During asynchronous, online mathematics discussions, new ideas and justifications (knowledge content) and evaluations and invitations to participate (social metacognition) can influence the likelihood of a correct, new idea (CNI) in the current message. Using statistical discourse analysis, we modeled 894 messages by 183 participants on 60 high school mathematics topics on a mathematics problem solving website not connected to any class or school. Results showed that CNIs, justifications, and social metacognition (correct evaluations and questions) in recent messages increased the likelihood of a CNI in the current message. Meanwhile, more experienced participants (who had posted more messages on the website) had more CNIs, and participants who initiated topics had fewer CNIs. Applied to practice, these results suggest that teachers can facilitate students’ creation of CNIs by encouraging them to justify their ideas, evaluate one another’s ideas carefully, and ask questions during online mathematics discussions.
Students are increasingly using asynchronous, online discussions to aid their learning (Tallent-Runnels et al., 2006), in part because these discussions allow participation at different places and times (asynchronous) – unlike traditional face-to-face discussions (Dubrovsky et al., 1991 and Harasim, 1993). As asynchronous, online discussions allow participants more time to gather relevant information, contemplate ideas, and evaluate claims critically before responding, they often display high levels of cognition (Hara et al., 2000 and Tallent-Runnels et al., 2006).
In this study, we examine how group processes affect the creation of correct, new ideas (CNIs) during asynchronous, online discussions of high school mathematics problems by small groups of individuals. We define a CNI as an expressed idea that is both correct (consistent with the problem situation and the mathematics) and new relative to the participants’ discussion of a topic. Past theoretical models have highlighted the importance of CNIs to group problem solving and suggested that groups with more CNIs are more likely to solve a problem correctly (e.g., Chiu, 2008a, Hinsz et al., 1997 and Orlitzky and Hirokawa, 2001). Hence, understanding the online group processes that affect CNI creation can help educators improve students’ online group mathematics problem solving.
In addition to finding correct answers, a productive mathematics discussion supports and reinforces desirable mathematics thinking processes such as expressing new ideas, supporting them with proofs, evaluating one another’s mathematics claims, and inviting others to evaluate their mathematics relationships (Chiu, 2000a and Chiu, 2008a). Through these processes, participants facilitate one another’s creation of mathematics relationships that facilitate mathematics solutions. For example, Chiu’s (2008a) study of face-to-face mathematics discussions showed that correct evaluations of mathematics ideas in the three most recent conversation turns raised the likelihood of a CNI in the current conversation turn. A natural extension of this research is how group processes might affect the likelihood of a CNI during online mathematics discussions.
However, past studies of online discussions typically focused on the isolated properties of each online discussion message (Gress, Fior, Hadwin, & Winne, 2010; Hara et al., 2000 and Tallent-Runnels et al., 2006) without systematically examining the relationships among online discussion messages to characterize the group processes that affect the likelihood of CNIs. By understanding how messages in online discussions create a context that influences a student’s CNI creation, educators can help students engage in beneficial group processes to aid correct outcomes.
In this study, we take a step in this direction by examining how new mathematics ideas and justifications (knowledge content) and evaluations and invitations to participate (social metacognition) in recent messages facilitate or hinder CNI creation during online discussions about mathematics problems. The useful knowledge content of a message includes its new ideas and justifications. Discussants monitor the correctness of the knowledge content in previous messages and use this information to influence the local discussion context and the knowledge content of subsequent messages through social metacognition (Chiu & Kuo, 2009). Whereas individual metacognition is monitoring and control of one’s own knowledge, emotions, and actions (Hacker & Bol, 2004), social metacognition is defined as group members’ monitoring and control of one another’s knowledge, emotions, and actions ( Chiu & Kuo, 2009). For example, students working on a problem together often agree or disagree with one another’s ideas (monitoring) and use questions or commands to influence one another’s actions (control).
This study contributes to the research literature in three ways. First, we introduce hypotheses regarding how knowledge content and social metacognition in recent messages might influence the likelihood of a CNI in the current message during online mathematics discussions. Second, we explicated a new method to model online conversations across multiple topics. Our coding framework consisted of mutually exclusive and exhaustive categories, sufficiently comprehensive to test our hypotheses. Meanwhile, the multi-dimensional simplicity facilitates the coding for large sample-size statistical analyses. Lastly, we applied this new method to analyze high school students’ small group mathematics discussions from an online discussion community not related to any class or school.
