Afor beginners, the students obtained data from all of the students in each class rather than taking arandom sample of students by grade.4 Analyze DataAfter collecting the data, each group entered their own data into TinkerPlots R© while the teacherhelped them to investigate the software and make various graphs of the data. TinkerPlots R© allowsone to use an actual descriptor as a variable name, such as maleorfemale. Since each group focusedon one grade level, their data pertained only to that grade. Grade-level work included tables ofgender and book bag weights as shown in Fig 2.Fig. 2: Table of data of gender and book bag weights from grade 3.As Fig 3 shows, dot plots of bag weight were also generated.Page 28 Ohio Journal of School Mathematics 68Fig. 3: Dotplot of book bag weights for grade 3.Dot plots of bag weight separated by gender were also created, as shown in Fig 4.Fig. 4: Dotplot of book bag weights separated by gender.The table and graphs come from the work of the group who investigated the 17 third graders.The small triangles on the dotplots represent the average (mean) for the book bag weight variable.TinkerPlots R© can also produce bar charts and circle graphs for categorical data.This hands-on experience within their groups helped the students understand the graphs of theirown data before it was combined with data from all the groups. Once the whole class was broughttogether, the teacher created a table to display the data for all 96 children in grades 1 through5. Together, the teacher and students created various graphs of these combined data: dotplotsof bookbag weights (Fig 5), bookbag weights separated by grade (Fig 6), and bookbag weightsseparated by gender (Fig 7).Fig. 5: Book bag weights for all students in grades 1 through 5.Ohio Journal of School Mathematics 68 Page 29Fig. 6: Book bag weights by grade level.Fig. 7: Book bag weights by gender.5 Interpret ResultsThe teacher then led a discussion of the three dotplots: book bag weight of all levels, grade levelvs book bag weight, gender vs book bag weight. The students noticed that the average weightof a book bag for all levels was between 3 and 4 pounds. Two groups had been close with theirconjecture of 2 lbs and of 5 lbs For the second question about grade level book bag weights, thestudents noticed it was actually 4th graders who had heavier book bags. The students interpretedthis data to mean that either 4th graders had homework the night before or that they were justgetting used to having four teachers giving homework of which they had to keep track. For thefinal question about gender and book bag weight (all groups previously thought boys would haveheavier book bags), they noticed that boys did have a heavier book bag average but not by much.The averages for book bags of both the boys and the girls were between 3 and 4 pounds, but theboys’ book bag weights were farther to the right on the graph, so their average was heavier.Page 30 Ohio Journal of School Mathematics 686 Assessing Students’ UnderstandingFor informal pre- and post-activity assessments the teacher provided students a dotplot of bookbag weights separated by grade level. The post assessment showed that all students recognized thegraph was showing who had the heaviest book bags, and students were now able to explain that bystudying the graphs they could determine that boys’ book bag weights were only slightly morethan girls’ book bag weights. It looked as though fourth graders had the heaviest book bag, becausethere were more book bags at the heavier weights (to the right on the graph).7 ConclusionsFrom studying the GAISE, Ms. Angel realized that all students who graduate from high schoolshould be able not only to read tables and graphs presented to them in the media every day, theyshould also be able to ask and determine if the graphs accurately represent the data. Furthermore,if the data aren’t included in the presentation, the students should know that they can find data andanalyze it themselves to determine if the claims are justified. In order to have these skills by highschool, they must start in elementary school. Through helping her students ask questions abouttopics of interest to them, and then gather the data to answer the questions, she concluded thatthird graders can carry out a statistical investigation at their appropriate developmental level. Todo this, the students were guided first with appropriate questions. She then guided her studentsthough collecting data, analyzing the data, and interpreting the results.In addition to answering her research questions, Ms. Angel found that her students became moreinterested in a project when they were involved in the whole process they got to be involved indecisions, data collection, and analyzing what the data meant. Students were excited because partof it happened outside of classroom, while gathering data from all of the students in the school.Students were more interested because the whole process of statistical problem solving was usedand not just one isolated piece.Although TinkerPlots R© was difficult for the students to understand, they were able to entertheir data into the tables and the graphs used as a whole class helped the student to answer theirquestions about book bag weights. They thus found that they could find the answers to theirquestions and did not have to rely on someone to tell them.8 The Investigation within the Framework of the Core CurriculumStandards for School MathematicsThe CCSSM (CCSSI, 2010) highlight individual parts of a statistical investigation and state in whichgrade students should experience part of an investigation. For example, in first grade, studentsshould be able to organize and represent data with up to three categories. Second graders needto generate measurement data by measuring lengths and work with bar graphs. Third gradersshould be able to represent several categories of data with scaled picture graphs and scaled bargraphs. During the investigation about student book bags, the third-grade students were focused onobtaining answers to their questions and, with the teacher’s help and using Tinkerplots R©, createdtables and dot plots of the data. The whole class then studied these graphs and were surprised tofind that the results were not quite what they initially believed.Ohio Journal of School Mathematics 68 Page 31ReferencesFranklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2007). Guidelinesfor assessment and instruction in statistics education (GAISE) report: A preK-12 curriculum framework.Alexandria, VA: American Statistical Association. (Also available at http://www.amstat.org/)Common Core State Standards Initiative (2010). Common core standards for mathematics. (Also avail-able at http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf)National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics.Reston, VA: Author.Susann Mathews, susann.mathews@wright.edu, is a Professor in theMathematics and Statistics Department at Wright State University. Hermajor field of interest is the teaching and learning of mathematical mod-eling. She has developed and teaches courses in mathematical mod-eling for pre-service middle and secondary mathematics teachers andhas published several articles in this area.Michelle Reed, michelle.reed@wright.edu, is an Associate Profes-sor in the Mathematics and Statistics Department at Wright State Uni-versity. She teachers mathematics and statistics to preservice middleand high school students.Nancy Angel, nancy.angle@kettering.org received her Bachelor’s inElementary Education from Eastern Kentucky University and her Mas-ter’s in Elementary Mathematics from Wright State University. She cur-rently teaches third grade at Greenmont Elementary in Kettering, OH,where she has taught various grades for 14 years.Page 32 Ohio Journal of School Mathematics 68

Getting Students Excited about Data Analysis

https://kb.osu.edu/bitstream/1811/78149/1/OJSM_68_Fall2013_26.pdf

Getting Students Excited about Data Analysis

Abstract

Similar works

Full text

Available Versions

KnowledgeBank at OSU