The Australian Curriculum places a very heavy focus on deep-level understanding and mathematical reasoning. This means that students can no longer simply answer routine mathematical questions that look exactly the same as those they have seen before. These type of questions do not require deep-level understanding, logical reasoning, problem-solving or analytical thinking, but instead use only recall of memorised formulae or algorithms without any challenging thinking on the part of the student. The skills of mathematics are encompassed in the Proficiency Strands.
These changes mean that most maths classrooms need to change, and change significantly.
In many traditional mathematics classrooms teachers present an algorithm or formula to students, demonstrate how it works and explain its use, and then give students routine questions to practice until they have the new method memorised. In this environment there is almost never “inquiry and active participation in challenging and engaging experiences”, and it is therefore impossible to meet the new requirements.
The new requirements are best met though student inquiry and active participation in a problem-based teaching environment. Problem-based mathematics engages students through challenging, insightful problems, and leads them through the process of experimenting to develop new mathematical understanding by focusing on fundamental mathematical principles and patterns.