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.
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Relationships Between Opportunity to Learn Mathematics in Teacher Preparation and Graduates' Knowledge for Teaching Mathematics
James Hiebert, Dawn Berk, Emily Miller, Heather Gallivan, and Erin Meikle
Students' Conceptions of Sine and Cosine Functions When Representing Periodic Motion in a Visual Programming Environment
Anna F. DeJarnette
In support of efforts to foreground functions as central objects of study in algebra, this study provides evidence of how secondary students use trigonometric functions in contextual tasks. The author examined secondary students' work on a problem involving modeling the periodic motion of a Ferris wheel through the use of a visual programming environment. This study illustrates the range of prior knowledge and resources that students may draw on in their use of trigonometric functions as well as how the goals of students' work inform their reasoning about trigonometric functions.
Posing Cognitively Demanding Tasks to All Students
Rachel Lambert and Despina A. Stylianou
One middle school teacher developed classroom routines to make challenging questions accessible to all learners in her class.
