 Proceedings
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Invited TalksTopic 2 : Statistics education at the school levelIn many countries throughout the world Statistics, often consisting of two strands with names such as Chance and Data, has increasingly become a more significant component of the school mathematics curriculum. Many countries include statistics benchmarks or statistics learning goals in their national curriculum or standards documents for all levels of school mathematics. In addition, the relatively recent introduction of innovative technology can have an impact on the ways that data handling and statistics are taught at the school level. This topic will focus on issues related to statistics, particularly data investigations and data handling in schools, including-innovative teaching strategies at various levels, assessment issues at the school level, developments and uses of technology to teach statistics in the schools, and research on teaching statistics at the school level.Session 2A: Learners’ first experiences of handling data — focusing on 7 to 13 year olds2A1: National testing of data handling in years 3, 5 and 7 in AustraliaSteven Nisbet Griffith University, AustraliaThis paper provides a critical analysis of the data-handling items contained in the 2008 Australian national Years 3, 5, and 7 numeracy tests from a number of perspectives, namely, congruence with the concept of numeracy, alignment with the Australian National Statements of Learning for Mathematics (Curriculum Corporation, 2006), and alignment with the Statistical Thinking Framework developed by Jones et al. (2001). Overall the test items reveal a limited focus with respect to item content, type of tasks, and method of response. The majority of items limit students to analysing data presented in tables and graphs, with some items requiring interpretation of the data. Gaps in the data-handling skills required by students to answer the questions are identified. Paper 2A2: Does context expertise make a difference when dealing with data?Cynthia Langrall Illinois State University, United StatesThe statistical literacy exhibited by students in two Year 6 classes was examined during an 8-day unit of instruction carried out under two conditions. For one class, data sets were designed to be specific in nature and related to the interests of many of the students. For the other class, data sets were generic in nature. Although students rarely engaged the data context, when they did, it influenced their informal inferential arguments and supported them in taking a more critical stance toward the data. Paper 2A3: Linking problems, conclusions and evidence: primary students’ early experiences of planning statistical investigationsJill Fielding-Wells University of Queensland, AustraliaAn overview of many primary programs demonstrates the passivity of statistical learning in the junior years. Students are usually provided clean, orderly, simplistic data, or data representations, with which to work. When students are encouraged to collect their own data, it is limited to that which could be expected to cause little difficulty. The focus on contrived and unsophisticated data collection and analysis denies younger students the opportunity to design their own statistical investigations. The research reported here derives from the introduction of the statistical investigative cycle (Wild and Pfannkuch, 1999) to a classroom of 9-10 year old students. The students initially experienced difficulty envisioning the investigation process, despite both explicit instruction and multiple prior experiences with investigative learning. A focus on connecting problems and conclusions to evidence enabled students to plan investigations more efficiently. Paper 2A4: Engaging young children in informal statistical inferenceEfi Paparistodemou Ministry of Education, CyprusMaria Meletiou-Mavrotheris European University, Cyprus At the lower levels of schooling, students’ exposure to statistical concepts has been restricted to basic descriptive statistics. In recent years, however, leaders in mathematics education have advocated a much wider and deeper role for statistics in school mathematics. Reflecting the recent shift in statistics education research from a focus on specific skills and procedures towards a greater focus on statistical reasoning and thinking embedded in the process of a statistical investigation, the current study was designed to investigate ways in which the foundations of inferential reasoning can be laid at a very young age. This paper reports on how a group of young students formulated and evaluated data-based inferences. The term informal inference is used here to describe the drawing of conclusions from data that is based mainly on looking at, comparing, and reasoning from distributions of data. Paper Session 2B: Secondary-level statistical education2B1: Random walks in teaching probability at the high schoolHugo Hernández University of Mexico, MexicoVerônica Yumi Kataoka University of Bandeirante São Paulo, Brazil Marcelo Silva de Oliveira University of Lavras, Brazil Since there’s a need of supporting Probability teaching, it is important to present to teachers different didactical activities, to support their practice. In this context, the “Colegio de Ciencias y Humanidades (CCH)” in Mexico, offered a course for a pedagogical formation and even conceptual support to their recent-hired Stats teachers. In 2009, two professors were selected for being guided by a researcher and responsible of the course, to apply in their regular classes a didactical sequence for Probability teaching, named Mônica’s random walks. This work aims to present and discuss this didactical sequence applied to high school students in CCH. This activity allows the students to work with diverse probability concepts, such as, difference between random and deterministic experiments, theoretical and frequentist probability, and is a recommended activity to help teachers in improving the level of literacy probability of their students. Paper 2B2: Data analysis: linking mathematics, science, and social studiesJerry Moreno John Carroll University, United StatesThe topic of data analysis is usually found in the mathematics