TOPIC 2: Statistics education at the school level
Statistics is a significant component of the school curriculum. It is a truly interdisciplinary topic, since it has applications to virtually all other subjects in the school curriculum. Furthermore, statistics is introduced from the start of primary school, even kindergarten in some countries, with topics such as data gathering and pictographs being introduced in the first year of formal schooling. At the other end relatively sophisticated statistical analyses can be taught in the later part of secondary school. In recent years, statistics in school has seen major developments in curriculum, technology, innovative teaching methods, and research on learning and teaching.
Topic 2 sessions will focus on a variety of issues associated with school level statistics, including innovative curriculum and teaching strategies, the use of real data and technology in school statistics, statistics teacher training, CensusAtSchools, project based learning, research on school level statistics, student assessment, and socio-cultural issues. Colleagues attending Topic 2 sessions will have an opportunity to discuss the latest thinking regarding statistics at the school level.
SESSION 2A: Successfully implementing statistical education in primary schools
2A1: PROSPECTIVE TEACHERS’ AWARENESS OF YOUNG CHILDREN’S STOCHASTIC ACTIVITIES
Efi Paparistodemou
University of Cyprus, Cyprus
Despina Potari
University of Patras, Greece
Demetra Pitta
University of Cyprus, Cyprus
The present research focuses on prospective teachers’ planning, teaching and reflection on young children’s (4 to 6 year-old) stochastic activities. The research also concentrates on the way in which prospective teachers view the activity in terms of the mathematical challenge it offers and the development of children’s stochastic ideas (Potari & Jaworski, 2002). The methodology of this research is based on the qualitative approach. The researchers analysed twenty-three prospective teachers’ lesson plans and actual teaching, interviewed them after their lessons and finally analysed their self-assessment reports. An initial analysis of the data shows that prospective teachers appreciated the importance of using tools in their classrooms for teachings stochastics. However, from our classroom observations we identified that the activity was often mathematically trivialized and the children’s involvement was limited. The discussion and self-assessment that took place after the lessons indicated the different degree of prospective teachers’ awareness of pedagogical and mathematical issues.
2A2: STOCHASTICS, DIGITAL LEARNING OBJECTS AND THE PRIMARY CLASSROOM
Jennifer Way
University of Sydney, Australia
As part of the Australian national online curriculum initiative, The Learning Federation is developing hundreds of multimedia learning objects for use in schools. Some of these learning objects are designed to allow children to explore some basic concepts of probability and statistics, such as the relationships between random generators, sample spaces, likelihood of outcomes and both short and long run data on frequency of outcomes. This paper reports on the initial design development of these learning objects and on plans to research their use with children aged 6 to 12 years.
2A3: THE INTERPLAY BETWEEN STUDENTS’ STATISTICAL KNOWLEDGE AND CONTEXT KNOWLEDGE IN ANALYZING DATA
Cynthia Langrall
Illinois State University, United States
Steven Nisbet
Griffith University, Australia
Edward Mooney
Illinois State University, United States
In this study, we examined the role of context knowledge in data analysis tasks and investigated the interplay between students’ use of context knowledge and statistical knowledge. Findings showed that knowledge of context was an important factor contributing to students’ engagement in statistical tasks. Students used context knowledge in three broad ways: to rationalize the data or their interpretations, in taking a critical stance toward the data, and in ways that were not necessarily productive or pertinent in addressing the task at hand.
2A4: DEVELOPING A MODEL TO DESCRIBE THE USE OF CONTEXT KNOWLEDGE IN DATA EXPLORATIONS
Edward Mooney, Cynthia Langrall
Illinois State University, United States
Steven Nisbet
Griffith University, Australia
This study aimed to examine the role knowledge of context plays in supporting or interfering with middle school students’ statistical thinking. A model of context knowledge use was developed based on a model of context support developed by Beck, McKeown and McCaslin (1983) to describe students’ use of context knowledge. The results of the study showed that students’ use of context knowledge fell into three categories.
