 Proceedings
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Invited TalksTopic 8 : Research in statistics educationMore and more policymakers and companies ask for data and modelling in context to make their decisions evidence-based. In the context of statistics education this implies there is a need for research that informs stakeholders in education about what works and what is relevant. What counts as evidence in different communities, however, differs widely, but a well-developed and accessible research literature is clearly essential for promoting the field of statistics education. This ICOTS topic will therefore pay particular attention to the development of statistics education research, examining current research problems, directions for future areas of inquiry, and the use of theoretical models on which our research might be based. In addition to including sessions on teaching and learning statistics and probability, and the role of technology, we also plan a session on publishing in research journals.Session 8A: Research on developing students’ statistical reasoning in primary and middle school8A1: Developing primary students’ ability to pose questions in statistical investigationsSue Allmond University of Queensland, AustraliaKatie Makar The University of Queensland, Australia How do children develop their own questions to investigate in statistics? Often in school, teachers just give children questions to respond to, but rarely ask them to generate a question that they want to investigate. To write their own statistical questions, students need to envisage the processes and purpose of a statistical investigation. Curriculum documents in many countries have begun to recognise the benefits and importance of children developing their own questions, however little is known about children’s development in this area. This exploratory study aims to understand ways that 9 year old children can more confidently construct relevant and reasonable questions that can be answered with a statistical investigation. Results suggest that by using frameworks and peer negotiation to guide their experiences, students improve their ability to write purposeful investigative questions with richer statistical intent. Paper 8A2: How students’ spontaneous use of statistical tools shapes their thinking about precisionRich Lehrer Vanderbilt University, United StatesCliff Konold University of Massachusetts Amherst, United States Min-Joung Kim Vanderbilt University, United States We describe transitions in students’ conceptions of variability as they invented and revised a measure (statistic) of the precision of a collection of repeated measurements of a length. Our analysis highlights the role played by mediating agents (peers, teachers) and tools (TinkerPlots) in fostering transitions in students’ conceptions. We present two cases of student invention to illuminate how invention supported reasoning about multiple senses of variability and how these multiple senses were aligned in classroom conversations. We conclude by considering the role that TinkerPlots functions and representations played in spurring new lines of thought and in grounding conversations among students about the important representational characteristics of the measures they invented. Paper 8A3: Emergence of reasoning about sampling among young students in the context of informal inferential reasoningEinat Gil University of Haifa, IsraelDani Ben-Zvi University of Haifa, Israel This paper discusses students’ evolving statistical reasoning about randomness and sampling in the context of inquiry-based activities designed to develop their informal inferential reasoning (IIR). The knowledge of sampling and randomness are key concepts to understanding statistical inference (Garfield & Ben-Zvi, 2008). In the ‘Connections’ project (Ben-Zvi, Gil & Apel, 2007), sixth grade students were engaged in an inquiry-based learning environment using TinkerPlots (Konold & Miller, 2005) that was designed to develop their IIR. In this design experiment (Brown, 1992; Collins, 1992), the students’ intuitive concepts of sampling and randomness were used to design instructional activities that nurture the emergence of ideas of random vs. biased sample and inference. This knowledge was later applied by the students to investigate authentic data and draw informal statistical inferences from a random sample to a population. Paper 8A4: Developing statistical reasoning facilitated by TinkerPlotsNoleine Fitzallen University of Tasmania, AustraliaJane Watson University of Tasmania, Australia Of interest in this study, based in a class of 26 Year 5/6 students, is the way TinkerPlots facilitated the development of statistical reasoning for students with no previous data handling experience. The class completed four lessons related to data collection, data representation, data summary, and data inference based on a sporting activity, where they had recorded their heart rates before and after the event and used the software TinkerPlots to analyse the data. A month later 12 of the students were individually interviewed with a three-part protocol using TinkerPlots to assess their reasoning in relation to comparing two data sets, to hypothesising relationships and providing evidence, and to interpreting differences in large data sets. The consolidation and transfer of reasoning evidenced in the student interviews demonstrated the value of employing TinkerPlots in the classroom. Paper Session 8B: Research on developing students’ statistical reasoning at secondary and tertiary levels8B1: Inferential reasoning: learning to “make a call” in theoryChris Wild University of Auckland, New ZealandMaxine Pfannkuch University of Auckland, New Zealand Matt Regan University of Auckland, New Zealand Nicholas