Girls' First-Grade Spatial Skills and Arithmetic Decomposition Strategy Preferences Predict Fifth-Grade Math Reasoning

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

Abstract

Rationale:
There is a strong and established relationship between object-based spatial skills and relative success and failure in math/science fields – particularly in STEM careers in which women are underrepresented (Wai et al., 2009). Starting at around age four (Uttal et al., 2013), females have been found to be at a disadvantage on spatial tasks relating to mental transformations. To understand the spatial-math association for females in greater depth, in a prior study, it was found that first-grade girls’ spatial-transformation skills predicted fifth-grade analytical math-reasoning skills (algebra/numerical) as well as spatial math-reasoning skills (geometry/measurement). Why might spatial skills predict analytical-based mathematics? One possible explanation is that young students with good spatial skills might use more high-level mental strategies, such as decomposition and retrieval (rather than procedural strategies) when solving arithmetic problems. This, in turn, may predict use of more conceptual strategies when solving analytical-reasoning problems in fifth grade.

Purpose:
This longitudinal study was designed to compare early spatial skills to other early predictors of later analytical math reasoning in girls. First-grade girls' spatial skills were compared with first-grade verbal skills, arithmetic skills, and arithmetic strategy-preferences as predictors of analytical math reasoning in fifth grade. The study was also designed to determine whether there was a pathway leading from spatial skills to higher mental arithmetic strategies in first-grade girls, which in turn predicted analytical math reasoning in fifth grade. Another goal was to determine whether the two types of high-level mental strategies at first grade (decomposition vs. retrieval) have differential long-term benefits.

Methods/Data Source:
First-grade girls were given assessments measuring: (1) spatial skills (WISC-IV Block-Design subtest, and mental-rotation tasks), (2) verbal skills (Peabody Picture Vocabulary Test), (3) arithmetic skills (addition/subtraction), and (4) preferred arithmetic strategy usage was also examined. In fifth grade, a math reasoning test, assessing math-reasoning-spatial and math-reasoning-analytical was administered.

Results/Discussion/Significance:
The findings showed that in first grade, girls' spatial skills were associated with higher-frequency of both decomposition and retrieval strategies in solving arithmetic problems. Secondly, both spatial skills and higher use of decomposition (but not retrieval) in first grade were predictive of analytical math reasoning skills in fifth grade. These predictors were stronger than first-grade retrieval-strategy preference, arithmetic skills, and verbal skills in predicting fifth-grade analytical math reasoning. The estimated path model accounted for approximately half the variance in math reasoning.

Thus, first-grade spatial skills already function as key long-term predictors of analytical as well as spatial math-reasoning skills as late as fifth grade. One possible implication of the present findings is that young students with good spatial skills might use more flexible and high-level conceptual strategies (possibly involving visualizations) at both grade levels, rather depending on retrieving known algorithms or math facts. The present research adds to the extensive literature showing the important role of spatial skills in girls’ success in math and science. Unfortunately, at present, spatial skills are rarely systematically taught in schools (National Science Board, 2010). The next step is to intervene at every level of the educational curriculum to focus on fostering these critical skills, as indicated in the following presentations.

Authors

• Beth Casey, Boston College

• Caitlin Lombardi, Boston College

• Amanda Pollock, Boston College

• Bonnie Fineman, Boston College