Dr. Giang-Nguyen T Nguyen

Function concepts are essential in K-12 and post-secondary mathematics (CCSSM, 2010; Carraher & Schliemann, 2007). Understanding function concepts is complex for students, even for high-performing undergraduates who finished calculus (Breidenback, Dubinsky, Hawks, & Nichols, 1992). Students mainly focused on algebraic manipulations in courses (Carlson & Oehrtman, 2005). Previous studies have documented students’ misconceptions and difficulties when learning the function concepts (e.g., Breudenback et al., 1992); however, there is a dearth of research examining how misconceptions related to functions are similar or different among multiple age groups. There have been multiple efforts to design tasks to help students develop a robust understanding of functions concept tasks (such as Identify Functions developed by Steketee and Scher,2012). Examining the effectiveness of such efforts is essential to promoting the intervention in classrooms.
In this proposal, we report our preliminary analysis of an ongoing research study investigating how student understanding of function concepts in different K-16 levels. We examined the following research questions:
1. How do students define and represent functions?
2. How do students’ definitions of functions change as the result of completing the tasks identify functions?

This research was a quantitative approach to describe how teachers’ participation in a Research Experience for Teachers program influences aspects of teacher thinking (pedagogical discontentment) science teaching practice. Data were collected from 58 teachers before and after their participation two different RET programs: authentic scientific research (SciRes) and scientific research and pedagogy (SciPed). Pre and post program data were a survey of pedagogical discontentment and a science -teaching episode. SciPed teachers showed a statistically greater increase in reform-oriented practice than those in the SciRes program. SciPed teachers enter the program with a significantly higher pedagogical discontentment score but leave with a significantly lower score. As SciPed teachers became more reform oriented in their practice, their discontentment with their practice decreased.