Horton Smith College, Northampton, United States Drawing on recent research in statistics education, the new New Zealand Statistics curriculum plans for three years of instruction in informal statistical inference to lay conceptual foundations for instruction in formal statistical inference. We discuss issues involved in formulating beginning versions of statistical inference and present some specific and highly visual proposals. These are built upon simple metaphors and novel ways of experiencing sampling variation. They are designed to give students practically useful tools for data analysis as well as underpinning more advanced and formal methods of making inferences to be encountered later. Our proposal uses visual comparisons to enable the inferential step to be made without taking the eyes off relevant graphs of the data. This allows the time and conceptual distances between questions, data and conclusions to be minimized, so that the most critical linkages can be made. Paper 8B2: Inferential reasoning: learning to “make a call” in practiceMaxine Pfannkuch University of Auckland, New ZealandBefore students are introduced to formal statistical inference procedures at Grade 12, it is necessary in the earlier years to start building concepts such as sample, population, sampling variability, and “making a call”. This paper reports on an initial study to determine whether proposed ideas about improving students’ inferential reasoning were possible in practice in terms of student capability. Interviews, assessment responses, and classroom experiences will be used to describe how three low-to-average ability Grade 11 students started to conceptualize that inferences about populations can be made from samples. The findings suggest that the proposed instruction methods, which focus on building concepts about sampling variability, can influence and develop students’ inferential reasoning. Issues arising from the study are discussed. Paper 8B3: Developing tertiary-level students’ statistical thinking through the use of model-eliciting activitiesRobert C delMas University of Minnesota, United StatesJoan Garfield University of Minnesota, United States Andrew Zieffler University of Minnesota, United States This paper reports on the development of specially designed Model-Eliciting Activities (MEAs) to help students develop statistical thinking. While MEAS have been successfully used in mathematics and engineering education (Lesh & Doer, 2003; Zawojewski, Bowman, & Diefes-Dux, 2008), their use in an introductory applied statistics course had not been investigated. The NSF-funded CATALST project has been studying the development and use of MEAs as a way of having students experience an authentic statistical problem that is based on a real data in order to expose students to the discipline of statistics and promote students’ statistical thinking. Paper 8B4: Students’ statistical reasoning about distribution across grade levels: a look from middle school through graduate schoolJennifer Noll Portland State University, United StatesMike Shaughnessy National Council of Teachers of Mathematics, United States Matthew Ciancetta California State University – Chico, United States This paper provides a synthesis of the findings from three studies that investigated students’ statistical reasoning about distributions of data and sampling distributions. Each study presented some of the same open-ended statistical tasks to students from different populations: middle school, high school, undergraduate or graduate students. The authors observed that students across all grade levels experienced difficulty in coordinating multiple aspects of a distribution. We will discuss two of the significant obstacles observed: lack of proportional reasoning skills when comparing different distributions, and difficulties in managing the natural tension between sampling variability and sample representativeness. Our research findings suggest that students throughout the grade levels need more opportunities to reason about empirical sampling distributions. Paper Session 8C: Making sense of risk8C1: Teaching uncertainty and risk in mathematics and sciencePhillip Kent University of London, United KingdomDave Pratt University of London, United Kingdom Ralph Levinson University of London, United Kingdom Cristina Yogui University of London, United Kingdom Ramesh Kapadia University of London, United Kingdom We are investigating how secondary teachers make sense of the concept of risk, how it figures in their teaching, and what possibilities exist when a cross-curricular and technology-enhanced approach is taken. We have developed decision-making scenarios for socio-scientific topics that involve modelling with personal value systems alongside strictly quantifiable mathematical models. Precise models are limited and may be hedged around with judgements about authority and validity, whilst value judgements are generally weakly-quantifiable. Nevertheless coming to a decision requires the weighing of these diverse forms of information, each having some associated estimation (not necessarily numerical) of ‘risk’. Going beyond the idea of risk in statistical theory, we are trying to understand how personal values and models influence thinking about risk and the process of decision-making, and the implications of this for classroom practice Paper 8C2: Conditions for risk assessment as a topic for probabilistic educationLaura Martignon Ludwigsburg University of Education, GermanyMarco Monti Max Planck Institute for Human Development, Germany Statistical literacy is a necessary condition for informed consent and competent citizenship in a modern society. We report data on risk assessment in the context of both medical and investment decision making, which demonstrate