An Approach to Geometric and Numeric Patterning that Fosters Second Grade Students’ Reasoning and Generalizing about Functions and Co-variation

  • Joan MossEmail author
  • Susan London McNab
Part of the Advances in Mathematics Education book series (AME)


In this chapter, we present illustrations of second grade students’ reasoning about patterns and two-part function rules in the context of an early algebra research project that we have been conducting in elementary schools in Toronto and New York City. While the study of patterns is mandated in many countries as part of initiatives to include algebra from K-12, there is a plethora of evidence that suggests that the route from patterns to algebra can be challenging even for older students. Our teaching intervention was designed to foster in students an understanding of linear function and co-variation through the integration of geometric and numeric representations of growing patterns. Six classrooms from diverse urban settings participated in a 10–14-week intervention. Results revealed that the intervention supported students to engage in functional reasoning and to identify and express two-part rules for geometric and numeric patterns. Furthermore, the students, who had not had formal instruction in multiplication prior to the intervention, invented mathematically sound strategies to deconstruct multiplication operations to solve problems. Finally, the results revealed that the experimental curriculum supported students to transfer their understanding of two-part function rules to novel settings.


Word Problem Function Rule Geometric Pattern Position Number Algebraic Thinking 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of Human Development and Applied Psychology, Ontario Institute for Studies in EducationUniversity of TorontoTorontoCanada
  2. 2.Ontario Institute for Studies in EducationUniversity of TorontoTorontoCanada

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