For Maths, what is Thinking & Working Mathematically (TWM) and why do Cambridge not report on TWM at sub-strand level?

Thinking and Working Mathematically (TWM) comprises of eight characteristics that are intertwined and interdependent. The process of thinking and working mathematically encourages learners to talk with others, challenge ideas and to provide evidence that validates conjectures and solutions. When learners are thinking and working mathematically, they actively seek to make sense of ideas and build connections between different facts, procedures, and concepts. In terms of assessment, TWM questions make up approximately 20% of each Checkpoint paper, split proportionally across several mathematical strands. While we aim to cover a range of the seven TWM characteristics (the 8th characteristic conjecturing is not examined) in the papers, we do not specifically report on the characteristic or pair of characteristics.

The TWM characteristics comprise of four complementary pairs (specialising and generalising, characterising and classifying, conjecturing and convincing, and critiquing and improving). TWM questions can therefore sometimes require more than one characteristic or can be approached using different characteristics to solve the problem. For example, in a question where learners are asked to identify a mistake in a graph drawn, learners may critique the graph by explaining an error, or may explain how to correct the graph, thus improving the work. Both approaches are valid.

The Checkpoint reporting does not allow the tagging of different characteristics to a question. Teachers should be able to use the reporting at TWM strand level as a meaningful way of understanding the learners’ level of proficiency in this area without necessarily knowing about the different characteristics. Additionally, the number of marks allocated to the question assessing the individual characteristics is not sufficient to be able to report meaningfully at the characteristic level. However, when combining the marks of the all the characteristics, this is sufficient to be able to report at the TWM strand level.