This study explores ways in which sixth graders without prior formal algebra instruction attempt to generalize algebraic growing patterns. In a teaching experiment setting, two pairs of students solved the growing pattern tasks while having access to a variety of manipulatives from which they could choose. Using multimodal analysis, two different levels of the students’ generalization skills were highlighted: (a) recursive-local and (b) functional-global generalization. Multimodality is an interdisciplinary approach to discourse analysis that treats communication and forms of representation to be more than about language and gestures. This theory defines communication practices in relation to the linguistic, written, auditory, spatial, haptic, and visual resources—or modes—used to communicate ideas. The findings suggest that students who immediately used manipulatives to model the patterns have not developed the skills to move from the concrete recursive-local stage to the abstract functional-global stage. The students with spatial thinking skills and strong number sense arrived at the functional-global stage without the help of concrete materials. Implications of these findings point to the importance of training elementary students in number sense to enable them for a successful start into formal algebra.
|Advisor:||Fernandes, Anthony, Stephan, Michelle|
|Commitee:||Cifarelli, Victor, Pugalee, David|
|School:||The University of North Carolina at Charlotte|
|Department:||Curriculum & Instruction|
|School Location:||United States -- North Carolina|
|Source:||DAI-A 80/04(E), Dissertation Abstracts International|
|Subjects:||Mathematics education, Middle School education|
|Keywords:||Generalization strategies, Growing patterns, Manipulatives, Mathematics education, Mode affordances, Multimodality|
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