Pre-service elementary teachers’ strategies for tiling and relating area units

• Published in: The Journal of mathematical behavior 2017-12, Vol.48, p.112-136
• Main Authors: Wickstrom, Megan H., Fulton, Elizabeth W., Carlson, Mary Alice
• Format: Article
• Language: English
• Subjects: Area measurement; Enumeration; Pre-service elementary teachers; Strategies; Tiling
• ISSN: 0732-3123; 1873-8028
• DOI: 10.1016/j.jmathb.2017.05.004

•We examined 39 pre-service elementary teachers’ (PSTs’) written and pictorial responses when asked to tile a region with different square units.•PSTs implemented 6 strategies as they used and related area units which revealed how they conceptualized tiling a space.•Tiling became more challenging when the side length of the tile was not a factor of the side length of the space.•Across strategies many PSTs incorrectly applied reasoning about length measurement to area measurement.•Results suggest that PSTs’ strategies exist along a continuum from conceptualizing area as discrete to conceptualizing area as continuous. It has been established that preservice elementary school teachers (PSTs) often employ procedural methods when solving measurement problems without conceptual understanding or flexibility, but a significant gap exists in the literature identifying why. Through the lens of discrete and continuous interpretations of area, this study extends the research base by describing strategies PSTs use to tile a two-dimensional space with varying size tiles and what these strategies imply about PSTs’ conceptions of area measurement. These strategies and implied conceptions enable further discussion on the multiple purposes of the area model as an illustrative measure for mathematics throughout the elementary school curriculum.