Faculty Research: Investigating Second-Grade, Urban Students’ Development of Number Sense of Fractions

Arthur B. Powell, Department of Urban Education, Rutgers University-Newark

Kendell V. Ali, Special Assistant, Mathematics Curriculum and Instruction,
Newark Public Schools


Fraction Study Project Description

Knowledge of rational numbers is essential for mathematical achievement (Siegler, Thompson, & Schneider, 2011; Torbeyns, Schneider, Xin, & Siegler, 2015) and, in turn, for access to STEM disciplines and careers. This project intends to facilitate such access for urban, low-income students by investigating the affordances and obstacles of ‘fractions-of-quantity’ as a cognitive vehicle to extend second-grade students’ number sense of fractions. Focusing on conceptual understandings of fraction magnitude (equivalence, inequality, and order), a collaborative team composed of two teachers from the Newark Public Schools, their mathematics supervisor, and a university mathematics educator are designing tasks and, in two afterschool classrooms, working with 30 students on the tasks to understand how to increase students’ fraction sense. The afterschool classrooms and students are located at the 13th Avenue/Dr. MLK, Jr. School. The expected outcome is that students become conversant with fraction magnitude and view fractions as a multiplicative comparison between two commensurable quantities. In previous investigation (Empson, Junk, Dominguez, & Turner, 2005), researchers have underscored this view as critical for students’ successful acquisition of fraction knowledge.

* Support for this comes from a grant from the Mathematics Education Trust of the National Council of Teachers of Mathematics. Additional support comes from the Newark Public Schools and Rutgers-Newark’s Cornwall Center for Metropolitan Studies and the Department of Urban Education. 


Empson, S. B., Junk, D., Dominguez, H., & Turner, E. (2005). Fractions as the coordination of multiplicatively related quantities: A cross-sectional 
             study of children's thinking. Educational Studies in Mathematics, 63(1), 1-28. doi:10.1007/s10649-005-9000-6
Siegler, R. S., Thompson, C. A., & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 
             62(4), 273-296. doi:doi:10.1016/j.cogpsych.2011.03.001
Torbeyns, J., Schneider, M., Xin, Z., & Siegler, R. S. (2015). Bridging the gap: Fraction understanding is central to mathematics achievement in 
             students from three different continents. Learning and Instruction, 37, 5-13. doi:http://dx.doi.org/10.1016/j.learninstruc.2014.03.002