 Proceedings
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Invited TalksTopic 3 : Learning to teach statisticsOur understanding of teaching statistical thinking and reasoning has changed quite dramatically in the past decade. Where statistics was once not introduced until the upper secondary or tertiary level, many countries now incorporate chance and data into curriculum as early as kindergarten. Furthermore, a traditional focus on teaching procedural knowledge has shifted towards creating opportunities for all learners to develop the statistical understandings needed to cope with an increasingly complex technological society. As statistics education evolves towards enabling learners at all ages to engage with more authentic contexts and deeper understandings of statistical processes and concepts, the importance of improving the preparation of those who teach statistics is critical. This topic will focus on several aspects to consider in preparing those responsible for teaching of statistics, including innovative approaches for the preparation and training of teachers at school and tertiary levels, capitalizing on opportunities to embed context and data, embracing alternative statistical perspectives, and considering recent research findings on the teaching of statistics.Session 3A: Professional development of teachers3A1: Tools for fostering and guiding the statistics teachers’ reflection on their own practiceJuan D Godino University of Granada, SpainTeachers need to reflect on their own mathematical practices and on the teaching and learning processes experienced to acquire and adapt their didactical knowledge. Nevertheless, this didactical analysis and reflection requires of the mastering and application of adequate conceptual and methodological tools. In this paper we present a model for the statistical and didactical training of teachers that has resulted from our experience as mathematics educator, and is based on the application of the “onto-semiotic approach” to mathematical knowledge and instruction. We also apply a set of “guidelines for didactical analysis”, based on our theoretical framework, to design, implement and assess a teaching and learning process about statistics with a group of student teachers. Paper 3A2: Statistics teacher of the new era: another specialized mathematician or a totally different person?Theodore Chadjipadelis Aristotle University of Thessaloniki, GreeceEfi Paparistodemou Ministry of Education, Cyprus Maria Meletiou-Mavrotheris European University, Cyprus The majority of mathematics teachers have received a purely formalistic education, with little, if any, specific training in probability and statistics. Their formalist mathematical background has a negative effect on their statistical reasoning and their development as teachers of statistics. In the paper, we describe EarlyStatistics, an online professional development course in statistics education targeting European elementary and middle school mathematics teachers. To help teachers go beyond procedural understanding of statistics, the course emphasizes statistical problem-solving. Through participation in projects, experiments, computer explorations with real and simulated data, group work and discussions, participating teachers learn where the “big ideas of statistics apply and how, and develop a variety of methodologies and resources for their effective instruction. Paper 3A3: Teaching primary teachers to teach statistical investigations: the uniqueness of initial experiencesKatie Makar The University of Queensland, AustraliaExperience with statistical inquiry has been advocated in statistics education as vital for learners’ understandings of statistical processes. Research has suggested, however, that practices at the school level have focused almost solely on graphs and procedures. While important, these skills do not develop learners’ abilities to cope with the decisions that arise in the face of uncertainties and ambiguities that accompany statistical investigations. A longitudinal study in Australia researched experienced primary teachers’ evolving experiences in teaching statistical inquiry. This paper will report on the uniqueness of teachers’ early experiences in teaching statistical inquiry, an issue that emerged in the first three years of the study. Critical skills that teachers need to develop to teach statistical investigations that are often neglected in teacher professional development are discussed, including implications for research and teacher education. Paper 3A4: Training in-service teachers to develop statistical thinkingAna Luisa Gómez Blancarte National Polytechnic Institute, MexicoErnesto Sánchez National Polytechnic Institute, Mexico This paper describes the acquisition of statistical thinking by five in-service middle school teachers during a professional development course and the difficulties they encountered. The main activities of teachers were to plan, teach and analyze classroom lessons that would promote and enhance their students’ statistical thinking. The question then is: “How do teachers develop statistical thinking by means of designing and implementing classroom activities to promote it in their students?” Teachers attended a three-year professional development project. In the first year, they studied basic concepts of statistics. In the second, they planned and implemented a lesson, with the principal goal of developing their students’ statistical thinking. The topics of the lesson were graphs and arithmetic mean. In the third year, the lesson was reviewed, improved, and