PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
Exploring a pre-service teacher’s conceptions of area and area units
Page: 613
This paper highlights the data from a one-semester course with pre-service teachers in an ongoing study of their conceptions of area at a public university in the western United States. Their meanings of area and area units, both standard and non-standard, were explored throughout the semester. Analysis of our interviews with these pre-service teachers about their responses to area tasks allowed us to uncover three cognitive conflicts in conceptualizing area, namely: 1) how can non-square units be square(d)?, 2) how can we find the area of a shape when the area unit is neither square nor polygonal?, 3) how can we use square or polygonal area units to measure the area of a shape with curved boundaries? The work of one representative case study is reported here. This work will help educators develop tasks to initiate these cognitive conflicts for improved conceptualizations of area.