ICOTS-7, 2006: Ben-Zvi 1 SCAFFOLDING STUDENTS’ INFORMAL INFERENCE AND ARGUMENTATION Dani Ben-Zvi University of Haifa, Israel dbenzvi@univ.haifa.ac.il This paper focuses on developing students’ informal ideas of inference and argumentative skills. This topic is of current interest to many researchers and teachers of statistics. We study fifth graders’ learning processes in an exploratory interdisciplinary learning environment that uses TinkerPlots to scaffold and extend students’ statistical reasoning. The careful design of the learning trajectory based on growing samples heuristics coupled with the unique features of TinkerPlots were found instrumental in supporting students’ multiplicative reasoning, aggregate reasoning, acknowledging the value of large samples, and accounting for variability. These processes were accompanied by greater ability to verbalize, explain and argue about data-based inferences. In the light of the analysis, a description of what it may mean to begin reasoning and arguing about inference by young students is proposed. INTRODUCTION In the context of an interdisciplinary exploratory learning environment that uses the software TinkerPlots (Konold and Miller, 2005), we focus on developing students’ informal ideas of inference. As new statistics courses and curricula are developed at all levels, a greater role for informal types of statistical inference rather than on formal methods of estimation and tests of significance is anticipated, introduced early, revisited often, and developed through use of simulation and technological tools. We also focus on argumentative activity that was found beneficial for knowledge building and evaluation of information in some conditions (Schwarz, Neuman, Gil and Ilya, 2003). In the following paragraphs, we briefly describe the theoretical underpinnings of the study, the design of the curriculum, and the type of results and implications that will be presented in ICOTS. THEORETICAL BACKGROUND: INFERENCE AND ARGUMENTATION Statistical inference is “the theory, methods, and practice of forming judgments about the parameters of a population, usually on the basis of random sampling” (Collins English Dictionary, 2000). There are two important themes in statistical inference: hypothesis testing and parameter estimation and two kinds of inference questions: generalizations (surveys) and comparison and cause (experiments). In general terms, the first is concerned with generalizing from a small sample to a larger population, while the second has to do with determining if a pattern in the data is due to cause and effect. Most of what is usually done in statistics in primary level is part of the exploratory data analysis approach to data (EDA, Tukey, 1977). The emphasis is mostly on ways to uncover, display, and describe interesting patterns in data. Inferences are informal, based on what we see in the data, and apply only to the individuals and circumstances for which we have data in hand. The problem is that the deficient inferential reasoning may result in shaky conclusions and give students a wrong deterministic sense of statistics. Rudimentary statistical methods taught at primary level, such as tabulating and graphing data, can help students look for interesting patterns in simple data sets, but are not enough to take them beyond the data in hand. Our project concentrates on helping young students “to draw conclusions about a wider universe, taking into account that variation is everywhere and the conclusions are uncertain” (Moore, 2000, p. xxx). Since formal inference ideas and techniques are beyond the reach of young students, an informal approach to teaching and learning is necessary. Rubin, Hammerman and Konold (2006) view “informal inference” as statistical reasoning that involves consideration of multiple dimensions: Properties of aggregates rather than properties of the individual cases themselves, signals and noise, various forms of variability, sample size, controlling for bias, and tendency (claims that are always true and those that are often or sometimes true). Research in statistics education has however demonstrated that students at all levels have many difficulties in reasoning about these dimensions (cf., Ben-Zvi and Garfield, 2004; Bakker et al., 2004).