Supporting Elementary Mathematics Teacher Candidates' Use of Divergent Formative Assessment

Abstract

In this chapter, the authors consider the purposeful design of two mathematics content courses (Content 1 and Content II) and one methods course (Methods) as a means of helping teacher candidates (TCs) learn about divergent formative assessment (DFA), which seeks to explore what students understand rather than only if they understand a concept or skill. The authors leverage the research of groupworthy tasks and the Rights of the Learner to describe three tasks they use to help TCs learn mathematics through problem-solving and to learn to teach through problem-solving. The chapter outlines three commonalities across the courses: 1) Shifting from implicit to explicit and informal to formal practices of DFA that reflects teaching through problem-solving; 2) Using DFAs to transition TCs' identities from learners to teacher-learners; and 3) Supporting TCs' self-assessment through DFAs in multiple ways.

Using Revision and Specifications Grading to Develop Students’ Mathematical Habits of Mind

“…Pryor and Croussard continue by asserting that one type of formative assessment is not necessarily better than the other, and in most teaching situations, it is important to balance both. The grading scheme described in this paper largely falls under the category of convergent formative assessment, but I often use divergent formative assessment in my course by engaging students in open-ended problem-solving tasks and by presenting them with opportunities to explore student thinking (see [4]). [6] outlines some of the pillars of this form of grading for mastery.…”