Challenges and Innovations in Statistics EducationEdited by Péter Kovács. University of Szeged, January 2018ISBN 978-963-306-575-4Proceedings of Challenges and Innovations in Statistics Education Multiplier Conference of ProCivicStatACTIVITIES FOR PROMOTING CIVIC STATISTICAL KNOWLEDGE OFPRESERVICE TEACHERSDaniel Frischemeier, Susanne Podworny and Rolf BiehlerPaderborn [email protected] statistical thinking and a sustainable knowledge in civic statistics is inevitably to become aconcerned citizen. This kind of thinking and knowledge can already be enhanced in secondaryschool. For the implementation of civic statistics in mathematics classrooms in secondary school,teachers themselves have to be well educated in the field of civic statistics. For this purpose, wehave designed and realized a university course about civic statistics in the winter term 2016/2017at the University of Paderborn, where preservice teachers worked on projects and activities inregard to civic statistical contexts. For instance, they have analyzed official open data of theGerman Statistical Office on the German gender pay gap with digital tools, explored thedistribution of net assets in German households and investigated the unemployment situation indifferent countries in the European Union via Google Public data files. In this paper, we willpresent some activities and derive first implications for re-designing these activities.INTRODUCTIONSince decisions in society, politics and economy are often based on civic statistics,responsible citizens in the sense of “Mündigkeit” (responsibility, emancipation) (see Schiller 2017)need statistical and also, more specifically, civic statistical skills. When we talk about civicstatistics we mean statistics about key phenomena in society such as employment, health,education, social welfare or inequality (Ridgway 2016; Engel 2017). The process of criticalthinking in regard to civic statistics contexts is preferably supposed to start already at school level.In Germany mathematics teachers are not necessarily educated in this special area of statisticseducation. To teach civic statistics, teachers need not only statistical content knowledge but alsopedagogical content knowledge, technological knowledge and a positive stance towards civicstatistics. The project ProCivicStat, funded by the ERASMUS program of the EuropeanCommission, aims at supporting teachers with specific courses, materials, tools, and datasets forteaching civic statistics ( the University of Paderborn, we have the following situation. There is a compulsorycourse on elementary statistics and probability and a compulsory course on didactics of statistics instudents’ bachelor studies. In their master studies, preservice teachers can choose a seminar whichis supposed to deepen and expand their knowledge they have gained in the compulsory courses.GENERAL INFORMATIONWe have designed the seminar “Statistical literacy in mathematics classroom” in the frameof a Design-Based-Research setting (Cobb, Confrey, diSessa, Lehrer, & Schauble 2003) and haverealized the first cycle in winter term 2016/2017, the next -second- cycle will take place in winterterm 2017/2018. In this paper, we refer to the cycle of winter term 2016/2017 only. Our seminarhad 21 participants in the winter term 2016/2017. All participants have been preservice teachers formathematics in lower secondary school and have been at the end of their studies, havingsuccessfully attended the course on “Elementary statistics” and “Didactics of statistics”. Theseminar consisted of 15 sessions, each session lasted 90 minutes. The main idea of the seminar wasto build on the statistical content knowledge our participants have gained in the previous courses sothat the participants on the one hand can apply their statistical content knowledge in civic statisticscontexts and on the other hand develop a specific pedagogical content knowledge, so that thepreservice teachers get prepared to implement civic statistics ideas into mathematics classroom atsecondary school. For distinguishing the several knowledge domains, see for example (Wassongand Biehler (2010)).So, there are learning goals on two dimensions learning goals in regard to statisticalcontent knowledge, and learning goals in regard to pedagogical content knowledge.

Learning goals of the courseOur learning goals with regard to statistical content knowledge are to deepen students knowledge about reading and interpreting summary statistics and graphicaldisplays (also in the sense of reading beyond data of Friel, Curcio, & Bright 2001).to introduce students into statistical concepts and constructs (like correlation and causality orSimpson s paradox) relevant in civic introduce into the definition and operationalization of concepts such as explore multivariate datasets on the base of given and self-generated statistical questions. Our learning goals with regard to the pedagogical content knowledge areto consider contents in civic statistics across get to know relevant material (articles, links, tools, datasets, etc.).to learn to “simplify” complex situations in civic statistics for classroom develop ideas for implementing civic statistics activities in classrooms. The general goal is to evoke a critical thinking towards statistics and analyses given forexample in media reports.General design principlesThe underlying general design principles of our course are similar to the principles of theStatistical Reasoning Learning Environment from Garfield and Ben-Zvi (2008, p.48). For instance,we focus on the development of central statistical ideas, we use real and motivating data sets, weuse classroom activities to support the development of our students reasoning, we integrate the useof technological tools, we promote classroom discourse and we also promote assessment tomonitor the cognitive development of our participants.REALIZATION OF THE COURSEIn this paragraph, we will describe the realization of some of the sessions in our course.Sessions 1-3: IntroductionTo confront our participants with civic statistics issues immediately we started the coursewith the task (“Interpret the statistical display in the context of inequality in German net assets”) tointerpret a complex statistical display showing the distribution of net assets in Germany in theyears 2003 and 2012 (see Figure 1).Figure 1: Diagram of the task on German net assets, similar to the diagram in lung/