implemented again. Wild & Pfannkuch’s (1999) model was used as a guide in this study. Paper Session 3B: Pre-service preparation for primary teachers3B1: Student teachers developing their knowledge about data handling using TinkerPlotsCarlos Eduardo Monteiro Federal University of Pernambuco, BrazilAndreika Asseker Federal University of Pernambuco, Brazil Liliane Carvalho Federal University of Pernambuco, Brazil Tânia Campos Bandeirante University of São Paulo, Brazil Ainley (1995) and Pratt (1995) suggest that more effective teaching in data handling can be developed using computer based activities in which students developed active processes of interpretation. TinkerPlots is an example of software which has different tools to handle data and allows students develop different strategies of interpretation (Konold & Miller, 2005). This study explored the use of TinkerPlots among 8 Brazilian primary student teachers who were taking an undergraduate education course. The volunteers participated in four research sessions in which we collect data about their background in data handling; proposed a reflection about data handling processes, explored TinkerPlots possibilities to handle data and shared what they had learnt from their participation. The results showed evidence of the role of TinkerPlots for processes of teacher education which aim for the development of data handling knowledge. Paper 3B2: Preparing elementary school teachers to teach statistics — an international dilemmaTim Jacobbe University of Florida, United StatesMost teacher preparation programs neglect statistics during common coursework. Although students may take an introductory statistics course, they are not necessarily prepared to teach statistics content at the elementary school level. Recommendations for the types of experiences elementary school teachers should have are discussed. Paper 3B3: Teaching statistics at the primary level: identifying obstacles and challenges in teacher preparation from looking at teachingAisling Leavy University of Limerick, IrelandPreparing preservice primary teachers to teach statistics is a complex endeavor. The challenge is to enrich content knowledge, advance pedagogical understandings, and develop the types of thinking and dispositions necessary to support instruction. This paper reports on two studies of 51 final year preservice primary teachers engaged in “lesson study”. Working with preservice teachers provided unique insights into the types of understandings they draw on and the difficulties they encounter when teaching and reflecting on design lessons. The study revealed that for participants the teaching of statistics is perceived as straightforward, content knowledge understandings tend to be weak and limited to procedures, and experiences of investigation is limited. Experiences planning lessons and teaching in classrooms, however, present opportunities for the development of content understandings and for developing sophisticated perspectives on data. Paper Session 3C: The impact of technology on learning to teach statistics3C1: A model for teacher knowledge as a basis for online courses for professional development of statistics teachersThomas Wassong University of Paderborn, GermanyRolf Biehler University of Paderborn, Germany The paper will report from an ongoing project that develops online courses for the professional development of secondary statistics teachers. The design of the course is to based on an analysis of knowledge and competencies that teachers need in their professional practice. We aim at relating the general discussion on teacher competence to the specific needs that statistics teaching requires. Our paper starts with an analysis of theories of professional development of teachers and their knowledge elements. We will combine content knowledge, pedagogical content knowledge and knowledge for technology use and make this concrete for the knowledge of statistics teachers. Paper 3C2: Students’ understanding and reasoning about sample size and the law of large numbers after a computer-intensive introductory course on stochasticsCarmen Maxara University of Paderborn, GermanyRolf Biehler University of Paderborn, Germany A post-course study of students who participated in an introductory course on stochastic (probability and statistics) for future mathematics teachers is the focus of this paper. In this course the software FATHOM was used. Students learn to use FATHOM as a (cognitive and culturally mediated) tool for exploratory data analysis, for simulation and for inferential statistics as well as a tool for experimenting with statistical methods. We will focus on the analysis of three interview-tasks and report on the students’ intuitions on the role of sample size in two tasks that were analogous to the maternity ward problem and about their understanding of the role of n (sample size) and N (number of simulations) in sampling distributions in a coin-tossing context. Although the students had encountered similar tasks before in the course, our analysis will show the fragility and partly contradictory nature of their knowledge. Paper 3C3: An attempt to reconcile teaching content, pedagogy, and software in an online course for teachersWilliam Finzer KCP Technologies, United StatesThis paper describes the issues confronting the development of an online course with the goal of improving teachers’ ability to use Fathom software in teaching statistics. Three important questions underly course development. Firstly, given the huge range of participants prior experience and statistical