that transparent (rather than opaque) communication of risks becomes essential for fostering coherent decisions. We also report on research that reveals how risk communication provided by the pharmaceutical industry or by financial advisors tends to be opaque and excessively complex, rather than transparent and simple. Transparent risk communication can be achieved by making use of frequency statements instead of single-event probabilities, absolute risks instead of relative risks and, in general, “natural” representations of conditional probabilities. We also propose methodologies for instructing children in risk assessments, at an early stadium. These methodologies are based on simple examples. Paper 8C3: Exploring risk through simulationTim Erickson Epistemological Engineering, United StatesTo understand risk, you have to connect statistics and probability. That makes risk a hard topic, but risky contexts are also interesting and meaningful; one can argue that they are some of the most important for our citizens to understand. The Data Games project is developing web-based games and lessons. These games produce data—often a lot of data—that students analyze in order to improve their performance. This paper discusses the role of risk in curriculum choice, and our experience field-testing one of these activities in US schools with students ages 16–18. Paper Session 8D: Research on technology in statistics education8D1: Introducing concepts of statistical inference via randomization testsJohn Holcomb Cleveland State University, United StatesBeth Chance California Polytechnic State University, United States Allan Rossman California Polytechnic State University, United States Emily Tietjen California Polytechnic State University, United States George Cobb Mount Holyoke College, United States For over a decade now, technology tools have been advocated to assist student understanding of statistical concepts. We have designed and used applets that simulate sampling and randomization tests as a means for introducing students to concepts of statistical inference. In this talk we present the results of our investigation on the impact of using applets for this purpose with tertiary students. The foci of our investigation include appreciating the reasoning process behind statistical significance, understanding what a p-value is, and recognizing factors that affect p-values. We present the results of small classroom experiments designed to help inform our curricular materials and manner of teaching. Paper 8D2: Development of ideas in data and chance through the use of tools provided by computer-based technologySibel Kazak Pamukkale University, TurkeyCliff Konold University of Massachusetts Amherst, United States To support middle school students’ learning of data and chance, we have developed a set of classroom activities along with a probability simulation tool integrated into a future version of the dynamic data analysis software TinkerPlots (Konold & Miller, 2004). The activities and the software were designed to build on students’ current intuitions. In this paper, we describe the modeling and simulation capabilities of TinkerPlots and how particular features influence the formation of new ideas as students begin to perceive data as comprising signal and noise. Paper 8D3: Developing students’ computer-supported simulation and modelling competencies by means of carefully designed working environmentsRolf Biehler University of Paderborn, GermanyAndreas Prömmel University of Kassel, Germany The GESIM material, developed in our research group, contains learning units with teacher guides for the first 4 weeks of a probability and statistics course at upper secondary school (age 17-18). The learning of subject matter is linked to the acquirement of simulation competencies and the acquisition of skills in handling the dynamic software FATHOM. We emphasize simulation, law of large numbers and the role of sample size and develop knowledge about distribution from the beginning. We use a “simulation scheme” for guiding students’ modelling and simulation activities. We videotaped the work of about 20 pairs of students working on simulation problems and we will present results of our analyses concerning the solution process and the resulting knowledge. Moreover, we will present data on students’ competencies, which were measured by means of tests and by analyzing their written and their computer work. Paper 8D4: Conceptual issues in quantifying expectation: insights from students’ experiences in designing sampling simulations in a computer microworldLuis Saldanha Arizona State University, United StatesWe report on part of a classroom teaching experiment that engaged a group of high school students in designing and running sampling simulation in a computer micro world. The simulation design activities provided a vehicle for engaging students with informal hypothesis testing and for fostering their (re)construal of contextualized situations as probabilistic experiments—that is, as a scheme of interconnected ideas involving an imagined population, a sample drawn from it, and repeated sampling as an imagistic basis for quantifying one’s expectation of particular sampling outcomes under an assumption about the composition of the sampled population. Our report highlights challenges that students experienced and that shed light on aspects of quantifying one’s expectation that a random sampling process will produce a particular type of outcome. Paper Session 8E: Theoretical frameworks in statistics education research8E1: Quality in statistics education: applying expectancy value models to predict student outcomes in statistics educationNel Verhoeven Roosevelt Academy, The NetherlandsMany freshmen at University sign up for Statistics