Preschoolers' strategies for solving visual pattern tasks

a b s t r a c t This study examined preschoolers’ (N = 66) strategies for solving a range of visual repeating pattern tasks. An analysis of the kinds of patterning tasks preschoolers encounter, such as duplicating, extending, and transferring patterns to superficially different materials, suggested the tasks could be solved using either a one-to-one appearance matching strategy or a relational similarity strategy. In the present study, preschoolers completed a series of patterning tasks and their strategies were examined by analyzing (1) accuracy, (2) errors, and (3) the relation of visuospatial short-term memory, working memory, and inhibitory control to accuracy and errors. The pattern of results indicated that preschoolers do use both kinds of strategies, but that the frequency with which they use each strategy depends on task complexity. Preschoolers tended to use an appearance matching strategy on duplicate and extend tasks and a relational similarity strategy on transfer tasks. Implications for understanding what patterning instruction is most likely to support relational reasoning are discussed.

[1]  Xiao-Li Meng,et al.  Comparing correlated correlation coefficients , 1992 .

[2]  R. Kessels,et al.  The Corsi Block-Tapping Task: Standardization and Normative Data , 2000, Applied neuropsychology.

[3]  R. Gelman,et al.  Preschoolers' counting: Principles before skill , 1983, Cognition.

[4]  C. Wood,et al.  The Role of Relational Reasoning in Children's Addition Concepts. , 2007 .

[5]  Jillian L. Fox,et al.  Child-Initiated Mathematical Patterning in the Pre-Compulsory Years. , 2005 .

[6]  R. Siegler,et al.  Individual differences and adaptive flexibility in lower-income children's strategy choices , 1993 .

[7]  J. Sarama,et al.  Early Childhood Mathematics Education Research: Learning Trajectories for Young Children , 2009 .

[8]  Megan M. McClelland,et al.  A structured observation of behavioral self-regulation and its contribution to kindergarten outcomes. , 2009, Developmental psychology.

[9]  Jo-Anne LeFevre,et al.  The role of working memory in mental arithmetic , 2004 .

[10]  Maria Chiara Passolunghi,et al.  The relationship between working memory, IQ, and mathematical skills in children , 2011 .

[11]  Kelly S. Mix,et al.  Surface similarity and label knowledge impact early numerical comparisons , 2008 .

[12]  Jillian Waters,et al.  Mathematical Patterning in Early Childhood Settings , 2004 .

[13]  J. Mason Expressing Generality and Roots of Algebra , 1996 .

[14]  G. Halford Children's Understanding: The Development of Mental Models , 1993 .

[15]  Ronald H. Heck,et al.  An Introduction to Multilevel Modeling Techniques , 1999 .

[16]  R. Siegler Emerging Minds: The Process of Change in Children's Thinking , 1996 .

[17]  A. Orsini Corsi's Block-Tapping Test: Standardization and Concurrent Validity with WISC—R for Children Aged 11 to 16 , 1994, Perceptual and motor skills.

[18]  Lynn S. Fuchs,et al.  The Prevention, Identification, and Cognitive Determinants of Math Difficulty. , 2005 .

[19]  John Seely Brown,et al.  Diagnostic Models for Procedural Bugs in Basic Mathematical Skills , 1978, Cogn. Sci..

[20]  Emily R. Fyfe,et al.  Emerging Understanding of Patterning in 4-Year-Olds , 2013 .

[21]  U. Goswami Analogical Reasoning: What Develops? A Review of Research and Theory. , 1991 .

[22]  Kelly S. Mix,et al.  The construction of number concepts , 2002 .

[23]  K. Singer-Freeman Analogical Reasoning in 2-Year-Olds: The Development of Access and Relational Inference. , 2005 .

[24]  D. Gentner,et al.  Comparison and Categorization in the Development of Relational Similarity , 1996 .

[25]  D. Gentner,et al.  Language and the career of similarity. , 1991 .

[26]  Kelly S. Mix,et al.  It's All Relative: Different Levels of Relational Similarity Used in Children's Comparisons. , 2008 .

[27]  Elizabeth Warren,et al.  Using Repeating Patterns to Explore Functional Thinking , 2006 .

[28]  Megan M. McClelland,et al.  Touch your toes! Developing a direct measure of behavioral regulation in early childhood , 2008 .

[29]  S. Calkins,et al.  Regulatory Contributors to Children's Kindergarten Achievement , 2003 .

[30]  Robert Bickel,et al.  Multilevel analysis for applied research , 2013 .

[31]  S. Wiebe,et al.  Short-Term Memory, Working Memory, and Executive Functioning in Preschoolers: Longitudinal Predictors of Mathematical Achievement at Age 7 Years , 2008, Developmental neuropsychology.

[32]  Frederick J. Morrison,et al.  Early gender differences in self-regulation and academic achievement. , 2009 .

[33]  Psychology and Mathematics Education , 1999 .

[34]  P. Alexander,et al.  Relational Reasoning and Its Manifestations in the Educational Context: a Systematic Review of the Literature , 2013 .

[35]  Sharon M. Carver,et al.  Teaching Math to Young Children. Educator's Practice Guide. What Works Clearinghouse. NCEE 2014-4005. , 2013 .

[36]  Martha W. Alibali,et al.  Knowledge Change as a Function of Mathematics Experience: All Contexts are Not Created Equal , 2005 .

