Conference Paper

  • The knowledge and application of the problem context and its relation to data analysis is a key component in the development of students' informal inferential reasoning. This case study analyzes children's emergent understanding of the relationship between the context world and the data world while making informal statistical inferences in an inquiry-based learning environment using TinkerPlots. We focus on two fifth grade students (aged 11) who participated in the 2010 Connections design experiment in Israel. We observe and analyze their first steps in the two worlds – data and context – in growing samples investigations. They developed gradually and inconsistently an understanding of making informal inferences considering both context and data. They moved from an initial conception of context and data as separate entities to two interconnected and relevant dimensions. We finally discuss this development and what might have supported it. 

  • This longitudinal study follows the development of students’ reasoning about sample and sampling from 6th to 9th grade (age 12 to 15). The students took part in the Connections project (Ben-Zvi, Gil & Apel, 2007), an inquiry-based learning environment using TinkerPlots (Konold & Miller, 2005) in grades 4–6. One of the main goals was to develop their reasoning about sample and sampling in the context of making informal statistical inferences. After three years in which these students hardly had any formal statistics teaching at all, a series of inquiry-based activities were designed and administered in the 9th grade to evaluate aspects of continuity and change in their reasoning about sample and sampling. The SRTL-7 paper will present preliminary results which are part of the first author's Ph.D. study. 

  • Research on informal statistical inference has so far attended little to developing students' reasoning about samples and sampling. This SRTL-7 pre-paper will prepare the ground for analyzing children’s reasoning about sampling when making informal statistical inferences in a collaborative, project- and inquirybased learning environment. Using data from a design experiment in Israeli Grade 5 (age 11) classrooms, we focus on the emergent reasoning of two boys working with TinkerPlots on investigations with growing sample size. 

  • 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. 

  • The role of context is discussed in the setting of an extended curriculum development and research project in primary school designed to develop and study students' reasoning about statistical inference. Qualitative research methods are used to critically dissect the roles of context in the emergence of sixth grade students' informal inferential reasoning (IIR). Context is examined as part of a complex network of themes, such as inquiry, norms, knowledge of statistical concepts and tools, beliefs and expectations, and meaning making and explanations. The paper analyzes and discusses these themes and the role context plays in the emerging inferential reasoning of these students.