To promote appropriate reflective thought the constructivist mathematics teacher in structuring mathematics lessons should consider the following:
This enables students to feel comfortable trying out ideas sharing insights, challenging others, seeking advice from other students and the teacher, explaining their thinking, and taking risks.
No one is a passive observer in such a classroom. There are expectations, respect, and belief that all children can learn mathematics.
It requires students and teachers alike to respect one another, listen attentively and learn to disagree without offending.
A mathematics community is where students evaluate their assumptions and those of others and argue about what is mathematically true.
This makes students believe that they are the authors of mathematical ideas and logical arguments.
The mathematics that students learn must be problematic. It must make students wonder why things are, inquire, search for solutions, and to resolve incongruities.
Instructions should begin with problems, dilemmas, and questions for students.
The teacher should design tasks or problems to engage students in the content of the curriculum.
Which is based on knowledge of the mathematical content and a guess about concepts students bring to the task.
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