Davis - Mathematical Thinking and Learning 2007

Real-World Contexts, Multiple Representations, Student-Invented Terminology, and Y-Intercept
Mathematical Thinking and Learning
2007, Vol. 9, No. 4, Pages 387-418

Jon D. Davis
Department of Mathematics, Western Michigan University

One classroom using two units from a Standards-based curriculum was the focus of a study designed to examine the effects of real-world contexts, delays in the introduction of formal mathematics terminology, and multiple function representations on student understanding. Students developed their own terminology for y-intercept, which was tightly connected to the meaningfulness and implicit/explicit temporality of the contexts that students investigated as part of their classroom activities. This terminology held great promise for promoting the concept of y-intercept within a multiple representation environment. However, the teacher's interpretation of different activities and his assumptions about the transparency of different representations, as well as students' past experiences left the student-generated terminology and the concept of y-intercept disconnected from one another. This resulted in student-generated terminology that had limited applicability, a fragile understanding of y-intercept within different representations, and for some students, interference between their invented terminology and the concept of y-intercept itself.