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  • Author or Editor: Angela Murphy Gardiner x
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Isil Isler, Tim Marum, Ana Stephens, Maria Blanton, Eric Knuth and Angela Murphy Gardiner

Engage your students in functional thinking—an important precursor to algebra—with this classroom activity.

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Ana Stephens, Maria Blanton, Eric Knuth, Isil Isler and Angela Murphy Gardiner

Researchers find that these classroom activities and instructional strategies support the development of third-grade students' algebraic thinking.

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Maria Blanton, Ana Stephens, Eric Knuth, Angela Murphy Gardiner, Isil Isler and Jee-Seon Kim

This article reports results from a study investigating the impact of a sustained, comprehensive early algebra intervention in third grade. Participants included 106 students; 39 received the early algebra intervention, and 67 received their district's regularly planned mathematics instruction. We share and discuss students' responses to a written pre- and post-assessment that addressed their understanding of several big ideas in the area of early algebra, including mathematical equivalence and equations, generalizing arithmetic, and functional thinking. We found that the intervention group significantly outperformed the nonintervention group and was more apt by posttest to use algebraic strategies to solve problems. Given the multitude of studies among adolescents documenting students' difficulties with algebra and the serious consequences of these difficulties, an important contribution of this research is the finding that—provided the appropriate instruction—children are capable of engaging successfully with a broad and diverse set of big algebraic ideas.

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Maria Blanton, Bárbara M. Brizuela, Angela Murphy Gardiner, Katie Sawrey and Ashley Newman-Owens

The study of functions is a critical route into teaching and learning algebra in the elementary grades, yet important questions remain regarding the nature of young children's understanding of functions. This article reports an empirically developed learning trajectory in first-grade children's (6-year-olds') thinking about generalizing functional relationships. We employed design research and analyzed data qualitatively to characterize the levels of sophistication in children's thinking about functional relationships. Findings suggest that children can learn to think in quite sophisticated and generalized ways about relationships in function data, thus challenging the typical curricular approach in the lower elementary grades in which children consider only variation in a single sequence of values.