TOPIC 6: Research in Statistics education
The increasing importance of Statistics Education Research is demonstrated by IASE’s support of the Satellite Conferences at ISI Sessions, the International Series of Statistical Reasoning, Thinking and Literacy Research (SRTL) Forums and the developing Statistics Education Research Journal (SERJ). While familiar notions such as statistical literacy appear in these sessions more emphasis at this ICOTS meeting will be placed on the development aspect and will include reasoning and thinking aspects in both statistics and probability in learning environments.
Two particular focus sessions are understanding of variation and the ever important research into assessment. Two new directions are to be taken in these sessions, focusing on research as a discipline in statistics education and on those researchers who are new to the field. Sessions on methodologies, frameworks and longitudinal studies relating to research in statistics education will be complemented by a forum for researchers new to the statistics education field by providing mentoring through a panel and small group discussions with experienced researchers.
SESSION 6A: Research on statistical reasoning and thinking
6A1: LISTEN TO THE STUDENTS: UNDERSTANDING AND SUPPORTING STUDENTS’ REASONING ABOUT VARIATION
Chris Reading, Jackie Reid
University of New England, Australia
During a research project investigating understanding of variation students in a tertiary level introductory statistics course completed a questionnaire prior to, and at the end of, the course. This paper reports on interviews of selected students designed to determine whether more information could be gathered, and to identify those teaching and learning activities that assisted students to develop understanding. Prompting assisted students to develop better quality responses but cognitive conflict situations proved challenging. The diversity of activities identified by students as assisting development of understanding provides a challenge for educators in planning teaching sequences. Both educators and researchers need to listen to students to better understand the development of reasoning.
6A2: INFORMAL INFERENTIAL REASONING
Maxine Pfannkuch
The University of Auckland, New Zealand
Year 11 (15-year-old) students are not exposed to formal statistical inferential methods. Therefore, when drawing conclusions from data, their reasoning must be based mainly on looking at graph representations. This study investigates the type of reasoning that might develop students’ informal inferential statistical reasoning towards a more formal level. A perspectives model is developed for a teacher’s informal inferential reasoning from the comparison of boxplots. The model is then used to analyse her students’ responses to an assessment task. The resultant analysis produced a conjectured hierarchical model for students’ reasoning. The implications of the findings for instruction are discussed.
6A3: INVESTIGATING STATISTICAL UNUSUALNESS IN THE CONTEXT OF A RESAMPLING ACTIVITY: STUDENTS EXPLORING CONNECTIONS BETWEEN SAMPLING DISTRIBUTIONS AND STATISTICAL INFERENCE
Luis A. Saldanha
Portland State University, United States
Patrick W. Thompson
Arizona State University, United States
Reasoning proportionally about collections of a sample statistic’s values is central to developing a coherent understanding of statistical inference. This paper discusses key developments that unfolded in a classroom teaching experiment designed to support students constructing such understanding. Instruction engaged students in activities that focused their attention on the variability among outcomes of randomly drawn samples. There occurred a critical shift in students’ attention and discourse away from individual sample outcomes and toward the distribution of a collection of sample outcomes. This shift supported further developments concerning how to compare entire distributions of sample outcomes as a basis for conceptualizing a notion of statistical unusualness. We characterize aspects of these developments in relation to students’ classroom engagement.
SESSION 6B: Research on probabilistic reasoning and thinking
6B1: ELEMENTARY SCHOOL STUDENTS’ INFORMAL AND INTUITIVE CONCEPTIONS OF PROBABILITY AND DISTRIBUTION
Sibel Kazak, Jere Confrey
Washington University in St. Louis, United States
Data and chance are the two related topics that deal with uncertainty. On the discussions of probability and statistics in both research and instruction, the existing literature depicts an artificial separation, to which other researchers (Shaughnessy, 2003; Steinbring, 1991) have already called attention in recognition of the inseparable nature of data and chance. Hence, this paper addresses how to integrate the discussions of distributions and probability, starting from the elementary grades. We report on a study that examines fourth-grade students’ informal and intuitive conceptions of probability and distribution through a sequence of tasks for developing their understandings about probability distributions. These tasks include various random situations that students explore with a set of physical chance mechanisms and that can be modeled by a binomial probability distribution.