[37]  Catherine Sophian,et al.  Early Developments in Children's Understanding of Number: Inferences about Numerosity and One-to-One Correspondence. , 1988 .

[38]  L. Fuchs,et al.  Contributions of domain-general cognitive resources and different forms of arithmetic development to pre-algebraic knowledge. , 2012, Developmental psychology.

[39]  Susan E. Gathercole,et al.  Working memory assessments at school entry as longitudinal predictors of National Curriculum attainment levels , 2003, Educational and Child Psychology.

[40]  Joanne Mulligan,et al.  The Growth of early mathematical patterning: an intervention study , 2007 .

[41]  T. Cooper,et al.  Repeating Patterns and Multiplicative Thinking: Analysis of Classroom Interactions with 9 -Year- Old Students that Support the Transition from the Known to the Novel , 2007 .

[42]  M. Pe,et al.  Are patterns important? An investigation of the relationships between proficiencies in patterns, computation, executive functioning, and algebraic word problems , 2011 .

[43]  M. Lezak Neuropsychological assessment, 3rd ed. , 1995 .

[44]  Didi Suryadi,et al.  Open-ended Approach: an Effort in Cultivating Students' Mathematical Creative Thinking Ability and Self-esteem in Mathematics , 2016 .

[45]  B. Rittle-Johnson,et al.  Developing Conceptual Understanding and Procedural Skill in Mathematics: An Iterative Process. , 2001 .

[46]  Elida V. Laski,et al.  Learning from number board games: you learn what you encode. , 2014, Developmental psychology.

[47]  Jeff Shrager,et al.  SCADS: A Model of Children's Strategy Choices and Strategy Discoveries , 1998 .

[48]  Nancy Eisenberg,et al.  Effortful control: Relations with emotion regulation, adjustment, and socialization in childhood. , 2004 .

[49]  R. Glaser,et al.  Cognitive Variables in Series Completion. , 1983 .

[50]  M. Mitchelmore,et al.  Awareness of pattern and structure in early mathematical development , 2009 .

[51]  Robert Krikorian,et al.  Developmental Normative Data for the Corsi Block-Tapping Task , 2006, Journal of clinical and experimental neuropsychology.

[52]  Julie K. Kidd,et al.  Effects of Patterning Instruction on the Academic Achievement of 1st-Grade Children , 2013 .

[53]  R. Siegler The perils of averaging data over strategies: An example from children's addition. , 1987 .

[54]  C. Papagno,et al.  Verbal and spatial immediate memory span: Normative data from 1355 adults and 1112 children , 1987, The Italian Journal of Neurological Sciences.

[55]  A. Miyake,et al.  Models of Working Memory: Mechanisms of Active Maintenance and Executive Control , 1999 .

[56]  M. Mitchelmore,et al.  Assessing the Development of Preschoolers' Mathematical Patterning , 2011 .

[57]  M. Pe,et al.  The cognitive underpinnings of emerging mathematical skills: executive functioning, patterns, numeracy, and arithmetic. , 2012, The British journal of educational psychology.

[58]  Priti Shah,et al.  Models of Working Memory: Models of Working Memory: An Introduction , 1999 .

[59]  C. Raver,et al.  Preliminary Construct and Concurrent Validity of the Preschool Self-Regulation Assessment (PSRA) for Field-Based Research. , 2007 .

[60]  Lindsey E. Richland,et al.  Early Executive Function Predicts Reasoning Development , 2013, Psychological science.

[61]  Lynn S. Fuchs,et al.  The cognitive correlates of third-grade skill in arithmetic, algorithmic computation, and arithmetic word problems , 2006 .

[62]  K. Holyoak,et al.  The role of working memory in analogical mapping , 2000, Memory & cognition.

[63]  Timothy J. Robinson,et al.  Multilevel Analysis: Techniques and Applications , 2002 .

[64]  D. Gentner,et al.  More evidence for a relational shift in the development of analogy: Children's performance on a causal-mapping task , 1998 .

[65]  Dedre Gentner,et al.  Mechanisms of Analogical Learning. , 1987 .

[66]  Tracy Packiam Alloway,et al.  Verbal and visuospatial short-term and working memory in children: are they separable? , 2006, Child development.

[67]  Lyn English,et al.  Analogical reasoning and the development of algebraic abstraction , 1996 .

[68]  Patricia A. Alexander,et al.  Analogical reasoning in young children. , 1987 .

[69]  Marina Papic,et al.  Promoting Repeating Patterns with Young Children - More Than Just Alternating Colours! , 2007 .

[70]  Jillian L. Fox Connecting algebraic development to mathematical patterning in early childhood , 2006 .

[71]  Lieven Verschaffel,et al.  Children's solution processes in elementary arithmetic problems: Analysis and improvement. , 1981 .

[72]  Elizabeth S. Spelke,et al.  Toward exact number: Young children use one-to-one correspondence to measure set identity but not numerical equality , 2014, Cognitive Psychology.

[73]  Hendrik Radatz,et al.  Error Analysis in Mathematics Education. , 1979 .

[74]  R. Kessels,et al.  The Backward Span of the Corsi Block-Tapping Task and Its Association With the WAIS-III Digit Span , 2008, Assessment.

[75]  Mary K. Hoard,et al.  Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability. , 2004, Journal of experimental child psychology.