| The study of reflection and reflective thinking has a long history in research on teaching and learning. However, in the assessment of gifted students, quantitative measures are generally utilized these tend to measure only what is observable and discount affective aspects of learning. This study argues that intellectually gifted children, in particular, are not well understood in terms of how they conceptualize or "come to know" mathematics. To explore these phenomena, the researcher applied the portraiture method with three mathematically gifted students in seventh grade. Subjects were selected who had, in the fifth grade, written mathematics autobiographies in which they described their views of mathematics. The study was conducted at the Arrow University Campus Schools (a pseudonym) for intellectually gifted students. Data collection procedures included a review of institutional and student records, a written statement by each subject and his or her parent, and open-ended, semi-structured interviews. Each subject was interviewed three times for l-2 hours each a parent and the student's current mathematics teacher and available former mathematics teachers were interviewed once each for 30-40 minutes. Finally, the researcher observed each student during three mathematics classes. Themes emerged from the various data sources and were triangulated to yield an in-depth portrait of each subject's conceptualization of mathematics. It was found that parents equated potential for adult success to IQ measured at a very young age, and that students enjoyed and were empowered to reflect on their conceptual views of mathematics (Nickson, 2000). Emergent themes appeared to support multidimensional conceptions of giftedness and intelligence. Overall, the research supported McLeod (1992) and Lester's (2000) arguments on the importance of implementing alternative qualitative research tools to uncover students' mathematics beliefs and experiences. |
