The roles of patterning and spatial skills in early mathematics development☆
Section snippets
Math education standards
The Common Core State Standards (2010), or local variations of them, are currently being implemented in schools across the country. However, these standards give minimal attention to patterning or spatial skills in the early grades. Patterning skills encompass the ability to notice and use predicable sequences, such as a predictable array of shapes or sounds or functional relations between two variables (Burgoyne, Witteveen, Tolan, Malone, & Hulme, 2017). With young children, the focus is on
Spatial skills
First consider spatial skills. Young children regularly engage their spatial skills as they play with blocks, puzzles, and videogames (Jirout & Newcombe, 2015; Levine, Ratliff, Huttenlocher, & Cannon, 2012; Newcombe, 2010; Verdine, Golinkoff, Hirsh-Pasek, Newcombe, et al., 2014). In one large, representative sample, 75% of 4- to 7-year old children were reported to play with blocks, puzzles and board games at least sometimes (i.e., three to five times per week), and 25% were reported to play
Links between spatial skills and math knowledge
How might spatial skills influence math knowledge? The most common theoretical perspective is that mathematical thinking is supported by spatial representations (Mix & Cheng, 2012). From mental number lines to geometric figures, information about locations in space are often processed when solving math problems. For example, some people generate schematic representations of math problems that include the spatial relations described in the problems, and these people are more likely to solve the
Repeating patterning skills
Young children, teachers, and parents all regularly work with repeating patterns. For example, some children spontaneously create patterns during their free play at preschool (Ginsburg, Inoue, & Seo, 1999; Ginsburg, Lin, Ness, & Seo, 2003). Further, U.S. preschool teachers often view patterning activities as important (Clarke, Clarke, & Cheeseman, 2006; Economopoulos, 1998). In one small study, U.S. teachers reported engaging their students in frequent repeating patterning activities, and
Links between repeating patterning skills and math knowledge
How might repeating patterning skills support math knowledge? Identifying, extending, and describing predictable sequences (patterns) in objects and numbers are core to mathematical thinking (Charles, 2005; Sarama & Clements, 2004; Steen, 1988). Both counting and arithmetic principles describe generalizations of predictable sequences. For example, the next number name in the count sequence represents a magnitude that is exactly one more than the previous number name (i.e., the successor
Potential relations between spatial and repeating patterning skills
Although both spatial and repeating patterning skills play an important role in math development, they have been studied independently in past research. Thus, little is known about the relations between the two types of skills. For example, children may rely on spatial skills to complete repeating patterning tasks, especially when the tasks include working with visual patterns constructed with objects. The spatial skill of form perception is likely needed to distinguish and match objects that
Research goals and hypotheses
The goal of this research was to explore the cross-domain development of repeating patterning skills, spatial skills, and math knowledge in prekindergarten. We focused on prekindergarten children (ages 4 and 5) because some patterning and spatial skills are in place by age 4, and individual differences in these skills in prekindergarten are already predictive of later math knowledge (Rittle-Johnson et al., 2013, Rittle-Johnson et al., 2016; Verdine et al., 2017). Further, much less is known
Participants
Initial participants were 79 children who were recruited from six preschool programs: three public, one Head Start center, and two private. Two children would not assent to participate in the study, one child was withdrawn from the study because of other commitments, and three children were no longer attending the participating preschools at Time 2 and could not be located. In the final sample of 73 children (57.5% females), children were an average age of 4 years 7 months (SD = 4 months; range = 4
Relations among variables
Descriptive statistics and correlations among key variables at both time points are presented in Table 3, with raw correlations presented above the diagonal. To provide a sense of the global relation between repeating patterning and spatial skills, we created composite scores for each (by averaging standardized scores on relevant measures) and include those composite variables in the Table. Significant positive correlations were found among all tasks. In most cases, these positive relations
Discussion
The current study highlights the contribution of two important, but often overlooked, skills in early math development: spatial and repeating patterning skills. The two skill sets were related, and each set of skills was a unique predictor of math knowledge concurrently and 7-months later. We discuss the development of a new patterning skills measure, the potential relations between repeating patterning and spatial skills, and the relations between each of these skills and math knowledge. We
References (85)
- et al.
The involvement of working memory in children's exact and approximate mental addition
Journal of Experimental Child Psychology
(2012) - et al.
Alternating imputation posterior estimation of models with crossed random effects
Computational Statistics and Data Analysis
(2011) - et al.
Preschoolers’ strategies for solving visual pattern tasks
Early Childhood Research Quarterly
(2015) Building number sense with number worlds: A mathematics program for young children
Early Childhood Research Quarterly
(2004)- et al.
