Schoenfeld (1985) and others express concern that individuals approach mathematical problems as mechanical exercises and seem to possess little awareness of what they are doing.  They also engage in random strategies and give up easily if not immediately successful.  You are the consultant to assist the teachers in revising the curriculum.

Develop an approach to this task, using metacognitive theory.

1. According to the theory, what assumptions about human learning were violated in the past?
2. In what ways must the learner/teacher configuration change to correct the problem?
3. Recommend a concrete corrective strategy in accordance with the theory, and supportive rationale for each strategy.

ANSWER

 Enhancing Mathematical Problem Solving Through Metacognitive Strategies: A Curriculum Revision Approach

Introduction

The concern expressed by Schoenfeld (1985) and others regarding students’ mechanical approach to mathematical problems highlights the need for a comprehensive approach to address this issue. Metacognitive theory offers a promising framework to tackle this challenge. This essay outlines an approach to revising the curriculum by integrating metacognitive strategies to enhance students‘ problem-solving abilities. The discussion includes identifying violated assumptions about human learning, suggesting changes in the learner/teacher configuration, and recommending concrete corrective strategies supported by metacognitive theory.

Assumptions About Human Learning Violated in the Past

In the past, assumptions about active and reflective learning were violated. Traditional teaching methods often emphasized rote memorization and procedural knowledge, neglecting the importance of understanding and metacognition. Students were not encouraged to reflect on their problem-solving processes or engage in self-regulation, leading to a lack of awareness of their strategies and approaches.

Changes in Learner/Teacher Configuration

To correct this issue, a shift in the learner/teacher configuration is essential. Teachers should transition from being mere disseminators of information to becoming facilitators of metacognitive development. Students need to be empowered to take control of their learning process and develop self-regulation skills. Collaborative learning environments that encourage peer discussions and problem-solving reflections can foster metacognitive growth.

Corrective Strategies in Accordance with Metacognitive Theory:
Explicit Metacognitive Instruction: Introduce metacognitive strategies explicitly within the curriculum. Teach students techniques such as think-alouds, self-questioning, and problem-solving planning. This approach enables them to monitor and control their cognitive processes while engaging with mathematical problems.

Reflective Practices: Incorporate regular opportunities for students to reflect on their problem-solving experiences. Encourage journaling or group discussions where students can analyze their approaches, identify challenges, and strategize for improvement. This practice enhances their awareness of their cognitive processes.

Scaffolded Problem Solving: Design problem-solving tasks that gradually increase in complexity. Provide scaffolding tools such as step-by-step guides, concept maps, and graphic organizers. As students gain confidence in their abilities, gradually reduce the scaffolding, allowing them to independently apply metacognitive strategies.

Metacognitive Monitoring and Evaluation: Teach students to monitor their learning progress. Set specific goals for problem-solving activities and have them assess their performance against these goals. This practice promotes self-regulation and self-directed learning.

Rationale for Each Strategy

Explicit Metacognitive Instruction: By explicitly teaching metacognitive strategies, students become conscious of their thought processes and can select appropriate strategies based on problem characteristics.
Reflective Practices: Reflecting on experiences fosters deeper understanding and encourages students to revise their strategies based on past successes and challenges.
Scaffolded Problem Solving: Gradual removal of scaffolding enables students to internalize metacognitive strategies, enhancing their ability to approach complex problems independently.
Metacognitive Monitoring and Evaluation: Setting goals and evaluating progress instills a sense of accountability and motivates students to refine their strategies for optimal outcomes.

Conclusion

Integrating metacognitive strategies into the curriculum offers a promising solution to the concerns raised by Schoenfeld and others. By correcting past assumptions about learning and restructuring the learner/teacher dynamic, students can develop a deeper understanding of mathematical problem-solving. By incorporating explicit instruction, reflective practices, scaffolded problem-solving, and metacognitive monitoring, educators empower students to approach mathematical problems with greater awareness, efficacy, and metacognitive competence.