- Prof Dev
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.
Recent investigations of technology-supported learning conducted from an instrumental perspective provide a powerful framework for analyzing the process through which artifacts become conceptual tools and for characterizing the ways students come to understand and implement a tool in solving a task. In this chapter, we focus on instrumentation – the process of transforming an artifact (component/s in the tool) into an instrument that is meaningful and useful to the learners – in the context of statistics education. Our goal is to characterize children’s instrumentation in solving Exploratory Data Analysis (EDA) tasks. To illustrate this process, we bring short episodes from a case study of two fifth graders studying EDA with TinkerPlots in the 2012 Connections project. We suggest three types of instrumentation: unsystematic, systematic, and expanding. We also note that expanding instrumentation is hindered sometimes by instrumented fixation. We conclude by presenting several challenges stemming from the implementation of instrumental theory in the context of learning statistics.
In this chapter learning experiences that teachers need in order to develop their ability to think and reason statistically are described. It is argued that teacher courses should be designed around five major themes: developing understanding of key statistical concepts; developing the ability to explore and learn from data; developing statistical argumentation; using formative assessment; and learning to understand students’ reasoning.
Statistics is a discipline in its own right rather than a branch of mathematics, and the knowledge needed to solve statistical problems is likely to differ from the knowledge needed to solve mathematical problems. Therefore, a framework that characterizes creative performance in learning to reason about informal statistical inference is essential. In this paper we present an initial framework to assess creative praxis of primary school students involved in learning informal statistical inference in statistical inquiry settings. In building the suggested framework, we adapt the three common characteristics of creativity in the mathematics education literature, namely, fluency, flexibility, and novelty, to the specifics of learning statistics. We use this framework to capture creative praxis of three sixth grade students in a 60-min statistical inquiry episode. The episode analysis illustrates the strengths and limitations of the suggested framework. We finally consider briefly research and practical issues in assessing and fostering creativity in statistics learning.