Do it this way! Metacognitive strategies in collaborative mathematical problem solving

Goos, Merrilyn; Galbraith, Peter

doi:10.1007/bf00304567

Cited by 103 publications

(74 citation statements)

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“…A finer grained analysis of conversational turns (referred to as Moves in the protocol) was then carried out to identify the metacognitive function of the students' dialogue, using a coding scheme developed in an earlier study (Goos & Galbraith, 1996). The first type of metacognitive event, New Idea, occurred when potentially useful information came to light or an alternative approach was mentioned.…”

Section: Data Gathering and Analysis Methodsmentioning

confidence: 99%

Understanding metacognitive failure

Goos

2002

The Journal of Mathematical Behavior

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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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Section: Data Gathering and Analysis Methodsmentioning

confidence: 99%

Understanding metacognitive failure

Goos

2002

The Journal of Mathematical Behavior

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“…Furthermore, students might be tempted to engage in off-task social interaction (Goods and Galbraith, 1996). Students may also receive differential status in groups.…”

Section: Group Work In Mathematicsmentioning

confidence: 99%

“…Wood and Sellers, 1997;Maher, 1991;Verschaffel and De Corte, 1993;Leikin and Zaslavsky, 1997;Townsend and Hicks, 1997;Goods and Galbraith, 1996).…”

Section: Group Work In Mathematicsmentioning

confidence: 99%

The Effective Teaching of Mathematics: A review of research

David¹,

Muijs²

1999

School Leadership & Management

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“…Goos and Galbraith (1996) investigated how students used metacognitive strategies in small group settings. Grave, Boshuzien and Schmidt (1996) (2001) showed that students' propensity to enhance their metacognition and learning process can be linked to the use of a constructivist framework.…”

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confidence: 99%

Learning Chemistry in a Metacognitive Environment

Pulmones¹

2008

Asia-Pac.Educ.Res.

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Thinking about one's own thinking and of how one learns and solves problems is described as metacognition. The important dimensions of metacognition are knowledge of one's own thinking as one plans, monitors, and evaluates academic tasks. This paper presents a qualitative study on metacognition, on how academic tasks in Chemistry are designed and structured in a constructivist environment that promotes students' metacognitive behaviors and meaningful learning of Chemistry. Sample metacognitive profiles of two cases (low and high metacognitive index), generated from analyses of various qualitative data are also presented. As a conclusion, the paper reiterates a research finding which indicates that prolonged engagement of students in classroom activities designed in a constructivist environment gives ample opportunities for students to demonstrate their overt planning, monitoring and evaluation behaviors. Purposely asking students to answer metacognitive questions afforded them the opportunity to reflect on their thinking, thus fostering their metacognition.

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Do it this way! Metacognitive strategies in collaborative mathematical problem solving

Cited by 103 publications

References 13 publications

Understanding metacognitive failure

Understanding metacognitive failure

The Effective Teaching of Mathematics: A review of research

Learning Chemistry in a Metacognitive Environment

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