A Spatial Approach to Early-Years Geometry: Effects of a Yearlong Teacher-Led Intervention

• In Event: Lesson Learned About Increasing Mathematics Achievement Through Spatial Instruction

Abstract

Early mathematics performance is a strong predictor of later academic success (Duncan et al., 2007). Providing young children of all backgrounds with a strong mathematical foundation is thus of great importance (Ginsburg et al., 2008; NAEYC/NCTM, 2002). One proposal to achieve this objective is to increase instructional efforts aimed at improving young children’s spatial thinking (Newcombe, 2010). Research indicates that spatial thinking is fundamental to concurrent and later mathematics performance (Verdine et al., 2014). Yet, spatial thinking remains a neglected aspect of early years mathematics instruction (Clements, 2004) despite strong recommendations for its inclusion, e.g., NCTM, 2006; NRC 2006). To address this problem, we have been engaged in a professional development research project for early years educators, (e.g., authors 2015) to foster spatial reasoning and geometry learning with at-risk populations.
In this talk, we present methods and results of a 7-month intervention, part of the larger project, designed to target spatial visualization skills; i.e., forming, maintaining, and manipulating visual-spatial information. The intervention, comprised of quick image activities, games and specially designed geometry lessons, (see Table 1 for examples) was co-designed with early years (K-2) teachers and carried out in their classrooms (average 45 hours) as part of the regular mathematics program.
This quasi-experimental study involved the three lowest performing schools in a remote Canadian school district with more than 70% of students identified as Aboriginal. Two of the schools (6 classrooms) were assigned to the experimental condition; the third school (6 classrooms) served as an “active” control group (teachers received a comparable yearlong intervention on inquiry-based science pedagogy).
In total, 66 children, randomly selected from the participating classrooms, took part in the same measures, pre- and post, consisting of assessments of spatial language, visual-spatial reasoning, 2D mental rotation, number knowledge, and magnitude comparison (symbolic and nonsymbolic).
The main research objectives were to: 1) assess the potential of this teacher-led intervention, consisting of in-class spatial/geometry activities, to improve children’s spatial reasoning; and 2) to determine whether training-related improvements in spatial thinking would transfer to more general mathematics performance. Based on research indicating that spatial thinking is both malleable (Uttal et al., 2013) and strongly involved in numerical processing skills (Hubbard et al., 2009), we hypothesized that the intervention would support improvements in spatial skills and that the associated gains would generalize to children’s basic number competencies.
Results revealed that, compared to the control group, children in the spatial intervention demonstrated significant gains on the three separate measures of spatial thinking; spatial language, visual-spatial geometry, and 2D mental rotation—thus demonstrating that improvements in children’s spatial skills are possible within classroom contexts using an assortment of spatial tasks (see Clements and Sarama (2007) for similar conclusions).
Moreover, compared to the control group, the spatial group demonstrated gains in numerical magnitude comparison—a task shown to be longitudinally predictive of children’s overall mathematics achievement (Nosworthy et al., 2013). This novel finding confirms the importance of supporting children’s spatial thinking in an effort to provide them with a strong mathematical foundation.

Authors

• Joan Moss, University of Toronto

• Zachary Hawes, University of Toronto

• Beverly A. Caswell, University of Toronto