6B2: AN EXPLORATORY STUDY OF STUDENTS’ DIFFICULTIES WITH RANDOM VARIABLES
Blanca R. Ruiz Hernández, José Armando Albert Huerta
ITESM – Campus Monterrey, México
Carmen Batanero
University of Granada, Spain
In this research we approach a fundamental stochastic idea. The random variable is based on other mathematics and probabilistic concepts and, in turn, is the support of many probability and statistics subjects. In this paper, we present some results from an exploratory study carried out with two university students. The aim was observing the difficulties the students face when they try to solve a problem that involves the concept of random variable.
6B3: USING EXPERIMENTAL APPROACHES FOR TEACHING PROBABILITY: WORKING ON A PROJECT USING FACE TO FACE AND VIRTUAL SESSIONS
Cileda de Queiroz e Silva Coutinho
Pontifícia Universidade Católica de São Paulo, Brazil
In this paper we discuss the teacher’s role in the introduction of probability to students aged from 11 to 18 years old. Coutinho (2001) has showed that model-building approaches enable students to attend to the duality of the probability concept. However, Gonçalves (2004) argues that teachers do not easily appropriate such teaching situations, because their conception are associated with their own practices, built from classic approaches to probability. In this paper, we discuss a teacher education project on teaching and learning probability problems, in which teachers and researchers collaborate during face-to-face and virtual sessions, to reflect upon and about teaching practices and especially about the possibilities associated with a model-building approach to probability.
6B4: USING DATA, STUDENT EXPERIENCES AND COLLABORATION IN DEVELOPING PROBABILISTIC REASONING AT THE INTRODUCTORY TERTIARY LEVEL
Helen Louise MacGillivray
Queensland University of Technology, Australia
In the focus over the past decade on data-driven, realistic approaches to building statistical literacy and data analysis curriculum, the explicit development of probability reasoning beyond coins and dice has received less attention. There are two aspects of probability at the introductory tertiary level: for use in introductory data analysis; and as foundation for further study in statistical modelling and applications, and increasingly in areas in information technology, engineering, finance, health and others. This paper advocates a minimalist objective-oriented approach in the former, and a constructivist, collaborative and data-linked approach in the latter. The latter is the main focus here, with strategies to help students unpack, analyse and extend what they have brought with them to tertiary study, enabling them to consciously develop coherent probabilistic understanding and linking with real investigations and processes.
SESSION 6C: Research on developing statistical literacy
6C1: ISSUES FOR STATISTICAL LITERACY IN THE MIDDLE SCHOOL
Jane M. Watson
University of Tasmania, Australia
Focusing on the word “literacy” in the phrase “statistical literacy,” the present study explored what happened to the non-numerically based aspects of statistical literacy when students in Grades 7 and 9 were exposed to a unit of work in chance and data that emphasized variation. To test the suggestion of transfer of thinking skills to the literacy side of statistical literacy, 20 items from a larger survey were selected, upon which changes in literacy skills could be measured. Ninety students in each of Grade 7 and Grade 9 were asked the questions in a longer survey before and six weeks after taking part in a unit on chance and data devised by their usual classroom mathematics teacher as part of their schools’ mathematics programs.
6C2: INVESTIGATING A HIERARCHY OF STUDENTS’ GRAPH INTERPRETATION
Kazuhiro Aoyama
University of Tsukuba, Japan
The ability to extract qualitative information from quantitative information, and/or to create new information from qualitative and quantitative information is the key task of statistical literacy in the 21st century. This paper presents a hierarchy of the graph interpretation aspect of statistical literacy that includes such ability. Participants from junior high to graduate students took part and some of them were interviewed. The SOLO Taxonomy is used for decoding the students’ responses and the Rasch model is used for clarifying the construction of the hierarchy. Five different levels of graph interpretation are distinguished: Idiosyncratic, Basic graph reading, Rational/Literal, Critical, Hypothesising and Modelling. These results will supply guidelines for teaching statistical literacy.
6C3: DEVELOPING STATISTICAL LITERACY ACROSS SOCIAL, ECONOMIC AND GEOGRAPHICAL BARRIERS USING A “STAND-ALONE” ONLINE COURSE
Oded Meyer, Candace Thille
Carnegie Mellon University, United States
Carnegie Mellon University was funded to develop a “stand-alone” web-based introductory statistics course, openly and freely available to individual learners online. The goal of this project is to develop statistical literacy among people who do not have access to academic institutions because of remote locations, financial difficulties or social barriers. In order to achieve this goal, the design of the course has been a collaboration among statistics faculty, cognitive scientists and experts in human computer interaction. This paper discusses the challenges in developing such a learning environment and ways in which the course tries to address them. We also describe the design and results of a pilot study where the degree to which the course is successful in developing statistical literacy has been examined.