SESSION 2B: Successfully implementing statistical education in secondary schools
2B1: FACTORS CONSIDERED BY SECONDARY STUDENTS WHEN JUDGING THE VALIDITY OF A GIVEN STATISTICAL GENERALIZATION
Hanan Innabi
UAEU, United Arab Emirates
This study investigated the factors that 12th grade students in United Arab Emirates take into consideration when judging the validity of a given statistical generalization, in particular, in terms of the sample size and sample selection bias. The sample consisted of 360 students who had not studied sampling yet. Results show that a small percentage of the students take the sample size and selection bias into consideration properly. Many students based their judgment on their personal beliefs regardless of the properties of the selected sample. This study identified some pre- teaching misconceptions that students have with regard to ‘sampling’. Such misconceptions are ‘any sample represents the population’, and, ‘any sample does not represent the population’.
2B2: MEANING OF THE DISPERSION AND ITS MEASURES IN SECONDARY EDUCATION
Juan Ortega Moya
UNED, Spain
Antonio Estepa Castro
University of Jaén, Spain
In this paper we present an onto-semiotic macroscopic analysis of the measures of dispersion: range, interquartile range, average deviation, variance, standard deviation and coefficient of variation by following the theoretical framework of the Theory of Semiotic Functions. This research has been carried out with a sample of textbooks from the most representative publishers used by Spanish second-cycle Secondary students of 15 and 16 years of age. The paper finishes by presenting several useful conclusions for the planning of the teaching process and for the research on the issue.
2B3: A FRAMEWORK FOR TEACHING STATISTICS WITHIN THE K-12 MATHEMATICS CURRICULUM
Gary D. Kader, Mike Perry
Appalachian State University, United States
This paper reports on an American Statistical Association project which developed ASA-endorsed guidelines for teaching and learning statistics at the Pre K-12 level. A group of leading statistics and mathematics educators developed the report, “A Curriculum Framework for Pre K-12 Statistics Education.” These guidelines complement the
NCTM Principals and Standards of School Mathematics – providing additional guidance and clarity on the data analysis strand. A major goal of the document is to describe a statistically literate high school graduate and, through a connected curriculum, provide steps to achieve this goal. Topics for discussion include: developing statistical literacy within the Pre K-12 mathematics curriculum; links to the
NCTM Standards; impact of high stakes testing; differences between mathematics and statistics; key components and concepts associated with the data analysis process; examples illustrating connections in key statistical concepts across all grade levels.
2B4: INCREASING SECONDARY STUDENTS’ STATISTICAL KNOWLEDGE BY FOCUSING ON TEACHERS’ ENGAGEMENT AT LAVRAS, MINAS GERAIS, BRAZIL
Verônica Yumi Kataoka, Eric Batista Ferreira, C.S.F. da Silva, M.S. Oliveira
Federal University of Lavras (UFLA), Brazil
A prospective exam was performed to quantify the statistical knowledge of students before they start attending classes in college. A four question test (two of probability and two of descriptive statistics) was given to 95 students of Federal University of Lavras and 87 students of three secondary schools (two private and a public one). The mean scores were not statistically different and were considered poor. It was suggested that this poor student knowledge might be due to poor knowledge of their teachers or a lack of motivation and interest. To attempt to correct for this, secondary teachers attended a one-day class given by the authors of this paper. By examining student scores from before and after that information transference, it was found that teachers that attended the class could transmit more information and enhance their students’ scores.
SESSION 2C: Real data and project based statistical education
2C1: ENHANCING THE LINK BETWEEN STATISTICS AND MINERAL PROCESSING THROUGH PROJECT BASED LEARNING
Jeeva Periasamy
University of Johannesburg, South Africa
This paper is a culmination of the study carried out after using project work as an intervention to enhance the learning of statistics as a service subject. It discusses how a project encompassing real-world problems directly relevant to the learners chosen career-path helps in motivating and sustaining the students’ quest for learning statistics. The sample group comprised of learners studying towards the Diploma in Extraction Metallurgy and the project work was centred on the main-stream course Mineral Processing. This project was based on actual experiments conducted by learners in their Mineral Processing course so that learners could see the relevance of applied statistics to main-stream courses. The learners’ performance was tracked throughout this study.
