Understanding: “I understand the big ideas in maths and know how to solve math problems in many different ways”.
The Understanding goal is all about knowing how mathematics works. A key part of the Understanding goal is to know what factual knowledge to draw upon in a given context, and which strategy, or set of strategies, to apply to this knowledge in order to answer the question correctly. The Understanding goal is broader than the other goals, encompassing a larger variety of mental functions. It is focussed around meta-cognitive elements, that is, our capacity to think about our own thinking. It involves knowing how to answer the question and what your answer means.
For example, we learn and apply derived mental math strategies because they are efficient. However, the other important aspect of learning a broad repertoire of strategies is that it allows us to answer a question in a variety of different ways, and to check if our initial answer is correct. This cross-checking is a vital component of building mental flexibility. Consequently, it is necessary to have knowledge of multiple derived strategies which can be appropriately applied to any one question. Consequently, one of the “Big ideas” introduced to students early on under the Understanding goal is the notion that there is “More than One Way”. More Than One Way means that there are almost always multiple means of solving problems, and students should choose between these means based on contextual efficiency, and their individual strengths and preferences as learners.