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There are various problematic concepts which students and teachers tend to accept without thinking critically. The concept of cicumscription is one such concept. The attached document outlines a concept clarification session on circumscription.
Tagsexposition conceptual inquiry lesson plan mathematical inquiry
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Mathematics is the study of possible worlds. The attached document explores, through examples and exposition, the nature of mathematical inquiry as well as the concepts involved in the study of mathematics, namely axioms, definitions, conjectures, proofs and theorems.
Tagsexposition education conceptual inquiry inquiry oriented education mathematical inquiry
The attached documents are an example of a mathematical inquiry class. This is an example of a class which can be taken with students who are not yet ready for the rigor of proofs. It requires students to come up with conjectures after being exposed to curated examples of shapes made of straw.
Tagslesson handout mathematics justifying conjecturing proving lesson plan mathematical inquiry