2C2: A QUANTITATIVE STUDY OF COUNTRIES USING POPULATION DATA AND PYRAMID GRAPHS
Henry Kranendonk
Milwaukee Public Schools, United States
While an equation can be solved manually or by the click of a button in multiple ways, the information this equation communicates should also be a reason why students study it. Although the “how to’s” are important, they must be balanced with “why?” and “for what purpose?” The latter questions are essentially more meaningful, more interesting, and more engaging for many students. It is critical that students learn how to communicate their thinking to others. The project outlined in this paper was specifically designed for middle and high school students to improve their skills in posing quantitative questions and in articulating “why?” and “for what purpose?” these questions are asked.
2C3: LEARNING BASED ON REAL CONTEXT PROBLEMS AND NOTIONS OF PROBABILITY DISTRIBUTIONS AND EXPECTED VALUE
José Armando Albert Huerta, Juan Ernesto Colunga Cavazos, Juan Antonio López Esquivel
ITESM, Campus Monterrey, México
The following investigation explores the learning potential of college students, when using the technique of Problem Based Learning. Particularly it is directed towards probabilistic frequency, probabilistic distributions, and expected value notions. To achieve this, a scenario was designed. It was worked by students, in groups of four or five, in order to investigate relevant information about the given situation. Students were expected to relate the situation with real data. It could be verified that the students based much of their analysis and conclusions on the use of graphic representations. This work also reports on the role of the Exploratory Data Analysis mainly through the graphic representations, in which the students can get a possible solution to a problem of the scenario.
2C4: CONCEPTUALIZING APPLIED PROBABILITY THROUGH PROJECT-BASED LEARNING
Timothy I. Matis
Texas Tech University, United States
Several prominent educational institutions have recently increased their use of team-based projects to both enhance learning and aid in assessment. We present some of our ongoing research into the use of project-based learning for the instruction of applied probability and stochastic processes at the high school, undergraduate, and graduate levels. In particular, we will demonstrate how “real-world” multimedia modules may be integrated into the curriculum of existing educational programs to enhance learning. This includes the effective formation of teams, use of communication technologies, and the evaluation of various student reporting mechanisms. When implemented in a team-based setting, these modules have been shown to effectively aid students in conceptualizing key elements of probability and promote knowledge transfer beyond the presented contexts.
SESSION 2D: The use of technology to enhance the teaching of Statistics at school level
2D1: USING TINKERPLOTS TO SCAFFOLD STUDENTS’ INFORMAL INFERENCE AND ARGUMENTATION
Dani Ben-Zvi
University of Haifa, Israel
This paper focuses on developing students’ informal ideas of inference and argumentation. This topic is of current interest to many researchers as well as teachers of statistics. We study fifth graders’ learning processes in an exploratory interdisciplinary learning environment that uses the software TinkerPlots to scaffold students' statistical reasoning. The careful design of the learning trajectory based on increasing samples heuristics coupled with the unique features of TinkerPlots were found instrumental in supporting multiple dimensions of students reasoning about informal inference: multiplicative reasoning, aggregate reasoning, acknowledging the value of large samples, and accounting for variability. These were accompanied by greater ability to verbalize, explain and argue about data-based claims. In the light of the analysis, a description of what it may mean to begin reasoning about inference by young students is proposed, and implications to teaching, curriculum and research are drawn.
2D2: WORKING STYLES AND OBSTACLES: COMPUTER-SUPPORTED COLLABORATIVE LEARNING IN STATISTICS
Rolf Biehler
University of Kassel, Germany
Pairs of students use the computer software Fathom for working on problems from Exploratory Data Analysis. The exploratory study was interested in identifying how the software as a tool supports or hinders students’ thinking. Working styles of students related to distributional thinking in the context of group comparison tasks were studied.
