This study examined the genre of undergraduate mathematical proof writing by asking mathematicians and undergraduate students to read 7 partial proofs and identify and discuss uses of mathematical language that were out of the ordinary with respect to what they considered conventional mathematical proof writing. Three main themes emerged: First, mathematicians believed that mathematical language should obey the conventions of academic language, whereas students were either unaware of these conventions or unaware that these conventions applied to proof writing. Second, students did not fully understand the nuances involved in how mathematicians introduce objects in proofs. Third, mathematicians focused on the context of the proof to decide how formal a proof should be, whereas students did not seem to be aware of the importance of this factor.
Browse
Linguistic Conventions of Mathematical Proof Writing at the Undergraduate Level: Mathematicians' and Students' Perspectives
Kristen Lew and Juan Pablo Mejía-Ramos
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
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.
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.
