Investigating functional thinking in the elementary classroom: Foundations of early algebraic reasoning

Warren, Elizabeth; Cooper, Tom; Lamb, Janeen

doi:10.1016/j.jmathb.2006.09.006

Cited by 57 publications

(75 citation statements)

References 8 publications

(8 reference statements)

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“…Forty-five Australian children (mean age 8.5 years) were taught "growing" patterns in a study reported by Warren and Cooper (2008) and also by Warren, Cooper, and Lamb (2006). These were geometric patterns which could be extended according to some rule.…”

Section: Instruction On Complex Patternsmentioning

confidence: 99%

Empirical Studies of Patterning

Pasnak¹

2017

PSYCH

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Young children have been taught simple sequences of alternating shapes and colors, referred to as "patterning", for the past half century in the hope that their understanding of prealgebra and their mathematics achievement would be improved. The evidence that such patterning instruction actually improves children's academic achievement is scanty. However, recent research shows that instruction on more complex patterns produces advances in both mathematics and reading achievement. Patterning instruction should change accordingly. Further research is needed to assess the cognitive mechanisms involved, which children benefit from such instruction, and the patterns that will produce the greatest gains.

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Section: Instruction On Complex Patternsmentioning

confidence: 99%

Empirical Studies of Patterning

Pasnak¹

2017

PSYCH

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“…As mentioned above, the questionnaires were distributed to three separate groups at the same time, in accordance with the cross-section approach. This method does not seek to monitor development over time as in previous studies, such as Krebs (2003), Lanin et al (2006), Steele (2005), Warren et al (2006).…”

Section: Data Sourcesmentioning

confidence: 99%

“Rising to the challenge”: using generalization in pattern problems to unearth the algebraic skills of talented pre-algebra students

Amit

Neria

2007

ZDM Mathematics Education

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This study focuses on the generalization methods used by talented pre-algebra students in solving linear and non-linear pattern problems. A qualitative analysis of the solutions of three problems revealed two approaches to generalization: recursive-local and functional-global. The students showed mental flexibility, shifting smoothly between pictorial, verbal and numerical representations and abandoning additive solution approaches in favor of more effective multiplicative strategies.

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Section: Introductionmentioning

confidence: 99%

“…This subject matter has been taught across the USA for the last half-century, and many educators still view it as a necessary foundation for elementary school mathematics (National Council of Teachers of Mathematics, 1993; National Association for the Education of Young Children/National Council of Teachers of Mathematics Education, 2002/2010). Patterning is thought to improve young children's understanding of mathematics (Baroody, 1993; Clements &Sarama, 2007, a,b,c; Threfall,1993;Warren, Cooper, & Lamb, 2006); however, empirical evidence that instruction in patterning contributes to young children's understanding of mathematics is sparse.The limited research supporting the importance of patterning instruction for children's mathematical development includes a recent longitudinal study done by Fyfe, Rittle-Johnson, Hofer and Farren (2015). Significant regression coefficients (.17-.18) were found between children's performance on patterning measures as preschoolers and their performance on a mathematical composite score.…”

mentioning

confidence: 99%

The Effects of in-class tutoring of Kindergarteners on Patterning, Reading, or Mathematics

Shriver¹,

Lauderdale²,

Yassa³

et al. 2017

JEHD

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Kindergarten students were pretested on the Dynamic Indicators of Basic Early Literacy Skills (DIBELS), the Assessment of Basic Language and Learning Skills -Revised (ABLLS-R), and Woodcock-Johnson III (WJ-III).Following testing, the students were randomly assigned to tutoring groups which focused on patterning, reading, mathematics or social studies (control IntroductionPatterning instruction (i.e., instruction focusing on the alternating presentations of colors, shapes, or objects) is traditionally a part of early childhood education. Such instruction begins with simple ababab patterns such as red blue red blue red blue, and becomes increasingly complex. This subject matter has been taught across the USA for the last half-century, and many educators still view it as a necessary foundation for elementary school mathematics (National Council of Teachers of Mathematics, 1993; National Association for the Education of Young Children/National Council of Teachers of Mathematics Education, 2002/2010). Patterning is thought to improve young children's understanding of mathematics (Baroody, 1993; Clements &Sarama, 2007, a,b,c; Threfall,1993;Warren, Cooper, & Lamb, 2006); however, empirical evidence that instruction in patterning contributes to young children's understanding of mathematics is sparse.The limited research supporting the importance of patterning instruction for children's mathematical development includes a recent longitudinal study done by Fyfe, Rittle-Johnson, Hofer and Farren (2015). Significant regression coefficients (.17-.18) were found between children's performance on patterning measures as preschoolers and their performance on a mathematical composite score. Another correlational study done by White, Alexander, and Daugherty (1998) found a strong correlation (.56) between preschoolers' ability to extend alternating patterns and their scores on analogical reasoning as measured by the Georgia Kindergarten Assessment Program (GKAP). Both of these studies support the conclusion that an early understanding of alternating patterns is related to later mastery of mathematics. However, there was no instructional component to these studies, and correlational studies alone cannot prove causality. A more direct approach is to instruct children in patterning and to then measure the resulting benefits on mathematical ability.

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Investigating functional thinking in the elementary classroom: Foundations of early algebraic reasoning

Cited by 57 publications

References 8 publications

Empirical Studies of Patterning

Empirical Studies of Patterning

“Rising to the challenge”: using generalization in pattern problems to unearth the algebraic skills of talented pre-algebra students

The Effects of in-class tutoring of Kindergarteners on Patterning, Reading, or Mathematics

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