2D3: EXPLORING INFORMAL INFERENCE WITH INTERACTIVE VISUALIZATION SOFTWARE
Andee Rubin and James K.L. Hammerman
TERC, United States
Cliff Konold
University of Massachusetts – Amherst, United States
Most statistics educators would agree that statistical inference is both the central objective of statistical reasoning and one of the most difficult ideas for students to understand. In traditional approaches, statistical inference is introduced as a quantitative problem, usually of figuring out the probability of obtaining an observed result on the assumption that the null hypothesis is true. In this article, we lay out an alternative approach towards teaching statistical inference that we are calling “informal inference.” We begin by describing informal inference and then illustrate ways we have been trying to develop the component ideas of informal inference in a recent data analysis seminar with teachers; our particular emphasis in this article is on the ways in which teachers used TinkerPlots, a statistical visualization tool. After describing teachers’ approaches to an inferential task, we offer some preliminary hypotheses about the conceptual issues that arose for them.
2D4: USING TECHNOLOGY TO SUPPORT DIAGRAMMATIC REASONING ABOUT CENTER AND VARIATION
Arthur Bakker, Jan Derry
University of London, United Kingdom
Cliff Konold
University of Massachusetts – Amherst, United States
We conducted two design experiments aimed at engaging sixth graders (11 years old) in statistical reasoning about center and variation. We examine in particular students’ informal notion of a “modal clump.” Using Peirce’s concept of diagrammatic reasoning, we analyze the interplay of 1) making plots with TinkerPlots – a computer data analysis tool, 2) experimenting with those plots, and 3) developing a language to talk about features of the data sets as represented in the plots by reflecting on judgments. More generally, we draw on Brandom’s recent work in philosophy to argue that an “inferential” view should be privileged over a “referential” view of teaching and learning statistics.
SESSION 2E: Training teachers for statistical education
2E2: A POST-CALCULUS INTRODUCTION TO STATISTICS FOR FUTURE SECONDARY TEACHERS
Allan Rossman, Elsa Medina, Beth Chance
California Polytechnic State University, United States
We describe our experiences with developing and teaching a new introductory statistics course for prospective teachers of secondary mathematics. The course emphasizes statistical concepts through their applications in the context of recent scientific studies, and it uses an interactive technology-enhanced pedagogical approach that models recommended practice for teachers. A concurrent seminar course introduces students to seminal articles and research findings in statistics education, and encourages them to reflect on their learning experiences in the course as a way to prepare for their own teaching of statistics. Feedback and evaluation from students will be discussed.
2E3: ENHANCING ELEMENTARY PRESERVICE TEACHERS’ CONCEPTIONS OF VARIATION IN A PROBABILITY CONTEXT
Dan Canada
Eastern Washington University, United States
While recent and ongoing research has begun to reveal ways that precollege students think about variation, little research has been done with the preservice teachers who will eventually serve such students. Specifically, more research is needed to understand what are the conceptions of variation held by elementary preservice teachers (EPSTs), and also how to shape the university courses where those preservice teachers learn. This paper, sharing an excerpt from an exploratory study aimed at EPSTs, describes changes in class responses to a probability task where variation is a key component. Overall, going from before to after a series of instructional interventions, responses reflected a more appropriate sensitivity to the presence of variation.
2E4: ANALYZING TEACHER RESISTANCE TO TEACHING PROBABILITY IN COMPULSORY EDUCATION
Ana Serradó, Pilar Azcárate
Universidad de Cádiz, Spain
José María Cardeñoso
University of Granada, Spain
From the beginning of the nineties, the different curricular reforms in Spain have favoured the introduction of probability. However, the reality in the classroom is very different since teachers show resistance to accepting this curricular innovation. To explain this situation, the “Professional Development Teachers” research group in the University of Cadiz carried out research dealing with teachers’ conceptions of probability, the sources of professional knowledge used to teach probability, and the probability content in Spanish textbooks. In this particular paper we will present results form a case study where teachers’ arguments to justify their resistance to introducing probability in Compulsory Secondary Education are analyzed. A theoretical framework related to the knowledge of probability and pedagogical professional knowledge is introduced in order to interpret the teachers’ reasoning and understand the evolution of teachers’ intervention in the teaching and learning process.