6C4: STATISTICAL LITERACY SURVEY ANALYSIS: READING GRAPHS AND TABLES OF RATES AND PERCENTAGES
Milo Schield
Augsburg College, United States
In 2002, an international survey on reading graphs and tables of rates and percentages was conducted by the W. M. Keck Statistical Literacy Project. Respondents included US college students, college teachers worldwide and professional data analysts in the US and in South Africa. The survey focused on reading informal statistics – rates and percentages in tables and graphs. Some high error rates were encountered, but helping students learn these skills takes considerable time. A new on-line tool has been developed to help students practice using ordinary English to describe and compare rates and percentages. This tool decreased the class time necessary to teach this skill and helped make it possible to teach statistical literacy online. Statistical educators now have both the rules and the tools to teach students how to read and interpret summary data, and for teaching students to read and write comparisons of rates and percentages correctly.
SESSION 6D: Researching assessment in Statistics education
6D1: ASSESSING STATISTICAL LITERACY: A QUESTION OF INTERPRETATION?
Rosemary Callingham
University of New England, Australia
Current school curriculum documents stress the need for assessment to support learning. Teachers use assessment information to infer students’ development and plan appropriate intervention. In order to do this, a framework is needed within which the assessment can be developed and interpreted, and a suitable task is required to obtain the necessary information about students’ performances. The responses of 586 students to performance assessment tasks developed for the purpose of assessing a numeracy construct, rather than statistical understanding, were analysed against a previously identified hierarchy of Statistical Literacy. The findings suggest that the tasks provided reliable and interpretable evidence of performance in Statistical Literacy, using a classroom-based process rather than a traditional test.
6D2: REASONING WITH EVIDENCE – NEW OPPORTUNITIES IN ASSESSMENT
Jim Ridgway, James Nicholson, Sean McCusker
University of Durham, United Kingdom
Computers facilitate reasoning with complex data. We report a study where 195 students aged 12 to 15 years were presented with computer based tasks that require reasoning with multivariate data, together with paper based tasks from a well established scale of statistical literacy. All the tasks fitted well onto a single Rasch scale; computer tasks were cognitively more complex, but ranked only slightly more difficult than paper tasks on the Rasch scale. Implications for assessment, the curriculum, and public presentations of data are discussed.
6D3: ASSESSING STUDENTS’ STATISTICAL REASONING
Robert delMas, Ann Ooms, Joan Garfield
University of Minnesota, United States
Beth Chance
California Polytechnic State University, United States
This paper describes the ARTIST project which was designed to address the assessment challenge in statistics education. The goals of the ARTIST project are to assist faculty who teach statistics across many disciplines in assessing student learning of statistics, enabling them to better evaluate individual student achievement, to evaluate and improve their courses, and to allow them to assess the impact of reform-based instructional methods on the attainment of statistical literacy, reasoning, and thinking. ARTIST consists of a website that provides resources designed to meet these goals. Among the resources are a large, searchable assessment item database, several online topic tests, and a comprehensive test of statistical literacy and reasoning (CAOS). Details of the development of the ARTIST resources, results from an extensive evaluation of the project, and the development of future ARTIST resources are presented.
SESSION 6E: Research on the role of technology in learning and teaching Statistics
6E1: ANALYSING TEACHING AND LEARNING PROCESS FOR THE LAW OF LARGE NUMBERS: IMPLICATIONS OF USING SOFTWARE IN TEACHERS EDUCATION
Juan D. Godino, Rafael Roa, Ángel M. Recio, Francisco Ruiz, Juan L. Pareja
University of Granada, Spain
In this paper we analyse an intuitive approach to the study of the empirical law of large numbers by a pair of student teachers. The learning is based on the use of a random experiment simulation applet with feedback by a lecturer. The analysis is based on some theoretical tools taken from the onto-semiotic approach to mathematical cognition and instruction (Godino, 2002). In particular we assess the epistemic, cognitive and instructional suitability of the study process. We deduce some requirements of the simulation device characteristics and the lecturer's role to increase the suitability of the teaching and learning process.
6E2: DEVELOPING A COMPUTER INTERACTION TO ENHANCE STUDENT UNDERSTANDING IN STATISTICAL INFERENCE
Kay Lipson, Glenda Francis, Sue Kokonis
Swinburne University of Technology, Australia
Prior investigation of student experiences with a computer interaction indicated that the simulation was only partly successful in facilitating developmental learning of statistical inference. The simulation was re examined in the light of subsequent multimedia design research and cognitive theory. A new simulation was developed with less extraneous information and reduced on screen text. In addition the new simulation incorporated audio narration and a higher degree of student control in progressing through signalled stages of development.
