It can be difficult for teachers to make in-the-moment decisions about which solution strategies to cognitively challenging tasks should be included in the whole-class discussion (Stein, Engle, Smith, &s Hughes, 2008). Teachers can purposefully select and sequence the solution strategies to help create a whole-class discussion that promotes the mathematical learning goal. An intervention was implemented in a middle school methods course that aimed to understand preservice teachers' (PSTs') competencies in formulating rationales for their selecting and sequencing choices. Results from the intervention suggest that PSTs' sequencing rationales can be grouped into three categories.
Erin M. Meikle
For orchestrating whole-class discussions, note these suggestions to fine tune problem-solving techniques into cognitively challenging tasks.
James Hiebert, Dawn Berk, Emily Miller, Heather Gallivan, and Erin Meikle
We investigated whether the mathematics studied in 2 content courses of an elementary teacher preparation program was retained and used by graduates when completing tasks measuring knowledge for teaching mathematics. Using a longitudinal design, we followed 2 cohorts of prospective teachers for 3 to 4 years after graduation. We assessed participants' knowledge by asking them to identify mathematics concepts underlying standard procedures, generate multiple solution strategies, and evaluate students' mathematical work. We administered parallel tasks for 3 mathematics topics studied in the program and one mathematics topic not studied in the program. When significant differences were found, participants always performed better on mathematics topics developed in the program than on the topic not addressed in the program. We discuss implications of these findings for mathematics teacher preparation.