understanding, what is the proper balance of focus on technology, statistical concepts, and pedagogy? Secondly, to what extent should the course develop mastery of Fathom’s powerful simulation techniques as opposed to clarity in how to make effective use of simulation for student learning? Finally, given participants’ widely varying teaching styles, how can the course engage participants in meaningful and useful discussions of how to integrate use of Fathom into their classrooms? Paper 3C4: High school teachers’ reasoning about data analysis in a dynamics statistical environmentSantiago Inzunsa Autonomous University of Sinaloa, MexicoJosé Alfredo Juárez Autonomous University of Sinaloa, Mexico In this article results of a study about statistical reasoning that high school teachers develop in a computer environment are presented. The results indicate that despite the abundance of representations provided by the software, teachers focus on the calculation of averages to describe and compare distributions, rather than on the important properties of data such as variability, shape and outliers. Many teachers were able to build interesting graphs reflecting important properties of the data, but cannot use them to support data analysis. Hence, it is necessary to extend the teachers’ understanding on data analysis so they can take advantage of the cognitive potential that computer tools to offer. Paper Session 3D: Learning to use context in teaching statistics at school and tertiary level3D1: The multiple roles of context in the development of students’ informal inferential reasoningDani Ben-Zvi University of Haifa, IsraelThe multiple roles of context will be discussed in the setting of an extended development and research project in primary school. An inquiry-based technology-rich learning environment was designed to develop and study students’ reasoning about statistical inferences. Qualitative research methods are used to critically dissect the roles of context in the emergence of students’ statistical reasoning. Context is not perceived in isolation but rather as part of a complex network of themes, such as inquiry and reasoning norms, statistical concepts and tools, beliefs and expectations, and meaning making and explanations. For example: Context is utilized by the students when they search for interesting and intriguing inquiry theme; context provides linguistic scaffolds for sense making of the data; context provides the basis for students' expectations regarding the situation, which are compared with the results of the data analysis and may give rise to building critical stance towards inferences and statistical concepts. Paper 3D2: Structuring contexts for statistical treatment: initializing statistical reasoningErna Lampen Wits School of Education, South AfricaTeaching from everyday contexts drew my attention to the importance of learning to structure situations for statistical treatment. In this theoretical paper I argue that Mallows’ notion of solving a zeroth problem as part of the data-handling process should receive priority in introductory statistics courses for teachers who learn statistics through solving authentic problems. I discuss an example of such a structuring process and reflect on the demands it posed for the students and for me as lecturer. Paper 3D3: Educational versions of authentic practices as contexts to teach statistical modelingAdri Dierdorp Utrecht University, The NetherlandsArthur Bakker Utrecht University, The Netherlands Jan van Maanen Utrecht University, The Netherlands Harrie Eijkelhof Utrecht University, The Netherlands For the teaching of modeling correlation and regression an 11th-grade unit was designed on the basis of authentic practices in which practitioners use linear regression models. These practices include identifying suitable sports training programmes, dike monitoring and calibration of measurement instruments. The question we intend to answer is how educational versions of such practices can support students in learning to make data-based predictions in authentic situations. For example, the authentic practice of dike monitoring is used to motivate students to study scatter plots of dike height over time and learn how to model a regression line for finding a possible trend to predict when the dike needs to be heightened. The analysis of three teaching experiments shows that most students worked eagerly and with good results, but many continue to struggle with coordinating statistical and contextual knowledge. Paper Session 3E: Learning to teach data-based statistics at school and tertiary level3E1: Towards evaluation criteria for coherence of a data-based statistics curriculumAnneke Verschut University of Utrecht, The NetherlandsArthur Bakker Utrecht University, The Netherlands As coherence is one of the objectives of a new data-based statistics curriculum for grades 10-11 (age 15-17) in the Netherlands, this paper explores the notion of curriculum coherence. Although policy-makers and educators around the world look for more coherent curricula, it is often not clear what this actually means. This paper works towards an operational definition of a coherent statistics curriculum by analyzing the results of interviews and email discussions with national and international experts on statistics education who were asked for their opinions on what constitutes a coherent statistics curriculum. The results are a first step towards evaluation criteria for coherence of the three common representations of a curriculum: the intended, implemented and attained curriculum. Paper 3E2: Some issues of data production in teaching statisticsCarl Lee Central Michigan University, United StatesStatistics educators, for a long time, have stressed the importance of using real data and focusing on variability of data in teaching statistics. Real data are messy. Due to the difficulty of creating a ‘real’ process of data production in a classroom setting, the issues of data production seem to be ignored in teaching statistics. Some of the issues may include (a) choice of measurement units, (b) robustness of measuring techniques, (c) the importance of operational definition, (d) subjective sampling vs. random sampling (e) observational vs. experimental studies (f) outliers Vs. errors, and (g) underlying target population. The use of real-time hands-on activities to teach students how to handle the issues of data production in a classroom setting is demonstrated. Paper 3E3: Models of teacher preparation designed around the GAISE FrameworkChristine Franklin University of Georgia, United StatesGary Kader Appalachian State University, United States Statistical literacy is a must have competency for any citizenry to thrive in an information rich society. Sound statistical reasoning skills take time to develop and cannot be honed in a single general-purpose statistics course. To acquire proficiency in statistics foundational concepts should be introduced and nurtured in the elementary grades, and strengthened and expanded throughout the middle, high school and post-secondary grades. In this paper, examples will be presented that illustrate developmental learning trajectories for statistical concepts as proposed in the American Statistical Association’s Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K-12 Curriculum Framework (2007). The GAISE Report describes a cohesive and coherent framework for statistical education at Grades PreK-12 in the United States. Models of teacher preparation that integrate both the content and pedagogical knowledge as proposed in the GAISE Framework will be described. Paper Session 3F: Similarities and contrasts in teaching mathematical and statistical thinking3F1: Chance and necessity: the languages of probability and mathematicsRamesh Kapadia University of London, United KingdomThe idea of viewing mathematics as a language of communication has been espoused for many years. In England, this was the starting point for the influential report on the teaching of mathematics by Cockcroft. A much earlier reference is that of Tobias Dantzig in his seminal book, Number–The Language of Science; this would now perhaps be called, Mathematics–The Language of Scientific and Social Disciplines. In some ways, probability can be seen part of mathematics and would be a strong sub-discipline which drives and underpins much work in the social sciences, as well as in science such as quantum mechanics and genetics. The original subsets of mathematics were number, algebra, and geometry, though there are many other fields of mathematics now; it can be argued that probability is quite distinctive, as is statistics. This paper will explore the similarities and differences between the languages of probability and mathematics. Paper 3F2: Mathematical logic and statistical or stochastical ways of thinking: an educational point of viewÖdön Vancsó University of Budapest, HungaryAt least partially, statistical thinking is based on logic different from classical logic, which causes many troubles for students. To implement didactical considerations on this issue into teaching seems to be advantageous. Some examples will be outlined to illustrate the differences in logic and how this could be transformed to actual teaching. For our school experiments we implement analogies throughout and also examples from physics teaching. Paper 3F3: Exploration and induction versus confirmation and deductionKathryn Laskey George Mason University, United StatesLaura Martignon Ludwigsburg University of Education, Germany Application of the scientific method involves two interacting kinds of reasoning: heuristic exploration and inference to arrive at hypotheses and deductive reasoning to confirm or refute them. Theoretical statistics draws on abstract mathematical reasoning, much of which lies beyond the capability of young students. Nevertheless, they can acquire a sophisticated understanding of statistical concepts by drawing on natural intuitions. There is an analogy in physics with its mathematical basis, which may be understood heuristically. In a similar way, many concepts in probability and statistics have physical analogues. Analogues such as the familiar ball and urn model connect to natural cognitive structures the brain has evolved to enable survival in a complex world. By drawing on these natural cognitive tools, teachers can have greater success both in developing intuitions and in facilitating the formation of abstract concepts. Paper Session 3G: Diversity in types of teaching at the tertiary level3G1: How technology can help or complicate the teaching of statistics depending on the class sizeBruno de Sousa New University of Lisbon, PortugalJosé Vicente Novegil Souto University of Vigo, Spain Technology is part of the new reality in the educational system. Students use it, and teachers need to find new ways to engage students. Web 2.0 is the turning point in which the World Wide Web can be used to fully enhance the creativity of its users with its many instruments available, such as blogs, social-networking sites, video sharing sites and wiki pages, just to mention a few. The richness and diversity of subjects that