SESSION 2F: Developing a curriculum for the meaningful learning of Statistics at the school level
2F1: INTRODUCING STATISTICS AT SCHOOL LEVEL IN SOUTH AFRICA
Delia North, Temesgen Zewotir
University of KwaZulu-Natal, South Africa
South Africa is currently in the process of implementing C2005, a new school curriculum in South Africa. This paper focuses on the statistics content of the new school curriculum and describes some steps taken to assist teachers in coping with the imminent new data handling component. Particular emphasis is placed on the influence of ICOTS6, on this process.
2F2: REASONING WITH EVIDENCE – DEVELOPING CURRICULUM
James Nicholson, Jim Ridgway, Sean McCusker
University of Durham, Ireland
Reasoning from multivariate evidence is pervasive in political speeches and in the media, but is largely absent in UK schools. Currently, we do not prepare young people to understand important social debates, nor to make informed decisions about their personal well-being. We have evidence that students can work with multivariate data if supported appropriately with technology, and are working with teachers of mathematics, citizenship, and geography to develop curriculum materials designed to develop an understanding of complex issues in the curriculum, and reasoning from evidence in general. Examples of the use of survey data on sexually transmitted diseases, which students explore using powerful interfaces, are shown to illustrate our approach.
2F3: AN EVALUATION STUDY OF THE PROCESS OF REFORM OF STATISTICS TEACHING AT THE SECONDARY LEVEL IN BENIN: ASSESSMENT AND PERSPECTIVES
Félicien Donat E. T. Accrombessy
University of Abomey-Calavi (UAC), Cotonou, Republic of Benin
The introduction of statistics training course in the secondary school since 1996, has hardly met success. This laudable initiative should help pupils to complete their secondary school education in good conditions. The curricula supported by basic concepts and notions of descriptive statistics are progressively scheduled from third to sixth form in order to provide pupils the faculty to develop reasoning and judgement skills. But unfortunately, 10 years after its launching, we are compelled to notice that there are still serious problems at the secondary school authorities, teachers and pupil’s levels. Consequently, all those factors create a lack of rigour in the implementation of the program. The paper strongly suggests some proposals and recommendations in direction of all the actors concerned by the secondary school educational system. Applied, such suggestions should improve the consideration for statistics and give pupils the opportunity to become statisticians in the future.
SESSION 2G: Socio-cultural aspects of learning Statistics
2G1: STUDENT TEACHERS INTERPRETING MEDIA GRAPHS
Carlos Monteiro
Universidade Federal de Pernambuco, Brazil
Janet Ainley
The University of Warwick, United Kingdom
The official inclusion of the teaching of graphing in school curricula has motivated increasing research and innovative pedagogical strategies such as the use of media graphs in school contexts. However, only a few studies have investigated knowledge about graphing among those who will teach this curricular content. We discuss aspects of the interpretation of media graphs among primary school student teachers from Brazil and England. We focus on data which came from questionnaires which gives evidence of elements of “Critical Sense,” which involves the mobilisation of several kinds of knowledge and experiences, in the interpretation of statistical graphs.
2G2: ACCOUNTING FOR TEACHERS’ INSTRUCTIONAL REALITIES WHEN SUPPORTING THEIR PROFESSIONAL DEVELOPMENT IN STATISTICS
José Luis Cortina
Universidad Pedagógica Nacional, México
Qing Zhao, Jana Visnovská
Vanderbilt University, United States
In this paper we analyze a design experiment aimed at supporting the professional development in statistics of twelve middle-school teachers in the United States. We explain how adopting a sociocultural framework allowed us to account for teachers’ struggles to make sense of instructional practices in statistics that place students’ reasoning at the center of instructional decision-making. We also account for how the adoption of the sociocultural framework allowed us to envision a viable way in which to better support the professional development of the participating teachers.
