A formative approach to understanding (and supporting) prospective teachers’ capabilities with modeling mathematical thinking
摘要
There has been increased attention to instructional practices that teachers can use to support students in constructing an understanding of mathematics through discourse-rich lessons. Teachers need to support the class in synthesizing ideas at the end of such lessons so that students know what to take away from the lesson. We focus on the instructional practice of modeling, one strategy for supporting such synthesis. A decomposition of the practice of modeling content was developed and used to design a prototype formative assessment task that gathers information about prospective elementary teachers’ capabilities with modeling content. In order to establish the potential of the task to elicit variation in performance at a level of granularity sufficient for formative purposes, we examined the following questions: What patterns of PTs’ capabilities with modeling can be revealed through the assessment? Is the level of detail conducive to the provision of feedback and to design subsequent instruction? Ten first-year teachers who graduated from various teacher education programs participated in the study. Findings reveal that our prototype formative assessment works to gather information about prospective teachers’ capabilities with modeling and is capable of eliciting variation in performances. Further, the level of specificity of the associated tools has the potential to support both feedback to teachers and planning for supporting teachers’ learning. This suggests that such a task and associated tools could support the formative assessment of the developing capabilities of prospective teachers.