6E3: SAYING THE SAME (OR A DIFFERENT) THING: HOW SHAPE AFFECTS IDEAS ABOUT DISTRIBUTION IN A SOFTWARE EXPLORATION ENVIRONMENT
James K. L. Hammerman, Andee Rubin
TERC, United States
Educational software for statistics and data analysis provides a variety of tools for seeing and expressing ideas about data distributions. However, the ideas that learners find important to express often depend on an interaction between software and the shape of the distributions themselves. In this interview study of teachers participating in the VISOR professional development program, we investigate how distributional shape (symmetric or skewed) and choice of software tool (
TinkerPlots or
Fathom) affect the variety of ways that teachers discuss data distributions when comparing groups. We find teachers’ confidence is increased when different measures or ways of viewing data “say the same thing,” which more often holds true with symmetric distributions. When these seem to conflict, typically with skew distributions, teachers work to understand the measures themselves, and introduce new ways of characterizing data, so that they can make coherent sense of the distributions. The paper introduces a distinction between
rule-driven and
value-driven measures which we find important in understanding teachers’ analytic methods.
6E4: INVESTIGATING THE USE AND USEFULNESS OF INSTANT MESSAGING IN AN ELEMENTARY STATISTICS COURSE
Rachel Cunliffe
University of Auckland, New Zealand
Instant messaging is a way of sending short messages to other users who are currently online in “real time” and is a rapidly growing medium by which many students are choosing to communicate with each other. A pilot study into the use of instant messaging was carried out with two large elementary statistics classes. This study will report back on the virtual office-hours service, advantages and disadvantages of online study groups and reflections on how instant messaging could change help-support services for students studying statistics.
SESSION 6F: Theoretical frameworks and Statistics education research
6F1: BEING CRITICAL ABOUT APPROACHES TO RESEARCH IN STATISTICS EDUCATION
Anna Reid, Peter Petocz
Macquarie University, Australia
Teachers undertaking educational research for the first time usually begin their explorations by evaluating some aspect of their practice. By contrast, experienced researchers will start from an argued research question supported by a defined theoretical framework. In this paper, we use a critical discourse approach to explore various interpretive research paradigms that are commonly used to investigate aspects of statistics education. By considering the underlying epistemological positions and critiquing the approaches and methods used to explore human action in social situations, we become more critical in the design, implementation and reporting of research in statistics education.
6F2: THE MEANING OF STATISTICS VARIATION IN UNIVERSITY BOOKS IN SPAIN
Antonio Estepa-Castro
University of Jaén, Spain
Juan Ortega-Moya
UNED, Spain
In this paper we fix the institutional reference meaning of variation and its measures in university books for the first university courses, using the six elements of meaning of the “ontologic-semiotic approach of mathematical cognition.” The elements of meaning in books are identified. The deficiencies and possible difficulties that students can find, are considered. From the descriptive point of view, the complexity of topic variation and their measures is established. We conclude by pointing out the usefulness of the results.
6F3: DESIGN RESEARCH AND DESIGN HEURISTICS IN STATISTICS EDUCATION
Koeno Gravemeijer
Utrecht University, The Netherlands
Arthur Bakker
University of London, United Kingdom
Design research projects can be characterized as iterative and theory based attempts simultaneously to understand and improve educational processes. To contribute to a framework for design in statistics education, this paper draws on two design research projects, one carried out by Cobb, Gravemeijer and colleagues in the United States and one by Bakker and Gravemeijer in The Netherlands, both focusing on distribution as a core concept in the instructional design. Both projects were inspired by the theory of realistic mathematics education, which includes design heuristics such as guided reinvention, historical and didactical phenomenology, and emergent modeling. Each of these heuristics is briefly illustrated with examples from these two projects.
6F4: A FRAMEWORK FOR EXAMINING TEACHER KNOWLEDGE AS USED IN ACTION WHILE TEACHING STATISTICS
Tim Burgess
Massey University, New Zealand
Research on teacher knowledge has typically examined teachers outside of the classroom in which they use their knowledge. Recognising that it is difficult to separate a teacher’s knowledge from the context in which it is used, there has been a move towards studies being conducted in the classroom. Statistics presents its own challenges for teaching and learning compared with mathematics teaching and learning, especially with the growing recognition of and research around statistical thinking. Consequently there is need for an approach to examining teacher knowledge in relation to the actual work of teaching of statistics. This paper suggests a framework for examining the knowledge of primary (elementary) teachers as they engage in teaching statistics. The framework recognises that teacher knowledge is dynamic and dependent on the context of the classroom and students within it.
