36 HOW CONFIDENT ARE YOU?

problem solving when they work together in groups with mathematics software (e.g., Monaghan, 2005; Wegerif & Dawes, 2004).

Another type of talk, called dialogic talk, extends the definition of exploratory talk by referring to collaborative and creative engagements with more emphasis on the dialogic quality of the relationships between students (as well as those between students and the shared task) than on the explicit verbal reasoning (Wegerif, 2013). Wegerif argues that dialogic talk entails openness to the other and to otherness in general to the extent that participating individuals are able to listen to each other and to change their minds. From a dialogic perspective inspired by the work of Bakhtin (1981, 1986), dialogic processes refer to the creative leaps required to understand things from the outside position of the witness or the “superaddressee” position in Bakhtin’s terms (Wegerif, 2013). According to Wegerif, this creativity is sometimes an emergent effect of the dialogic space that opens up in the gap between different perspectives, including virtual perspective such as that of the superaddressee.

In Kazak, Wegerif, and Fujita (2013), it is argued that the combination of tech- nology and students’ dialogic talk can play a critical role in helping students make noticeable shifts forward in their conceptual understanding of probability. The article describes a trajectory of two 11–12-year old students making conjectures about the fairness of a game, involving combined events (an earlier version of the Chips Game Task in the current chapter), testing and revising their initial theories based on simu- lation data using TinkerPlots™. It was found that the dialogic talk helped these two students in several ways. For example, they could articulate their thinking including half-baked or uncertain ideas. The dialogic approach used in the study encouraged students to ask for explanations because they began to feel that making mistakes and showing that they do not understand were acceptable. In this way they could help each other to understand. Moreover, the mechanism behind the initial switch in per- spective in one of the students was interpreted as dialogic in the sense that there was an invisible dialogue going on between the student and an absent ‘witness’. While taking an outside perspective in reconsidering the problem, he was able to question his initial view and change his mind.

2.4 Subjects and Methods

This exploratory study was carried out with six high achieving Year 6 (age 10–11) students, two boys and four girls (pseudonyms: Ozzy, Jake, Keyna, Flora, Gabby, and Blair), from a local primary school in Exeter, UK. The sample was selected as a convenience sample recruited through their classroom teacher.

2.4.1 Data Collection

The method of research employed was a design study. A design study entails an iter- ative process to develop theories of students’ learning and ways of supporting their learning of domain specific content (Cobb, Confrey, Lehrer, & Schauble, 2003). The initial design is improved through testing and revising conjectures based on continual

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analysis of students’ reasoning and the learning environment while the experiment is in progress. In this study, the research cycle involved designing instructional ma- terials and a learning environment that supported the desired learning goals in the domain of statistics, conducting teaching sessions, and retrospective analysis. The retrospective analysis of the first cycle was the basis for the new design phase in the second cycle.

During the study, students were seated to work in pairs or groups of three at tables with a laptop and manipulative materials, such as game chips and bags. Each group’s work was videotaped to capture the students’ interactions around the computer. Ad- ditionally, the computer screen of the group including Blair, Gabby, and Flora was recorded using Camtasia software (TechSmith, 2011) to capture their work in Tin- kerPlots™ environment during the Chips Game Task (see Section 4.2). Each group also answered questions on the given worksheets for each task. Pre-assessment items were used to evaluate students’ reasoning about combined events prior to the proba- bility tasks. The data for analysis included video footage of group work and lessons, computer screen captures, and student artifacts.

2.4.2 Procedures and Tasks

In this study, TinkerPlots™ (Konold & Miller, 2011) was used as the information and communication technology (ICT) tool. TinkerPlots™ is a distinct computer pro- gram compared to other graphing or spreadsheet programs as it builds on children’s intuitive knowledge about data representations and analysis. It enables students to construct their own graphs when organizing their data by ordering, stacking, and separating. TinkerPlots™ also includes a variety of tools, such as dividers and ref- erence lines, to intuitively analyze data in making inferences. A probability simu- lation/modeling tool (i.e., the Sampler) allows students to build models of random phenomena using variety of devices (i.e., mixer, spinner, bars, stacks, curve, and counter) that can be filled with different elements from which to sample (see Fig- ure2.1). This tool then enables students to collect measures and outcomes from the sampled elements. Another affordance of the tool is that it allows students to quickly generate a large number of outcomes with each run and to repeat this several times to look at the results from sample to sample.

In addition to the use of TinkerPlots™ to explore data and chance, the participants were introduced to a dialogic way of communicating during group work. Since not all types of student talk that occurred in groups would necessarily result in effective collaboration in joint activities (see Mercer, 1996), certain ground rules were explic- itly discussed and practiced with the students in order to set up the conditions for effective talk (Dawes et al., 2000). As an example, here is a set of negotiated expec- tations for group work in this study: (1) we should make sure that each person has an opportunity to contribute ideas, (2) we should ask each other ‘why?’ and listen to the explanation and try to understand, (3) we should ask others what they think, (4) we should consider alternative ideas or methods, and (5) we should try to reach an agreement before we do anything on the computer.