during their first year. In order to meet the requirements of the institution they attend, students of a broad spectrum of specialties must take this mandatory course. They often find the course difficult and it scares them to work with statistical software or formulas. As a result, teaching statistics requires a special didactical approach. So, teachers benefit from knowledge on how student outcomes can be modeled. The model presented here forms the starting point for a project that took place in the Netherlands and Flanders from 2005 until 2007. The application of the Expectancy Value Model discussed here predicts student achievement as a function of expectancies, motivation to be successful, previous experience, and social and cultural environment. For the aforementioned study the model was applied choosing a special position for Effort and Expectancies. Paper 8E2: Reasoning about variation: rethinking theoretical frameworks to inform practiceChris Reading University of New England, AustraliaJackie Reid University of New England, Australia There has been an increasing focus in recent years on theoretical frameworks to describe cognitive development of statistical concepts. There is now a need to encourage the use of these frameworks to inform practice in the teaching and learning of statistics. This paper focuses on frameworks that describe the levels of cognitive development of the concept of variation. Recent research proposing theoretical frameworks on, or referring to, reasoning about variation are synthesised. Discussion follows on the use of theoretical frameworks to inform the teaching and learning cycle for statistics courses, especially the design of curriculum, learning activities and assessment tasks. Paper 8E3: The transformation process from written curricula to students’ learningAndreas Eichler University of Education Freiburg, GermanyIn this report a theoretical framework that potentially facilitate to identify and to structure existing research results focusing on statistics teachers’ will be discussed. This framework involving a curriculum model and a specific understanding of beliefs will be outlined. Afterwards, existing research focusing on statistics teachers’ will be briefly discussed and possible shortcomings in this field of research will be identified. Paper Session 8F: Research methodologies in statistics education8F1: Multilevel modeling of educational interventions: educational theory and statistical consequencesFinbarr Sloane University of Colorado at Boulder, United StatesIn this paper issues of educational context are described. The implications of these issues for the design of educational research are then articulated. These context variables (e.g., that students are instructed in clusters, and that teachers require ongoing training to support and implement new and innovative curricula) are then used as a lens to examine the ASA’s 2007 report Using Statistics Effectively in Mathematics Education. A meta-model is offered to better address some of these concerns of educational context not fully articulated in the ASA report. The goal of the paper is to: (1) describe the component parts of this meta- model, and (2) generate the opportunity for richer conversation about the role and value of experimental statistics in education research. Paper 8F2: Randomized controlled trials and PhD level training in educational researchRobert Boruch University of Pennsylvania, United StatesErling Boe University of Pennsylvania, United States This invited paper reviews recent initiatives in teaching about randomized field trials at the graduate level in education research. Reports in Mosteller and Boruch (2002) are used as a benchmark. The initiatives have been driven heavily by recent governmental emphasis on “evidence based policy” in education, criminology, welfare and other sectors. This policy has been backed, in the US at least, by substantial investments in mounting randomized controlled trials to evaluate curriculum packages and programs in grades K-12, crime prevention programs, welfare, and other work. Accelerated growth in randomized trials has entailed cross discipline pre-doctoral and post-doctoral institutes and graduate education programs aimed at enhancing the quality in trial design, execution, and analysis of results. Specific illustrations of graduate education in this area of statistics are taken mainly from experience at the University of Pennsylvania’s Graduate School of Education and selected other institutions. Paper 8F3: Qualitative methods in statistics education research: methodological problems and possible solutionsSashi Sharma University of Waikato, New ZealandDespite being relatively new in statistics education research, qualitative approaches need special attention as attempts are being made to enhance the credibility and trustworthiness of this approach. It is important that researchers are aware of the limitations associated with these methods so that measures are put in place to try and minimize the effects of these limitations Philosophical roots and features of this paradigm are outlined. Challenges faced by qualitative researchers in terms of reliability, validity and generability are considered. Uses of the interview approach in research literature as a data gathering tool are considered next. Advantages and disadvantages of the interview approach are outlined. An example of a research in statistics education is provided to illustrate methodological problems and solutions related to qualitative methods. Paper Session 8I: Research into learning statistics in vocational educational and training8I1: The use of statistical tools by sales managers: forms of rationality and decision-makingCorinne Hahn School of Management for Europe, FranceIn this paper, we describe