school curriculum and seldom elsewhere. Perhaps this is so because the subject is so often viewed narrowly as a body of techniques and formulas, and not as an investigative problem-solving process that begins with asking a meaningful question for which data will be required to help develop an answer. It is completely natural when the subject of data analysis is viewed in this broader problem-solving process sense to look across the school curriculum, especially in science and social studies, to find contexts in which rich, interesting questions may be formulated. This paper suggests some examples that may be used in the school classroom discussions of the integration of mathematics, science, and social studies through data analysis. Paper 2B3: Helping mathematics teachers teach statistics: challenges and potentialsDoreen Connor Nottingham Trent University, United KingdomWhile in many countries Statistics is integrated into the Mathematics Curriculum many mathematics teachers still either view statistics with suspicion or tend to teach statistics in a very mathematical way. Various strategies to overcome these tensions are discussed and activities described and reviewed. Some of the challenges include; how to engage and interest mathematicians in statistics, how to show the differences between techniques and literacy, and how to persuade the teachers that maybe a different pedagogical approach should be taken when teaching statistics as opposed to mathematics. The author firmly believes that many of these challenges can be turned to potentials and that mathematics teachers are the right people to teach statistics in our secondary schools. They just need exposure to suitable activities and time to reflect on the similarities and differences between the subjects considering how to approach the teaching. Paper 2B4: Making sense of statistical studies: a capstone experience for secondary studentsDaren Starnes Lawrenceville School, United StatesRoxy Peck Cal Poly, San Luis Obispo, United States In the last decade, statistics and data analysis have become more visible components of secondary school mathematics in the United States. In most cases, statistics and data analysis topics have been spread through the mathematics curriculum. However, many important statistical concepts are not mathematical in nature and are not easily integrated into existing mathematics courses. As a result, most students complete their secondary education having encountered some graphical and numerical data analysis techniques, but not having engaged in meaningful statistical reasoning. Since the addition of a separate statistics course to the secondary curriculum is unlikely, an alternate approach is proposed. With support from the American Statistical Association/National Council of Teachers of Mathematics Joint Committee on Curriculum in Statistics and Probability, a capstone experience for secondary students has been designed. Making Sense of Statistical Studies is a coordinated set of investigations that can be used in existing mathematics courses to promote students’ conceptual understanding of the data analysis process. Paper Session 2C: Statistical education at the Secondary/Higher Education interface2C1: Approaches to extra-curricular statistics support for non-statistics UG and PG: facilitating the transition to Higher EducationLu Zou University of Sheffield, United KingdomChetna Patel University of Sheffield, United Kingdom Brigitte Garcia de Jager University of Sheffield, United Kingdom To address the growing diversity of ability and skills of the student intake the University of Sheffield has set up the Maths and Statistics Help Centre to provide extra-curricular support to help students make the transition to Higher Education. The provision of maths support has been around since the early 90’s and has developed into a sophisticated and valued means of addressing mathematical diversity. In contrast statistics support is new in its development and is being seen as a subject in its own right rather than as part of mathematics. This paper will provide the university’s attempt at enhancing statistics support. First it will review current provision of statistics support and consider feedback received, secondly it will draw up a plan for developing the support to better fit the need. Another element of this study is to examine how the effectiveness of statistics provision can be measured. Paper 2C2: SPoC – Statistics Poster Challenge for schoolsBrad Payne Conker Statistics, United KingdomEleanor Stillman University of Sheffield, United Kingdom The analysis and interpretation of data are important skills in everyday life. They help us understand and explain what is happening. From the age of 5 upwards children are expected to learn various graphical and descriptive measures to summarize data. A poster challenge provides an innovative outlet for these skills as well as demonstrating their relevance in general life. The Statistics Poster Challenge (SPoC) is based on the successful Statistics poster competition run in Michigan since 2000 and presented at ICOTS7. We discuss SPoC and the lessons learned by the SPoC team. Paper 2C3: Creating a World population model to analyze the dynamics of changeHenry Kranendonk Milwaukee Public Schools, United StatesThe transition from a secondary study of data analysis and statistics to a college level involves more than simply expanding a list of topics. Students’ reasoning is expected to more clearly address the questions “What if ...?” and “What is the story behind the data?” as they mature. The unit presented, “The World Population Project”, was designed for high school students as a way to explore how students answer those questions when given control of data. Students were provided authentic population data sets of the 10 largest countries. After a study of each country, students are provided opportunities to alter the dynamics of a country’s population given various scenarios. By having direct control over the data, they are provided opportunities through a model on a computer to directly answer authentic “What if ...?” questions. Their explanations to these questions provide opportunities to give students’ feedback in their transition to higher