2G3: A STRUCTURAL EQUATION MODEL ANALYZING THE RELATIONSHIP STUDENTS’ STATISTICAL REASONING ABILITIES, THEIR ATTITUDES TOWARD STATISTICS, AND LEARNING APPROACHES
Dirk Tempelaar
Maastricht University, The Netherlands
Recent research in statistical reasoning has focused on the developmental process in students when learning statistical reasoning skills. This study investigates statistical reasoning from the perspective of individual differences. As manifestation of heterogeneity, students’ prior attitudes toward statistics, measured by the extended Survey of Attitudes Toward Statistics (SATS: Schau, Stevens, Dauphinee and DeVecchio, 1995), and students’ learning approaches, measured by the Inventory of Learning Styles (ILS; Vermunt, 2005) are used. Students’ statistical reasoning abilities are identified by the Statistical Reasoning Assessment instrument (SRA; Garfield 1998, 2003). The aim of the study is to investigate the relationship between both attitudes and learning approaches versus reasoning abilities by estimating full structural equation models. Instructional implications of the models for the teaching of statistical reasoning are discussed.
SESSION 2H: LOCAL TEACHER SESSION (Held two days before the Conference)
Organisers
~ Lisbeth Cordani, Instituto Mauá de Tecnologia, Brazil
~ Lilia Carolina Costa, Universidade Federal da Bahia, Brazil
| Lecturers from Bahia | | Lecturers from São Paulo |
| ~ Lilia Carolina Costa | | ~ André Luiz Samartini |
| ~ Lia Terezinha de Moraes | | ~ Ângela Tavares Paes |
| ~ Rosana de Freitas Castro | | ~ Carine Savalli Redigolo |
| ~ Rosemeire Fiaccone | | ~ Marcelo Bueno Moreno |
| ~ Verônica Lima | | ~ Marília Costa Basile |
Session 2H will be held from Friday 30th June to Saturday 1st July at the Instituto Anísio Teixeira, Salvador, a very highly regarded Institution from Bahia State. Workshops on statistics education will be offered to local teachers (Medium Level) and the program is organized by the Brazilian Statistical Association (ABE) in cooperation with the Statistics Department of Universidade Federal da Bahia (UFBA). The content includes probability, data analysis and estimation, and the format is based on the active learning approach.
We expect to have about 150 secondary school teachers from public schools of Salvador and neighborhood in the workshops (5 rooms of 30 teachers each). The logistic of the teacher's selection is run by the Instituto Anísio Teixeira (http://www.bahia.ba.gov.br/saeb/perfil99/iat_fin.htm). Dr. Carmen Batanero, IPC chair, was invited to the workshop closing session.
Ten students of statistics from the University of Bahia (UFBA) will take part as volunteer monitors. We will also have some observers from the neighborhood of Bahia (like Sergipe). The sessions and workshops will be run in Portuguese and the teachers will receive special material with activities to be developed. Lunches and coffee breaks will be offered on those days.
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A Sessão 2H será organizada nos dias 30 de junho e 01 de julho no Instituto Anísio Teixeira, Salvador, uma instituição de ensino muito conceituada. As oficinas de educação estatística serão oferecidas para professores do nível médio e o programa foi organizado pela Associação Brasileira de Estatística em cooperação com o Departamento de Estatística da Universidade Federal da Bahia (UFBA). A oficina será baseada em atividades ligadas aos temas: probabilidade, estimação e análise de dados, em um processo do tipo “active learning approach”.
Esperamos ter cerca de 150 professores de escolas públicas de Salvador e redondezas participando da oficina (5 salas com 30 professores cada). A logística para a seleção dos professores será de responsabilidade do Instituto Anísio Teixeira (http://www.bahia.ba.gov.br/saeb/perfil99/iat_fin.htm), que está colaborando ativamente com esta programação. A profa. Dra Carmen Batanero, presidente da comissão internacional do ICOTS7, participará como convidada da cerimônia de encerramento da oficina.
Teremos 10 alunos do curso de estatística da UFBA que serão monitores voluntários bem como alguns alunos que atuarão como observadores de locais vizinhos à Bahia (como Sergipe, por ex.). A oficina será oferecida em português e todos receberão material com as atividades a serem desenvolvidas. Serão oferecidos almoços e coffee breaks no local nesses dois dias.
No paper available