a project carried out with Business school students, in order to find out how different forms of rationality shaped a statistical decision-making problem and the use of statistical concepts by students. Paper 8I2: Evaluating statistics education in vocational education and trainingPeter Martin University of Ballarat, AustraliaThis paper presents the design and development of a tool for the purposes of evaluating particular aspects of statistics education in Vocational Education and Training (VET), and in so doing draws from various spheres of activity. In February 2009, a forum on Building Networks in Statistics Education was held in Brisbane and the results from a discussion group on interactions of statistics educators with employers generated issues of concern from both sides. An overview of the research that has been done in VET, and adult training in particular, indicates there are problems with some VET programs. A summary of key issues arising from industrial consultancies involving statistics education will be presented, culminating with a presentation of the evaluation tool. Paper 8I4: The influence of technology on what vocational students need to learn about statistics: the case of lab techniciansArthur Bakker Utrecht University, The NetherlandsMonica Wijers Utrecht University, Netherlands Sanne Akkerman Freudenthal Institute, The Netherlands The presence of advanced technology in the workplace influences what employees need to know. This paper focuses on the question of what student lab technicians in vocational education need to learn about statistics in the presence of technology. Through interviews with lab apprentices, apprentice supervisors and teachers, a questionnaire administered to apprentices, and workplace observations we have identified what statistical knowledge is taught and required. The knowledge required turned out to diverge across labs and be highly influenced by the degree to which work is mediated by technology. For example, calibration and validation of measurement instruments is based on linear regression, but is often automated. Many computations are carried out on Excel sheets, but not all schools dedicate enough instruction time on spreadsheets. At least 30% of the apprentices (N=300) felt insufficiently prepared in terms of mathematics or statistics. Paper Session 8J: Evidence-based statistical practice8J2: The influence of presentation on the interpretation of inferential resultsRink Hoekstra University of Groningen, The NetherlandsHenk Kiers University of Groningen, The Netherlands Addie Johnson University of Groningen, The Netherlands Confidence intervals (CIs) have frequently been presented as an alternative for null-hypothesis significance testing (NHST). Earlier, it was shown that the frequency of misinterpretations for results presented by means of CIs are lower than those for data presented by means of NHST outcomes. Little is known, however, about whether the subjective estimates that arguably play an implicit role in most interpretations of results differ for results presented by means of CIs or NHST outcomes. In the present study, participants were asked to interpret outcomes of fictitious studies. For significant outcomes, participants tend to be more certain about the existence of a population effect and about replicability of their results when the results are presented by means of NHST than by means of CIs. Such a difference could not be found for clearly non-significant findings. Apparently, a significant finding presented by means of a p-value is more convincing than the same effect presented by means of a CI. Paper 8J3: The role of external representations in understanding probabilistic conceptsPeter Sedlmeier Chemnitz University of Technology, GermanyIn their role as statistics teachers, experts can easily fall into the trap of assuming that their students share the intuitions they have acquired about formal expressions in the course of decades of learning and hard work. There is strong evidence that statistically naive students do not share experts’ intuitions. Instead, it is argued that non-experts commonly hold at least two valid statistical intuitions that are helpful for understanding probabilistic concepts. One of these postulated intuitions, the ratio intuition, helps to solve different kinds of conditional probability problems and the other, the size-confidence intuition, conforms to the empirical law of large numbers and is helpful in understanding the impact of sample size in inference statistics. However, both of these intuitions seem to work well only with suitable external representations: static or dynamic frequency formats. Teachers are encouraged to exploit their students’ intuitions. Paper 8J4: Understanding, teaching, and using p valuesGeoff Cumming LaTrobe University, AustraliaThere are many problems with the p value. Is it an indicator of strength of evidence (Fisher), or only to be compared with α (Neyman-Pearson)? Many researchers and even statistics teachers have misconceptions about p, although p has been little studied, and we know little about how textbooks present it, and how researchers think about it, react to it, and use it in practice. The p value varies dramatically because of sampling variability, but textbooks do not mention this and researchers do not appreciate how widely it varies. I discuss the problems of p and advantages of confidence intervals, and identify research needed to guide the design of improved statistics education about p. I suggest the most promising teaching approach may be to focus throughout on estimation, use confidence intervals wherever possible, give p only a minor role, and explain p mainly as indicating where the confidence interval falls in relation to the null hypothesised value. Paper |