Effects of mental rotation training on children’s spatial and mathematics performance: A randomized controlled study
Trends in Neuroscience and Education
(2015) - et al.
A longitudinal analysis of sex differences in math and spatial skills in primary school age children
Learning and Individual Differences
(2006) - et al.
Spatial skills as a predictor of first grade girls’ use of higher level arithmetic strategies
Learning and Individual Differences
(2013) - et al.
Developmental gains in visuospatial memory predict gains in mathematics achievement
Public Library of Science
(2013) - et al.
Differential contribution of specific working memory components to mathematics achievement in 2nd and 3rd graders
Learning and Individual Differences
(2010) - et al.
The relation between space and math
Which preschool mathematics competencies are most predictive of fifth grade achievement?
Early Childhood Research Quarterly
Working memory and mathematics: A review of developmental, individual difference, and cognitive approaches
Learning and Individual Differences
On the relationship between math anxiety and math achievement in early elementary school: The role of problem solving strategies
Journal of Experimental Child Psychology
Beyond numeracy in preschool: Adding patterns to the equation
Early Childhood Research Quarterly
Learning from explaining: Does it matter if mom is listening?
Journal of Experimental Child Psychology
Building blocks for early childhood mathematics
Early Childhood Research Quarterly
Enhancing young children’s mathematical knowledge through a pre-kindergarten mathematics intervention
Early Childhood Research Quarterly
Finding the missing piece: Blocks, puzzles, and shapes fuel school readiness
Trends in Neuroscience and Education
Pathways to arithmetic: The role of visual–spatial and language skills in written arithmetic, arithmetic word problems, and nonsymbolic arithmetic
Contemporary Educational Psychology
The toolbox revisited: Paths to degree completion from high school through college
Risky business: Correlation and causation in longitudinal studies of skill development
American Psychologist
Item response theory parameter estimation techniques
The lme4 package version 0. 999375-26
Short-term memory, working memory, and executive functioning in preschoolers: Longitudinal predictors of mathematical achievement at age 7 years
Developmental Neuropsychology
Pattern understanding: Relationships with arithmetic and reading development
Child Development Perspectives
The development of spatial skills through interventions involving block building activities
Cognition and Instruction
Big ideas and understandings as the foundation for elementary and middle school mathematics
Journal of Mathematics Educational Leadership
Spatial training improves children's mathematics ability
Journal of Cognition and Development
The mathematical knowledge and understanding young children bring to school
Mathematics Education Research Journal
Other content domains
Learning and Teaching Early Math: The Learning Trajectories Approach
School readiness and later achievement
Developmental Psychology
What comes next? The mathematics of pattern in kindergarten
Teaching Children Mathematics
Easy as abcabc: Abstract language facilitates performance on a concrete patterning task
Child Development
Young children doing mathematics: Observations of everyday activities
Young American and Chinese children’s everyday mathematical activity
Mathematical Thinking and Learning
The relationship between math achievement and spatial abilities among elementary school children
Journal for Research in Mathematics Education
The relation between spatial skill and early number knowledge: The role of the linear number line
Developmental Psychology
Developmental test of visual perception
Enhancing children’s spatial and numerical skills through a dynamic spatial approach to early geometry instruction: Effects of a seven-month intervention
Types of visual–spatial representations and mathematical problem solving
Journal of Educational Psychology
Differential course of development of spatial and verbal memory span: A normative study
British Journal of Developmental Psychology
Cited by (103)
Validating a measure of growing pattern understanding in Chinese preschool children
2024, Early Childhood Research QuarterlyHigh variability in learning materials benefits children's pattern practice
2024, Journal of Experimental Child PsychologyIdentifying parental math talk styles and relations to child talk and skills
2024, Cognitive DevelopmentExploring the underlying cognitive process of computational thinking in primary education
2023, Thinking Skills and CreativitySelf-determined learning in a virtual makerspace: a pathway to improving spatial reasoning for upper primary students
2024, International Journal of Technology and Design EducationRepeating and growing patterns in early mathematics textbooks
2024, Journal of Curriculum Studies
- ☆
Research supported by Institute of Education Sciences grant R305A160132 to Bethany Rittle-Johnson. The authors thank Danielle Bice, Katherine Gross, Haley Rushing, Joyce Hwang, Mia MacLean-Vernic, and Yinghao Zhang for their assistance with data collection and coding as well as the staff, teachers, and children at A. Z. Kelley Elementary School, Hull Jackson Montessori School, Shayne Elementary School, McNeilly Center for Children, Blakemore Children’s Center, and Holly Street Daycare for participating in this research.