Observation of reasoning includes:
- watching students as they respond to set tasks. Both formal evaluation, which involves note-taking or other records, and informal evaluation can be equally useful
- observing students' work as they figure out the mathematics. Look for evidence of whether and to what extent students are able to reason analytically
- listening to students recount processes as well as explaining products
- listening to students' explanations, hypotheses and deductions. The Math Reasoning Inventory has an online formative assessment tool
- finding out if students understand other students' thinking (perhaps by asking them to repeat it)
- asking students to show their thinking or to provide evidence with numbers and words, drawings or materials. Talk to them about their thinking either in a group or individually.
Rows of squares
A fraction task which can prompt reasoning.