SESSION 6G: Research methodologies in Statistics education
6G1: AN EXAMPLE OF INDIVIDUALIZING LEARNING AND ASSESSMENT THROUGH COMPUTERIZED TESTING
Paul J. Fields, Edward Paul Johnson
Brigham Young University, United States
With the dual goal of providing individualized learning and assessment, while simultaneously preserving academic integrity, we have implemented a computerized testing system to generate, administer and grade quizzes in an introductory statistics course for graduate students. A fundamental reason for individualization is to permit each student to learn at his or her own pace. At the same time, administering individualized instruction must not increase the time involvement of the instructor. The ability of the computer to randomly select questions from a test bank, to randomly generate data for the questions, and to randomly order the answer choices makes it possible for learning and assessment to occur in accord with each student’s individual needs while maintaining fairness for the students and the instructor.
6G2: LEARNING GOALS: THE PRIMACY OF STATISTICAL KNOWLEDGE
Nick J. Broers
Maastricht University, The Netherlands
Amongst researchers of statistics education and statistics educators alike, statistical literacy, statistical reasoning and statistical thinking have gained prominence as important learning goals for the teaching of statistics. Careful examination of the three concepts shows that considerable disagreement on their definition still exists, creating problems in the attempts to develop valid and useful measurement instruments. It is argued that the fuzziness of the three constructs stems from the fact that their conception was not motivated by empirical regularities in need of explanation, but rather by the desire to create new perspectives on the future development of statistics education. The inherent ambiguity of the three concepts makes them unsuitable as learning goals for statistics education. By focussing on different aspects of statistical knowledge, however, the intended differentiation in meaningful learning goals can be met in a less disputable way.
6G3: ASSESSING STUDENTS’ UNDERSTANDING OF STATISTICS
Luc Budé
Maastricht University, The Netherlands
Statistical literacy, reasoning, and thinking may be the most prominent objectives of statistics education; they are unsatisfactorily defined and demarcated. Therefore, they are difficult to monitor, and assess. As a consequence they are impractical as educational goals. Instead, assessment could be focused on those aspects of specific statistical knowledge that are indicative for different levels of understanding. Factual knowledge directly derived from sources of information indicates a superficial level of understanding; a comprehensive, coherent knowledge structure indicates a more profound level of understanding, and the ability to transfer knowledge (the ability to flexibly engage statistical knowledge in novel tasks) indicates an expert level of understanding. This classification of hierarchically related levels of statistical understanding may produce adequate ways of measurement and assessment.
6G4: INDIVIDUAL CURRICULA – BELIEFS BEHIND TEACHERS’ BELIEFS
Andreas Eichler
Universität Bielefeld, Germany
This report focuses on a research project concerning individual curricula regarding the instruction of statistics and of probability theory. Individual curricula will be described as belief systems which contain teachers’ subjective knowledge and conceptions about mathematics, about learning and teaching mathematics, and particularly about statistics and probability. This report stresses two aspects: the theoretical settings, and the methodological settings of the research. The theoretical settings concern central assumptions and theoretical constructs. The discussion of the methodological settings which will be illustrated by research results, includes the description of a five-step-methodology used for investigating individual curricula.
SESSION 6H : PANEL DISCUSSION
6H1: NEW RESEARCHERS’ MENTORING FORUM
Michael Shaughnessy
~ Portland State University, United States
Cliff Konold
~ University of Massachusetts – Amherst, United States
Jane Marie Watson
~ University of Tasmania, Australia
Carmen Batanero
~ University of Granada, Spain
Rolf Biehler
~ University of Kassel, Germany
This session will bring together some experienced researchers in statistics education from a variety of disciplinary backgrounds to share their experiences and give advice to beginning researchers in this area. A general panel discussion of current research issues and important questions will for about one hour. This will be followed by small discussion groups of new researchers for about half an hour. Each group will be facilitated by a senior researcher who will respond to their specific questions and provide mentoring advice for them. The type of issues discussed by the panel will include: narrowing down good research questions, appropriate methodologies to use, the role of comparative studies, the benefits of collaboration, resources to utilize, and strategies for publishing research papers.