Statistics encompasses, together with the WWW, creates an environment of excellence in which students play an active role in the entire learning process. It is our goal to show how the use of these new technologies can promote, in both small and large classes, the knowledge and understanding of statistics in an environment that, although tailored for each student, encourages the student to interact with his/her classmates, creating a vivid environment that enhances their learning potential. Paper 3G2: Diversity and differentiated instruction and learningW Robert Stephenson Iowa State University, United StatesInstructors of statistics have struggled with the wide range of preparation of the students coming into statistics classes. This can include the mathematical preparation in secondary school for the introductory statistics course. This wide range of experience is complicated by the fact that different students have different learning styles. This paper will look at the idea of differentiated learning that allows students with weaker backgrounds to look at additional materials (through Web interfaces) to help fill in the gaps in their backgrounds so that they can be successful with the statistical content presented. Differentiated learning can also allow better students to go beyond the core statistical content to investigate more advanced topics (again on their own through Web interfaces). These differentiated learning experiences can be tailored to fit students’ learning styles. Paper 3G3: Equity and the increasingly diverse tertiary student population: challenges and opportunities in statistics educationLawrence Lesser University of Texas at El Paso, United StatesProfessional organizations and educators are increasing their focus on equity issues for the diverse (sub)populations they serve, such as second language learners. This focus is especially important in statistics because of the importance of context in both diversity and statistics, and because of the ways in which diversity issues interact with the actual practice and teaching of statistics. Also, there are many ways in which diversity and equity can be natural vehicles for motivating or exploring particular statistical concepts and content. Recently emerging evidence suggests that students in diverse classrooms can be motivated by such examples and there have been a variety of courses that have recently been developed to do this with varying emphases and degrees of integration. The totality of efforts in this area suggests that the challenges of teaching diverse populations ultimately yield opportunities, resources, and vehicles for student learning. Paper Session 3I: Practicum learning to teach statistics: perspectives from young staff3I1: Testing, testees, and tested: practical lessons from the first years at a small teaching-focused universityR Adam Molnar Bellarmine University, United StatesChanges in rank, responsibility, and duties make the first few years as a University professor substantially different from graduate student life. The shift comes with several stumbling blocks. This paper describes issues encountered at a small teaching-focused university in the United States. The shift to full responsibility for multiple courses, including syllabus and test design, involves skills acquirable through training and study. Less bookish, yet no less important, is learning about the students; their motivations and styles differ from those of graduate students and professional scholars. Then, dealing with academics through University politics has potential pitfalls. Also discussed are topics particular to small schools, such as the wide variety of requests for general statistics advice. Paper 3I2: Novice experience from teaching service courses in statisticsMatina Rassias University of Glasgow, United KingdomThe last few decades have been marked by a movement towards student centered teaching. This remains a real challenge for all educators but becomes even more demanding when dealing with service courses in Statistics. One of the main issues that statistical education has to face from the very early stages is introducing students into statistical thinking in the face of negative feelings such as discouragement and even frustration towards the subject area. In this paper we will study, from a novice educator’s perspective, ways to enrich the students’ learning processes transforming them into “intelligent citizens” who will communicate efficiently and effectively using Statistics. We will investigate how the educator can be assisted to become the facilitator in providing a highly stimulating and challenging environment in Statistics education that enables students to engage with the subject and make a smooth transition towards statistical literacy. Paper 3I3: How young statistics academics learn to teach statisticsHelen Johnson Queensland University of Technology, AustraliaHelen Thompson Queensland University of Technology, Australia Practicum learning to teach tertiary statistics is a common experience for young statistics academics and plays an important role in the transition from student to inexperienced tutor to confident academic lecturer. We discuss the development of statistics teaching skills and pedagogies through practicum learning in the context of young statistics academics with mathematical statistics backgrounds from a United Kingdom and Australian perspective. Approaches to teaching statistics are described and compared across a variety of introductory to upper-undergraduate statistics courses and for varying student cohorts. Paper |