ABSTRACT
In this chapter, we discuss how to document learners’ thinking and use it to inform instruction. We offer a scenario of three learners within an intervention designed to bolster learners’ conceptions of fractions, describe multiple tools that we used to determine learners’ incoming understanding, explicate how we designed intervention to leverage learners’ strengths, and introduce learners’ problem-solving strategies as a novel way to monitor learners’ understanding throughout the intervention. We offer tools that teachers can use to document learners’ daily strategies alongside more common formative assessments to gauge changes in thinking over time and adjust instruction. Finally, we provide a few tips to further differentiate Small Environments in response to unique fraction understandings.