The display in Figure 1 shows the distribution of net assets in households in Germany in2003 (see blue bars) and 2012 (see red bars). One first competence learners need is to recognizethat the bars displaying the situation in year 2003 and 2012 are overlapping. The distribution isdivided in ten deciles which are ordered ascending from left to right. First interpretations might bethat in most deciles the blue bars are higher than the red bars – but having a look at the tenth decileit is the other way around: the rich people have become even richer in the nine years from 2003 to2012. Another interpretation might be that there is a big difference in net assets between 90 percentof the German population and the richest 10 percent. Our participants worked on this task insession 1 and 2 and when observing the working processes of our students, it was obvious that thistask was very challenging for the students. There is a need to understand the definition of “netassets”, of “household”, and of “deciles”. A difficulty was to compare two overlapping bar graphsshowing the growing inequality between 2003 and 2012. In the next session 3, we wanted torefresh the technological Fathom knowledge. The students were familiar with using the Germanversion of the software in their previous courses (Biehler, Hofmann, Maxara, & Prömmel 2011).Our idea was that our participants use Fathom for their explorations and that they refresh theirtechnological Fathom knowledge when exploring a real dataset on leisure time activities ofGerman 11th grade students (Biehler, Kombrink, & Schweynoch 2003). So, for instance in session3, our participants had to work in pairs to investigate the question “in which way do boys and girlsdiffer in interest with regard to different leisure time activities (e.g., in playing games on thecomputer)”.Sessions 4-9: Students sessionsIn sessions 4-9, students as session leaders were responsible to design and moderate thesessions. We have had sessions on representation of data (session 4), percentages (session 5),percentages II (session 6), correlation & causation (session 7), Simpson’s paradox (session 8) andon the concept of unemployment (session 9). In Figure 2, we get an impression on the differenttasks and topics in these sessions.Figure 2. Examples of four different activities in sessions 4-9In the upper-left corner we see an example diagram of session 4 on manipulating statisticaldisplays similar to the diagram in Krämer (2007, p.38-39) – both graphs show the same data withdifferent axes. In the upper-right corner we see a diagram implemented in session 5 showing thewrong use of percentages (see Bauer, Gigerenzer, and Krämer (2014, p.19)). In the lower-left

corner we see an excerpt of a German online magazine (Spiegel online) article tml - in Figure 2 we present our English translation of it) assuming a relationship betweenbald-heads and career boost in the session on correlation and causation. Finally in the lower-rightcorner we see PISA data in the subjects mathematics, science and reading from two Germanfederal states, which turns out to be an instructive example of Simpson’s paradox. The commonstructure of all sessions was that the student session leaders began with an introduction ( 5minutes), followed by a presentation that was supposed to refresh relevant statistical knowledge ( 10 minutes) and providing examples for the theme ( 15 minutes). After these inputs there was aworking phase where all participants worked on activities in small groups ( 30 minutes) followedby a plenary discussion of the results ( 20 minutes). Each session 4-9 concluded with a reflectionon the session ( 10 minutes).Sessions 10-13: Gender Pay Gap projectAfter attending to the sessions 1-9 and after gaining statistical knowledge in regard torepresentation of data, percentages, correlation & causation, Simpson’s paradox and the concept ofunemployment, our aim was to provide our participants with a more complex task. We have chosenthe gender pay gap situation in Germany as we identified this as a meaningful topic for youngadults.Specifically, we wanted our students to explore the causes of the unequal pay situationbetween male and female employees in Germany and we wanted them to become familiar with theconcept of the gender pay gap so that our participants are able to distinguish between the adjustedand unadjusted gender pay gap. The unadjusted pay gap means that it is about 23% that men earnmore than women in Germany. Furthermore, we wanted our participants to explore the Germanincome structure data set from the German statistical office, to learn to reflect reports in the mediacritically and to relate them to their own data explorations. In total, we had four sessions dedicatedto the gender pay gap project. In session 10 our participants informed themselves by reading mediaand internet articles about the definition and explanations of the gender pay gap in Germany. Forsession 11 and 12 we provided our participants with a random stratified sample of all Germanemployees downloaded from the German statistical office and containing about 60,000 cases withvariables like gender, wage per month, region of Germany, kind of employment, age, etc. Inaddition, we provided five topics (profession, function, age, economy and region) according to thevariables in the dataset and asked our participants to choose one of these topics – for example thetopic “age” (see the precise task in Figure 3).Project on the Gender Pay Gap - Aspect: AgeWork in teams of two!Now, you are to carry out a project work on the gender pay gap with your knowledgegained in the seminar. In doing so, you should independently explore the data set for the2006 Income Structure Survey and get insights into possible explanations for the genderpay gap on the basis of the available data.You have learned that the differences in income between male and female workers, whichare published in the media, have to be interpreted with caution because of the differentfactors that determine the difference.Your TASKIn this article (see link below), the focus is on the factor “age”, which has an influence onthe differences in income. Under this perspective, examine the present data set and workout the extent to which income differences are caused by the aspect mentioned above. Inaddition, try to explore other aspects that affect differences in income.

