To Walk the Path or Collect the Chips: The Impact of Metaphors and Motions on Learning Integer Arithmetic

Julie Nurnberger-Haag

Effective instruction needs to be cognitively ergonomic, or fit the ways human brains work. To improve mathematics instruction we should assess how models for learning specific mathematics topics are cognitively ergonomic to design better models. Cognitive science research on conceptual metaphor and physical movement's influence on thinking could inform this work. By the term model, I mean the unique combination of representations (e.g., bingo chips or number lines) along with the particular words, physical motions, and processes students use with those representations. Although different models are used for integer arithmetic and understanding this topic is essential for most mathematics beyond middle school, pedagogical recommendations to address student difficulties have been contradictory, so new perspectives are needed. My dissertation will quantitatively and qualitatively compare the effects of two integer arithmetic models (chip and walk-it-off number line model) that draw on different conceptual metaphors. I will teach at least four intact classes using a pre-post-delayed-post design with random assignment of classes to models. I expect that affordances and constraints of the two models?different physical actions (consistent or inconsistent with mathematics) and conceptual metaphors (collecting objects, moving on a path, or measuring stick)?will affect how students reason and calculate, such that students find the walk-it-off model more cognitively ergonomic than a chip model for initial learning of some or all aspects of integer arithmetic. Broadly, this study should contribute to understanding students? cognitive processes to better understand why models may support or hinder specific aspects of learning mathematics topics.

About Julie Nurnberger-Haag

N/A