Curricula across the world are increasingly calling for critical thinking to be embedded within the wider curriculum. This is well exemplified within the discipline of mathematics.  The Australian Curriculum: Mathematics (ACARA, 2017) states that students should "develop critical and creative thinking as they learn to generate and evaluate knowledge, ideas and possibilities, and use them when seeking solutions. "

This study aims to examine the possibility of using an online  computer supported collaborative learning environment (CSCL) with upper primary school students to examine student critical thinking in mathematical problem solving. Specifically the question addressed is:

Is there evidence of critical thinking when students engage in ‘talk’ within online mathematical problem solving ?

There is strongly held opinion that much technology integration in primary level mathematics, at best emphasizes Fluency rather than Understanding, reasoning and problem solving. At worst, it is simply an exercise in keeping students busy with little emphasis on mathematical concept development.

The aim of the teaching and learning intervention developed for this study was to focus on an approach to technology integration for primary mathematics where problem solving, reasoning and critical thinking were outcomes. Consequently, an approach to assessing the types of Higher Order Thinking (specifically critical thinking in this case) that was occurring and developing was sought. A range of research was considered, for example that of Facione (2013) and Fleming (2008) for the purpose of informing the approach taken to coding and analysis of data in order to answer the research question. However, this research did not provide clearly articulated approaches to assessing the different components of critical thinking occurring within individual student online discussion. Perkins and Murphy (2006) provided a clear and practical tool to achieve this goal and therefore was used as a basis for analysis of student critical thinking.

A cyclical approach is taken to investigating student critical thinking in this study. The lens through which critical thinking is initially examined occurs at a macro level. After providing evidence that critical thinking is now a fundamental aspect of the Australian Curriculum, the Clarification, Assessment, Inference, Strategies (CAIS) framework (Perkins & Murphy, 2006) provides a macro level understanding of how a group of students engaged in different aspects of critical thinking. The framework allows inferences to be made about how various members of the group position themselves, according to which of the categories of critical thinking they display more or less of. The analysis of student online discussion then allows a micro level understanding of the types of talk that were more likely to be productive. Whether a higher density of technical mathematical vocabulary would be observed where productive talk was observed was also an area for investigation. A final aim is to align the identification of Exploratory Talk (Mercer and Wegerif, 1999) and a higher density of mathematical vocabulary use back to the prevalence of the Australian Curriculum prescribed general capability of Critical and Creative thinking (ACARA, 2017).

Exploratory Talk as discussed by Mercer and Wegerif (1999) appears to be closely linked to critical thinking. The facets of critical thinking, as indicated by both the CAIS framework (Perkins & Murphy, 2006) and the indicators of Critical and Creative Thinking as provided by the Australian Curriculum (ACARA, 2017) are represented when students engage in discussions involving critiquing, justifying, clarifying, analysing that Exploratory Talk describes. In this study we establish that Exploratory Talk is likely to exhibit a greater density of technical mathematical language use. We make the claim that it is likely that when students utilise a greater density of this type of vocabulary that they are also more likely to engage in critical thinking. This is supported by the greater prevalence of the CAIS categories identified in Exploratory Talk. As Exploratory Talk was found to be a more productive talk type, when compared with Disputational or Cumulative Talk (Mercer and Wegerif, 1999), online mathematical problem solving can provide a practicing teacher with an objective measure of the quality and nature of mathematical meaning making dialogue. All four of Perkins and Murphy’s (2006) CAIS categories were in greater evidence where Exploratory Talk was identified. Where a higher density of technical mathematical vocabulary, which was common in students Exploratory Talk, is present it is more likely that critical thinking will also be present.

ACARA. (2017). The Australian Curriculum: General Capabilities: Critical and Creative Thinking. Retrieved 30/5/2017, from ACARA http://www.australiancurriculum.edu.au/generalcapabilities/critical-and-creative-thinking/introduction/in-the-learning-areas Facione, P. A. (2013). Critical thinking: What it is and why it counts Retrieved from http://www.insightassessment.com/ Fleming, D. L. (2008). Using best practices in online discussion and assessment to enhance collaborative learning. College Teaching Methods & Styles Journal, 4(10), 21-40. Mercer, N., & Wegerif, R. (1999). Is exploratory talk productive talk? In K. Littleton & P. Light (Eds.), Learning with computers: Analysing productive interaction (pp. 79-101). London: Routledge. Perkins, C., & Murphy, E. (2006). Identifying and measuring individual engagement in critical thinking in online discussions: An exploratory case study. Journal of Educational Technology & Society, 9(1).