Reasoning about uncertainty is a key and challenging element in informal statistical inferential reasoning. We designed and implemented an “Integrated Pedagogic Approach” to help students understand the relationship between sample and population in making informal statistical inferences. In this case study we analyze two sixth grade students’ reasoning about uncertainty during their first encounters with making informal statistical inferences based on random samples taken from a hidden TinkerPlots2 Sampler. We identified four main stages in the students’ reasoning about uncertainty: Account for, examine, control, and quantify uncertainty. In addition, two types of uncertainties – contextual and a statistical –shaped the students’ reasoning about uncertainty and played a major role in their transitions from stage to stage. Implications for research and practice are also discussed.
Long-term effects of learning are a desirable outcome of any educational program and are far from being an obvious result in education. Furthermore, statistical concepts tend to be ambiguous and “short lasting” in students’ reasoning, even among tertiary students. In this longitudinal study, long-term impact of teaching and learning was sought among ninth graders, three years after their participation in a three-year intervention (grades 4-6) of the Connections Program. In a mixed methods study, students from two groups – those who have / have not taken part in the program – were closely followed and compared throughout three extended data inquiry activities and took a statistical knowledge and thinking proficiency test. Results and implications are presented.
Roles that students take in solving problems can help in guiding and scaffolding their learning and meaning making. We present a case study – part of a UK-Israel research project – that focuses on the emerging roles spontaneously developed by Israeli eighth-grade students (14 years old) in solving a scientific-statistical inquiry task using TinkerPlots2. The task integrated four design approaches: Exploratory Data Analysis, Active Graphing, modeling, and gaming. We examine how this task design played a role in this emergence of students’ roles and how they respectively adopted perspectives on uncertainty and modeling. Implications of the findings are discussed.
We present initial data from a collaboration between researchers in the UK and in Israel. We aimed to explore how young students (11-14 years of age) expressed uncertainty in partiallydetermined situations, where a signal might account for some, or even a substantial amount of, variation but additionally there is a need to account for noise in the system. The two teams collaborated to develop a task that drew on previous experience with Active Graphing and EDA. As well as collecting data through an experiment, the young students used the modelling functionality in TinkerPlots2 to create models (or ‘machines’) that generated similar data to that in the experiment. In the presentation, we describe the various ways in which the young students accounted for and expressed uncertainty verbally and through actions in TinkerPlots2.
We analyze students’ articulations of uncertainty during their first steps in exploring sampling distributions in a TinkerPlots2 inquiry-based learning environment. A new pedagogical “integrated approach” was implemented to help students understand the relationship between sample and population. We focus in this case study on two students (age 13, grade 7) who had previously participated in the Connections Project EDA activities. We describe the students’ articulations of uncertainty when they explore a sampling distribution of proportions, negotiate the interval of proportions they agree to accept as “correct results,” and express their confidence level in getting this interval.
This paper presents a case study of an exemplary blended graduate classroom learning community that showed students taking responsibility over their own collaborative learning. Specifically, the group went through a stage of productive subjective failure before intentionally deciding to explicate and negotiate their own group norms. This transition saw a marked increase in collaboration among group members. Using a micro-genetic interpretive approach, we analyzed the stages of group development that led to this outcome. Our findings indicate that the process of explicating and negotiating norms (PENN) was the climactic event whereby the group transformed their responsibility and collaborative learning behavior. We discuss the implications of our findings, which we believe inform both theory and design of productive failure in CSCL.