Rationale for the Focus on Spatial/Geometry Skills
The material below was excerpted from Casey, Kersh, and Mercer
Young (2004), an article published in the Early Childhood Research Quarterly:
Special Issue on Mathematics and Science.
“In
their latest version of the Principles and Standards, NCTM (2000) recommends
that approximately equal time be given to geometry and number content. When the proportion of time on measurement,
pre-algebra, and graphing is included, there is a dramatic shift away from
a primary focus on number sense, the traditional emphasis in early childhood
classrooms (see chart on p. 30). Thus,
part of the rationale for this supplementary book series was to develop a
more balanced mathematics curriculum for young children.
Furthermore, we designed
the books to have a strong visualization/ spatial reasoning component. Spatial concepts involve the ability to think
and reason through the transformation of mental pictures. Spatial reasoning is involved in geometry, estimation
and measurement, use of diagrams, graphs, and drawings, breaking fractions
down into geometric regions, or conceptualizing mathematical functions.
Our own research provides a rationale for a shift in focus in mathematics
education towards the development of spatial reasoning skills.
Among older students, we and other researchers have found
a relationship between spatial skills and mathematics achievement (Casey,
Nuttall, &
Pezaris, 1997; Battista, 1990). In addition, our research (Casey, Nuttall,
& Pezaris, 2001) and others’ (Johnson & Meade, 1987) have shown that
girls perform more poorly on spatial tasks involving mental transformations/rotations
when compared to boys. Finally, it's been demonstrated that gender
differences on these spatial skills mediate gender differences on the Math
SAT’s (Casey, Nuttall, & Pezaris, 1997).
Thus, part of our motivation for developing these mathematics materials
for young children was based on gender equity issues.”
Achieving Equity Through the Development of Spatial Skills
It is striking that spatial gender differences can be found as early as preschool and kindergarten. Researchers have provided evidence of early gender differences in mental rotation ability as well as in other types of mental transformations (Cronin, 1967; Rosser, Ensing, Gilder & Lane, 1984; McGuinness & Morley, 1991). Levine and colleagues (1999) found evidence of gender differences favoring males on part-whole relations tasks requiring mental transformations (slides) and two-dimensional mental rotations (turns) in children as young as four-and-a-half.
The material below was excerpted from Casey, Pezaris,
“Why do these findings have implications for young children in particular?…” [Spatial skills] “are useful for young math learners when constructing with blocks, estimating how many disks are in a jar, estimating the length of a pencil, or figuring out how to put together a tangram puzzle or a pattern block design….We believe that strategies that children choose for solving mathematics problems develop right at the outset of schooling, and that we need to start at this point in time to promote spatial as well as analytical strategies for solving mathematics problems. This is particularly critical for girls, since boys appear to be more likely to acquire these strategies on their own during the early years.”
Given the dearth of spatial and geometry skills taught in elementary schools, many girls may never tap their potential to think spatially. Therefore, it is important to provide a mathematics curriculum right from the start that attempts to equalize these spatial experiences, and that solidly connects spatial thinking to mathematical reasoning in a systematic way. We have designed the ‘Round the Rug Math series to be interesting to a wide range of girls by teaching the spatial concepts within the context of people-oriented adventure stories. At the same time, the interactive and spatial nature of the adventure stories make mathematics lessons more compelling to highly active boys.
The goal is to enable early childhood teachers to facilitate different styles of problem solving in all children.
References for the Excerpted Articles
Casey, B., Kersh, J. E., & Mercer Young, J. (2004).
Storytelling sagas: An effective medium for teaching early childhood mathematics.
Early Childhood Research Quarterly: Special Issue on Mathematics and Science,
19, 167-172.
Casey, B., Pezaris, B.,