Understanding metacognitive failure

Abstract

Running Head: Metacognitive failure 2 UNDERSTANDING METACOGNITIVE FAILUREThis paper reports on a study that investigated patterns of collaborative metacognitive activity in senior secondary school classrooms. Although peers working together on mathematical tasks may enjoy the metacognitive benefits of being able to monitor and regulate each other's thinking, collaboration does not guarantee that they will achieve a mathematically productive outcome. The notion of metacognitive "red flags", or warning signals that problem solving has gone astray, is developed in order to identify three possible scenarios for metacognitive failure. These scenarios, described by the metaphors of blindness, vandalism, and mirage, are illustrated via analysis of videotaped lesson transcripts obtained from a secondary school mathematics classroom. The results provide insights into the interactive constitution of metacognitive activity during small group work, and suggest implications for teachers concerning the fostering of communication and problem solving within a classroom culture of inquiry. 3 UNDERSTANDING METACOGNITIVE FAILUREResearch on the role of metacognition in mathematical thinking flourished during the 1980s and into the 1990s, in concert with the emergence of new mathematics curriculum and policy documents that placed increased emphasis on problem solving and mathematical reasoning (e.g. Australian Education Council, 1991; National Council of Teachers of Mathematics, 1989). At the same time, teachers have been urged to engage students in small group or whole class discussion as a means of developing mathematical understanding (National Council of Teachers of Mathematics, 1991). Problem solving and communication remain central to current visions of effective mathematics teaching (National Council of Teachers of Mathematics, 2000). However, our theoretical understanding of problem solving processes, and how students' mathematical thinking is shaped by their interaction with peers, is far from complete (e.g. Lester, 1994;Schoenfeld, 1992), suggesting that new frameworks are needed to bring together fundamentally cognitive and fundamentally social perspectives on human thought and action (Schoenfeld, 1999).It is widely acknowledged that metacognitive processes, that is, how students monitor and regulate their thinking, are crucial to successful performance on mathematical tasks, and many studies have investigated the metacognitive strategies which secondary school students use in problem solving. Many of these studies have focused on students working individually, in experimental settings, on tasks prescribed by the researcher (Fitzpatrick, 1994;Randhawa, 1994). The few classroom based studies that have investigated the metacognitive potential of small group problem solving have typically used researcher controlled interventions that impose group structures (e.g. based on ability) on students who are unfamiliar with this way of working (Artzt & Armour-Thomas, 1992Curcio & Artzt, 1998;Stacey, 1992).Despite increasing intere...

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“…Reflection forces designers to keep tabs on their process and products throughout the design process. Additionally, informed designers use metacognitive strategies to monitor their thinking and think about how their thinking has changed during the design process as a way to monitor their process (Crismond & Adams, 2012;Flavell, 1979;Goos, 2002;Perrenet, Bouhuijs, & Smits, 2000). Together, reflection and metacognition are essential skills students need, not only to monitor their design, but also to develop deeper levels of understanding about their skills and to understand their knowledge of problem solving and engineering design (Daly, Adams, & Bodner, 2012;Goos, 2002).…”

“…This could be a product of the format of the prompts and student habits of responding to teacher questions. However, it could also indicate that the prompts presented a metacognitive -red flag‖ (Goos, 2002) that prompted them to think metacognitively. For example, many students stated that they used to think one thing, but now thing something else or that they did not understand the problem at the beginning or identified that they know more now than they used to, especially in the Learned the depth of the problem and problem requirements and the Learned engineering design/problem solving themes.…”