education. Paper Session 2D: Using technology at school level to enhance statistical understanding2D1: Statistical software for teaching: relevant, appropriate and affordableStewart Andrews VSN International, United KingdomStudents need to have a good grounding in statistics given how important it is in many disciplines—scientific or otherwise. But it isn’t just the statistics that is important, it’s statistical software. Computer hardware and software developments together with the accessibility of data have accelerated the need for students to understand how their learning is used in the real world. It isn’t just a formula, it’s used by many through the world in their everyday life. In order to equip our young people with life skills we should be teaching them, not just the basics of statistics, but teaching them with tools they will encounter later in life. By using a software system that is and always has been designed by everyday users of statistical analysis, we can show students the relevance of their learning. GenStat for Teaching is a menu driven, world class statistics system used by statisticians, scientists and researchers across the world Paper 2D2: Enhancing students’ inferential reasoning: from hands on to “movie snapshots”Pip Arnold Cognition Education Limited, New ZealandMaxine Pfannkuch University of Auckland, New Zealand Computer simulations and animations for developing statistical conceptions are often not understood by beginners. Hands-on physical simulations that morph into computer simulation images are teaching approaches that can build students’ concepts. In this paper we describe an instructional sequence, from hands on to “movie snapshots”, which was trialed in a Grade 9 class. The instruction focused on developing students’ sampling variability concepts and on making inferences about populations from samples. Responses from three students’ interviews and two assessment items are explored, including the images they worked with when they reasoned and made a call from box plots. The findings suggest that students can use sampling variability ideas to support their inferential reasoning. Paper 2D3: Fathom that!: an ethnography of the use of interactive data analysis software in a statistics class of a high school serving low-income studentsVishakha Parvate Key Curriculum Press, United StatesThis paper explores a high school classroom integration of Fathom software in the teaching of statistics. A majority of the students at this high school, serving a lower income community, are aspiring to be first generation high school graduates and learning in English as a second language. This paper will attempt to capture the “spots of time that glow”—episodes that stand out as being particularly enlightening. The guiding questions for the exploration in this paper focus on student reports of the highlights of their interaction with the software and curriculum, the teacher’s strategies to integrate technology and how she adapts them as the year progresses, the nature of some of the challenges faced by the teacher, and the role that the software ends up playing in the classroom and the reasons for this role. Paper 2D4: Using data to make sense of statistics: the role of technology in scaffolding understandingGail Burrill Michigan State University, United StatesResearch and classroom experience identify topics with which students in introductory statistics struggle such as interpreting box plots, standard deviation or z-scores and the normal curve. One reason is that many core statistical concepts are subtle and difficult to sort out. Dynamic interactive technology can provide opportunities for learners to begin to make sense of these concepts by enabling them to generate large amounts of data, explore distributions, examine probability models and investigate the nuances that often seem to obscure reasoning and sense making in statistics. Interactive technology allows learners, using real and motivating data that stem from questions about ways of reasoning in statistics, to move between representations, looking for patterns and generating models related to hypotheses and to informed decision making. Paper Session 2E: Improving the teaching of statistics at school level2E1: Overcoming obstacles to supporting secondary teachers’ statistical content knowledge for teachingSandra Madden University of Massachusetts, Amherst, United StatesSupporting teachers’ statistical content knowledge for teaching poses a number of challenges. Many grades 6-12 mathematics teachers’ prior experiences with statistics insufficiently prepared them to support students grappling with big ideas of statistics. Teachers’ view of statistics tends to be procedural and cookbook-oriented. Many mathematics teachers feel that statistics has little place in their instruction, thus professional development is unnecessary. Finally, many teachers have not experienced learning statistics in an environment in which student-centered discourse, learner-centered technology, and worthwhile statistical tasks has been the norm. Research from two professional development projects in which significant changes in teachers’ understanding of statistical big ideas occurred is presented. Potential solutions to obstacles, tasks with potential for engaging and challenging teachers, and lessons learned are discussed. Paper 2E2: Teachers’ understanding of students’ conceptions about chance: an expert-novice contrastLucia Zapata-Cardona University of Antioquia, ColombiaThis exploratory study investigated teachers’ perception of students’ thinking about chance. In particular, the study explored how teachers anticipated and explained students’ difficulties with the idea of chance, and the strategies teachers claimed to use to help students reorganize their thinking. Two teachers, one expert and one novice, members of an AP Statistics learning community, participated in this study. They were observed in the learning community meetings, and interviewed in depth. The interviews explored four core ideas in statistics that have been associated with the source of students’ difficulties about chance: sample space, randomness, independence, and the law of large numbers. The results of this study highlighted that the expert and