Lecture 3 Notes by Zi

Non-Routine Problems

liziyan — 2024-09-03 16:34:54 UTC

Non-routine problems are those where the solution is not immediately apparent.
Emphasis on understanding the problem before attempting to solve it.
Reflect on the concept of "productive struggle," which is critical for deep learning. Progress should be evaluated periodically.

Conjecturing and Mathematical Arguments

liziyan — 2024-09-03 16:35:48 UTC

Conjecturing involves forming hypotheses based on observations during problem-solving.

Visual Proofs

liziyan — 2024-09-03 16:37:04 UTC

Visual proofs are powerful tools in mathematics, especially in primary and secondary education. It is an illustration of an identity or mathematical statement which can be demonstrated as self-evident by a diagram without any accompanying explanatory text.

Counterexamples and Proofs

liziyan — 2024-09-03 16:37:31 UTC

Disproving a conjecture requires only one counterexample, while proving it requires a general argument.
Emphasise the difference between proving and disproving a statement.

Victorian Curriculum

liziyan — 2024-09-03 16:38:20 UTC

Victorian Essential Learning Standards focus on conjectures in the curriculum.
Students should develop and test conjectures, understanding that a single counterexample can invalidate a conjecture.

Key strategies

liziyan — 2024-09-03 16:38:43 UTC

Understanding and clarifying the problem.
Representing the problem (e.g., diagrams, models).
Solving the problem.
Checking the solution.