STATSTALK · Studying the Development of Young Students’ Conceptual Understanding in Statistics through Mediation by Technological Tools and Talk

Studying the Development of Young Students’ Conceptual Understanding in Statistics through Mediation by Technological Tools and Talk

The knowledge of probability and statistics is of critical importance for ordinary citizens to make judgments and to take decisions. Statistics is a key subject for engaging young people in science issues and for enabling them to become scientifically literate citizens and consumers of data-based information. The STATSTALK project developed and evaluated a holistic approach to teaching statistical concepts combining a collaborative, ‘dialogic’, pedagogical approach with computer software that made it possible to learn intuitively using dynamic visual representations to see the patterns that form when working with large data-sets. In the STATSTALK project, we investigated the relationship between young students’ talk together, their use of ICT tools and their development of conceptual understanding of key ideas in statistics and probability in the context of making inferences based on data. To this end, we developed conjectures about how to support students’ learning of probability and statistics topics, and designed a sequence of tasks to promote students’ statistical and probabilistic understandings mediated through their use of TinkerPlots2.0 software and dialogic talk during joint activities. These tasks involved asking students to use the software for analysing data and modelling probability problems to make informal inferences based on data. From a dialogic perspective, our pedagogical approach encouraged students to engage openly with each other, to ask for explanations, to challenge and critique each other’s ideas in a constructive way, to actively listen to each other with understanding, and to acknowledge a change of mind by appropriating the perspective of the other. The first iteration of our design-based research study was conducted in two different settings to test the initial conjectures and sequence of tasks: an afterschool programme with five 11–12–year–old students (2 girls, 3 boys) and a mathematics enrichment class with six 10–11–year–old students (2 boys, 4 girls). The retrospective analysis of the first cycle became a basis for the next design phase. The second iteration of the study was conducted with eleven 10–11–year–old students (5 boys, 6 girls) as part of a mathematics enrichment class. The analysis of data included video footage of group work and lessons, computer screen captures, and student artefacts/worksheets allowed us to retest and revise our conjectures about students’ understanding of chance and data topics and ways of supporting their reasoning. We used the findings of the evaluation of the first iteration to re-design the lessons for the second iteration. These lessons focused on scaffolding for dialogue through off-computer pedagogic activities and scaffolding for content knowledge using TinkerPlots software. The findings from the STATSTALK project were considered both specific to the content area being researched and beyond that including contributions to the development of theory. At a specific level, data on performance on pre- and post-tests showed some growth particularly in students’ probabilistic reasoning and understanding of the concept of average when making inferences based on data. At a general level, our research has yielded findings relevant to both educational theory and practice. From a theoretical standpoint, the results suggested that a dialogic perspective was needed to understand the moments of mathematical insight leading to a conceptual development in students’ learning of probability and statistics. The data from the teaching experiments showed examples where a dialogic switch led students to see the problem as if from a new perspective when they made a shift in their understandings. Hence we were convinced that the Bakhtinian dialogic approach can augment the existing theories of conceptual development based on both Piagetian and Vygotskian perspectives by focusing on voices in dialogue and revealing the role of relationships between voices in enabling the shifts in students’ insights and growth of understanding. From a practical perspective, micro-genetic analyses of students’ development of understanding in various episodes during the teaching experiments revealed that the moments of probabilistic/statistical insight leading to a new understanding were facilitated by two kinds of support: a tool-based scaffolding for the content (by using TinkerPlots software) and a dialogue scaffolding (adopted ‘Thinking Together Programme’ for dialogic talk). These analyses convince us that a breakthrough in understanding is not simply in the scaffolding for content knowledge by the technology. Rather, new understanding is mediated through the combination of content scaffolding provided by TinkerPlots and the dialogic talk prompted and framed by the scaffolding for dialogue as part of our pedagogical approach. The potential impact of the project results is relevant to teachers, curriculum developers, educational scientists and policy makers. At the practice level, the findings show the importance of the combined use of technology and dialogic pedagogical approach in supporting the shift in students’ reasoning and understanding in probability and statistics. The curricular documents usually provide ‘loose’ advise on the use of ICT tools. So this research contributes to a better understanding about how to integrate the ICT tools in combination with promoting student talk in joint problem solving activities from a dialogic perspective and helps teachers to make informed decisions in their teaching in mathematics classrooms. At the research level, the results demonstrate the value of using a dialogic approach in addition to the other existing theories to explain the switches in perspectives when students have a new mathematical insight. From a broader perspective, these results also offer the potential for impact on educational policy beyond the existing goals in school curricula by focusing attention to transforming educational practice towards engagement in knowledge building and dialogues for collaborative decision-making using digital technologies. The STATSTALK project website provides relevant dissemination documents: http://socialsciences.exeter.ac.uk/education/research/projects/projectlinks/statstalk/ Contact Details Professor Rupert Wegerif University of Exeter, UK r.b.wegerif@exeter.ac.uk Dr Sibel Kazak Pamukkale University, Turkey skazak@pau.edu.tr

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