Supporting Elementary Mathematics Teacher Candidates' Use of Divergent Formative Assessment

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.

Facilitating Active Learning and Collaboration in Online Mathematics Content Courses for Secondary Teachers

This chapter reviews teachers' perceptions of the collaborative learning experiences when enrolled in an online course to determine strategies for engaging teachers in active learning and meaningful collaboration in an online learning environment. A survey was designed to solicit feedback from mathematics teachers of Grades 6-12 who have completed online mathematics content courses at the University of Nebraska – Lincoln (UNL) for professional development or for graduate credit. The survey specifically addresses the teachers' perceptions of the collaborative learning experiences during their online course. Combined with feedback from numerous course evaluations and the experiences of several online mathematics instructors from UNL's Department of Mathematics, results of the survey are utilized to determine strategies for engaging teachers in active learning and meaningful collaboration in an online learning environment.

Inviting Prospective Teachers to Share Rough Draft Mathematical Thinking

Engaging prospective elementary teachers (PTs) in participating productively by making their exploratory (rough draft) thinking public during class discussions remains a constant challenge for instructors of mathematics content courses for teachers, in part because of perspectives incoming PTs may hold about interacting in academic settings. In this article, we share the effects of an intervention designed to confront PTs' incoming perspectives. PTs were provided with opportunities to label the level of completeness and correctness of their thinking before they displayed and discussed their written work publicly during a mathematics content course for teachers. Results indicated that labeling their work increased PTs' level of comfort with sharing their thinking and awareness of the value of doing so. PTs also reported that the label served as a reflection tool. The label increased the PTs' productive disposition in terms of comfort level with taking intellectual risks when doing mathematics and reflecting on their work.