novice teachers exhibited differences in the way they perceived students’ difficulties and in the way they dealt with them. Paper 2E3: Using classroom video to identify development of teacher knowledgeTim Burgess Massey University, New ZealandTeacher knowledge for teaching statistics through investigations at the primary school level can be analyzed using a framework based on a combination of statistical thinking components and teacher knowledge. This paper focuses on the question of whether growth of teacher knowledge occurs through teaching, and if so, what types of teacher knowledge. In this research, classroom video and stimulated recall interviews with the teachers provided the main data, both of which were analyzed using the framework for teacher knowledge for teaching statistics. Growth in some categories of teacher knowledge was identified, but not for other categories. Implications for teacher education are discussed. Paper 2E4: Professional development through collaborative analysis of student workAndee Rubin TERC, United StatesThe original goal of this work was to create software support for teachers to use in analyzing the work their students had done using the educational data analysis software TinkerPlots. In pursuit of this goal, we designed three presentations of students’ work to be automatically generated for teachers. To evaluate these three presentation styles, we carried out a user test with a group of teachers. The conversation that ensued turned out to be an excellent example of professional development; we will continue to pursue this possibility in our future work. Paper Session 2F: Making connections between educational research and teaching statistics at the school level2F1: Teacher knowledge and confidence in grade 8 and 9 data handling and probabilityHelena Wessels University of Stellenbosch, South AfricaHercules Nieuwoudt North West University, South Africa This research reports on the profiling of teachers with regard to statistical knowledge, beliefs and confidence to inform the development of a professional development course for Grade 8 and 9 teachers. Poor TIMMS results and continuing disappointing mathematics results over the whole spectrum in South Africa necessitate more efficient professional development of in-service teachers. Watson’s profiling instrument (2001) was adapted and used to profile 90 mathematics teachers in Pretoria, South Africa. Although quite a number of these teachers attended professional development workshops and courses in statistics, they still teach traditionally, as opposed to a data driven approach using authentic data. Almost all teachers indicated high levels of confidence in teaching statistics but show low levels of statistical thinking when applying their knowledge in context. Paper 2F2: Helping teachers to make effective use of real-world examples in statisticsHelen Chick University of Melbourne, AustraliaRobyn Pierce University of Melbourne, Australia Real-world data can be used in the classroom to stimulate the learning of important statistical principles. A recent study with pre-service primary/elementary teachers highlighted that even when teachers were supplied with a suitable statistically rich example, some did not identify its affordances, and struggled to bring out the significant ideas in their planned lesson. This paper examines some of the issues associated with example use, and investigates whether a simple intervention might help teachers make more effective use of such examples. The results suggest that a simple framework of focus and planning questions may help teachers to identify significant statistical ideas for teaching and bring them out in their lessons. This is not to say that addressing content and pedagogical content knowledge issues more explicitly with teachers will not also be helpful, especially since some shortcomings in both areas were still evident in the lesson plans. Paper 2F3: Exploring relations of Vitruvian Man to develop students’ reasoning about variationCláudia Borim da Silva University of São Judas Tadeu, BrazilIrene Cazorla State University of Santa Cruz, Brazil Verônica Yumi Kataoka University of Bandeirante São Paulo, Brazil Sandra Magina Catholic University of São Paulo, Brazil This paper aims to explore reasoning about variation with twenty-five seventh and eighth graders. Anthropometric measures were collected and tasks developed, supported by dotplots. Coding schemes were used to classify students’ answers. Higher reasoning about variation levels in the posttest were observed in questions that asked for analyzing a situation by dotplot and by interpretation of mean, both concepts discussed during activities. Before the teaching session, students were asked to describe the size of shoes and the height of the person. We observed that they realized variation before expectation. Some students said that distributions were spread or grouped, used minimum and maximum values and chose to compare groups of male and female in an intuitive way. After the teaching session, students were more engaged in statistics tasks to analyze other variables, showing the importance of teaching statistics in school Paper 2F4: Researchers cultivating a long-term relationship with schoolsAnthony Bill University of Tasmania, AustraliaCultivating an effective working relationship with schools is of great practical importance to education researchers, but little research literature on this topic exists. This study is an extension of classroom based collaborative research between a university faculty of education and schools into the use of Fathom™ software. A preliminary review concluded the research may have been enhanced if a robust working relationship had existed prior to the original study. Interviews were then conducted with the two principals of the participating schools, with supporting information provided by teachers and a university education lecturer. The interviews identified seven themes, and, influenced by Lave and Wenger’s (1991) community of practice, a seven-element model for cooperation with schools is proposed. This model reconceptualises education research as only one element of a multi-faceted relationship with schools, rather than the principal objective. Paper |