For many years, theories of collaborative learning tended to focus on how individuals function in a group. More recently, the focus has shifted so that the group itself has become the unit of analysis. In terms of empirical research, the initial goal was to establish whether and under what circumstances collaborative learning was more effective than learning alone. Researchers controlled several independent variables (size of the group, composition of the group, nature of the task, communication media, and so on). However, these variables interacted with one another in a way that made it almost impossible to establish causal links between the conditions and the effects of collaboration. Hence, empirical studies have more recently started to focus less on establishing parameters for effective collaboration and more on trying to understand the role which such variables play in mediating interaction. In this chapter, we argue that this shift to a more process-oriented account requires new tools for analysing and modelling interactions.

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The evolution of research on collaborative learning

This paper reports on a three year study of patterns of student-student social interaction that mediated metacognitive activity in senior secondary school mathematics classrooms. Transcripts of small group problem solving were analysed to determine how a collaborative zone of proximal development could be created through interaction between peers of comparable expertise, and to investigate conditions under which such interaction led to successful or unsuccessful problem solving outcomes. Unsuccessful problem solving was characterised by students' poor metacognitive decisions exacerbated by lack of critical engagement with each other's thinking, while successful outcomes were favoured if students challenged and discarded unhelpful ideas and actively endorsed useful strategies. In reconceptualising metacognition as a social practice, the study contributes to the growing body of research applying sociocultural theories to understand learning in mathematics classrooms.

Socially mediated metacognition: creating collaborative zones of proximal development in small group problem solving

The purpose of the present research was to design an innovative instructional method for teaching mathematics in heterogeneous classrooms (with no tracking) and to investigate its effects on students’ mathematics achievement. The method is based on current theories in social cognition and metacognition. It consists of three interdependent components: metacognitive activities, peer interaction, and systematic provision of feedback-corrective-enrichment. The method is called IMPROVE, the acronym of which represents all the teaching steps that constitute the method: Introducing the new concepts, Metacognitive questioning, Practicing, Reviewing and reducing difficulties, Obtaining mastery, Verification, and Enrichment. The research includes two studies, both implemented in seventh grades: One focused on in-depth analyses of students’ information processing under the different learning conditions (N = 247), and one investigated the development of students’ mathematical reasoning over a full academic year (N = ...

Improve: A Multidimensional Method For Teaching Mathematics in Heterogeneous Classrooms

The study investigated the influence of metacognition on critical thinking skills. It is hypothesized in the study that critical thinking occurs when individuals use their underlying metacognitive skills and strategies that increase the probability of a desirable outcome. The Metacognitive Assessment Inventory (MAI) by Schraw and Dennison (Contemporary Educational Psychology 19:460–475, 1994), which measures regulation of cognition and knowledge of cognition, and the Watson-Glaser Critical Thinking Appraisal (WGCTA) with the factors inference, recognition of assumptions, deduction, interpretations, and evaluation of arguments were administered to 240 college students from different universities in the National Capital Region in the Philippines. The Structural Equations Modeling (SEM) was used to determine the effect of metacognition on critical thinking as latent variables. Two models were tested: (1) In the first model, metacognition is composed of two factors while (2) in the second model, metacognition has eight factors as they affect critical thinking. The results indicated that in both models, metacognition has a significant path to critical thinking, p < .05. The analysis also showed that for both metacognition and critical thinking, all underlying factors are significant. The second model had a better goodness of fit as compared with the first as shown by the RMSEA value and other fit indices.

The role of metacognitive skills in developing critical thinking

Recent research has shown that many upper elementary school children do not master the skill of solving mathematical application problems. In this design experiment, a learning environment for teaching and learning how to model and solve mathematical application problems was developed and tested in 4 classes of 5th graders. Pupils were taught a series of heuristics embedded in an overall metacognitive strategy for solving mathematical application problems. Meanwhile, pupils of 7 control classes followed regular mathematics classes. The implementation and effectiveness of the experimental learning environment were tested in a study with a pretest-posttest-retention test design with an experimental and a control group. The results indicate that the intervention had a positive effect on different aspects of pupils' mathematical modeling and problem-solving abilities.

Learning To Solve Mathematical Application Problems: A Design Experiment with Fifth Graders.

A framework is presented that explicitly delineates the roles of metacognition and cognition within small-group heuristic problem solving in mathematics. This framework is used to describe the videotaped behaviors of 27 seventh-grade students of varying ability working in small groups to solve a mathematical problem. The results suggest the importance of metacognitive processes in mathematical problem solving in a small-group setting. A continuous interplay of cognitive and metacognitive behaviors appears to be necessary for successful problem solving and maximum student involvement. Within the groups, students returned several times to such problem-solving episodes as reading, understanding, exploring, analyzing, planning, implementing, and verifying. Stimulated-recall interviews held after completion of the task underscored an additional dimension of importance. Attitudes, particularly those of high-ability students, seemed to affect the interactions and the problem-solving behaviors of fellow group mem...

Eleanor Armour-Thomas

Papers

Development of a cognitive-metacognitive framework for protocol analysis of mathematical problem solving in small groups.