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Teaching Developmentally (A summary)

This summary emphasizes the importance of active engagement in the learning process, advocating that knowledge and understanding are constructed uniquely by each learner. Reflective thinking is highlighted as a vital component for effective learning, particularly in mathematics. The sociocultural context of a learning community enhances the development of mathematical ideas. Effective teaching strategies include using models, cooperative learning, and encouraging discourse. These methods not only improve retention and problem-solving abilities but also foster a positive attitude towards learning.

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Teaching Developmentally (A summary)

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  1. Children construct their own knowledge and understanding; we cannot transmit ideas to passive learners. Knowledge and understanding are unique for each learner. Reflective thinking is the single most important ingredient for effective learning. Teaching Developmentally(A summary)

  2. The sociocultural environment of a mathematical community of learners interacts with and enhances students’ development of mathematical ideas. Models for mathematical ideas help students explore and talk about mathematical ideas. Effective teaching is a student-centered activity. Teaching Developmentally(A summary)

  3. Benefits of a Relational Understanding • Effective Learning of New Concepts and Procedures • Less to Remember • Increased Retention and Recall • Enhanced Problem-solving Abilities • Improved Attitudes and Beliefs

  4. Expanding the Idea of a Model Figure 3.11 Five different representations of mathematical ideas. Transitions between and within each can help develop new concepts Lesh, Post, and Behr (1987).

  5. Create a mathematical environment. Pose worthwhile mathematical tasks. Use cooperative learning groups. Use models and calculators as thinking tools. Require justification of student responses. Encourage discourse and writing. Listen actively. Strategies for Effective Teaching

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