Source/Link: 4.bild.htmlWrite a short article and create a PowerPoint presentation that you will present to yourfellow students.Figure 3. Task Gender Pay Gap Project (aspect: age)In this task our participants were asked to explore the gender pay gap data in peers withFathom and to work out in which way e.g. the aspect age might have an influence on the genderpay gap in Germany. To document their results and to be able to present them to their classmateswe asked our participants to prepare a PowerPoint-presentation.In session 13 the participants have presented their findings to their classmates via theirPowerPoint presentations.Sessions 14-15: Mini projectsOur course concluded with the sessions 14 and 15 where our participants worked in smallgroups on mini projects. These mini projects have the intention that the participants can apply alltheir competencies they have gained during the course in small projects using interactive graphsand tools that can be found on the Internet for free. One example of a mini project can be seen inFigure 4. It uses an interactive visualization from Google Public Data.Figure 4. Mini project on the rate of unemployment in the European UnionMini projects had the goal to analyze a specific topic with open data and free visualizationsfrom the internet to enhance a whole group discussion about the topic in the last session.In the mini project of Figure 4, our participants should use Google Public Data to comparethe development of unemployment rates in different countries of the European Union. In particular,our participants were asked to compare the unemployment rate of Germany to the unemploymentrates of other European countries they could choose on their own. The last session covered thepresentation of findings of the mini projects and whole group discussions about the context of thepresented findings, for example about unemployment rates in different European countries.CONCLUSION & FURTHER PLANSWe can state that our participants worked statistically on many civic statistics contexts.Especially in the project work of the Gender Pay Gap, our participants have been really engaged.The evaluation, which has been done in form of filling out evaluation sheets at the end of each

session (for details see Biehler, Frischemeier, & Podworny 2017), shows that our participants likedthe exploration of German income structure data and the presentation of their findings via PowerPoint very much.In the next winter term 2017/2018, we plan to teach a redesigned course. In this course, wewill keep the general structure of the previous one, but we plan to support our students in a moreconcrete way, especially when designing the students sessions and to implement more projectsessions, since our participants have worked on these activities very engaged, liked them verymuch and see potential in them to implement these activities in their further teaching.REFERENCESBauer, T., Gigerenzer, G., & Krämer, W. (2014). Warum dick nicht doof macht und Genmais nichttötet: Über Risiken und Nebenwirkungen der Unstatistik: Campus Verlag.Biehler, R., Frischemeier, D., & Podworny, S. (2017). Design, realization and evaluation of auniversity course for preservice teachers on developing statistical reasoning and literacywith a focus on civic statistics. Paper presented at the World Statistics Congress 61,Marrakech, Marocco.Biehler, R., Hofmann, T., Maxara, C., & Prömmel, A. (2011). Daten und Zufall mit Fathom:Unterrichtsideen für die SI mit Software-Einführung. Braunschweig: Schroedel.Biehler, R., Kombrink, K., & Schweynoch, S. (2003). MUFFINS: Statistik mit komplexenDatensätzen - Freizeitgestaltung und Mediennutzung von Jugendlichen. Stochastik in derSchule, 23(1), 11-25.Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design Experiments inEducational Research. Educational Researcher, 32(1), 9-13.Engel, J. (2017). Statistical Literacy for active Citizenship: A Call for Date Science Education.Statistics Education Research Journal, 16(1), 44-49.Friel, S. N., Curcio, F. R., & Bright, G. W. (2001). Making Sense of Graphs: Critical FactorsInfluencing Comprehension and Instructional Implications. Journal for Research inMathematics Education, 32(2), 124-158.Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning. ConnectingResearch and Teaching Practice. The Netherlands: Springer.Krämer, W. (2007). So lügt man mit Statistik. München: Piper.Ridgway, J. (2016). Implications of the Data Revolution for Statistics Education. InternationalStatistical Review, 84(3), 528-549.Schiller, A. (2017). The Importance of Statistical Literacy for Democracy – Civic-Education byStatistics. Paper presented at the Challenges and Innovations in Statistics Education,Szeged.Wassong, T., & Biehler, R. (2010). A Model for Teacher Knowledge as a Basis for Online Coursesfor Professional Development of Statistics Teacher. Paper presented at the 8th InternationalConference on Teaching Statistics, Ljubljana, Slovenia.

Statistical Reasoning Learning Environment from Garfield and Ben-Zvi (2008, p.48). For instance, . refresh the technological Fathom knowledge. The students were familiar with using the German version of the software in their previous courses (Biehler, Hofmann, Maxara, & Prömmel 2011). Our idea was that our participants use Fathom for their explorations and that they refresh their .