Posted on Mar. 14th 2007 | Comments Off
Investigators: Roy Pea, Shelley Goldman, A. Booker, K. Blair, I. Esmonde, O. Jimenez, L. Martin
Institution: Stanford University
Figure 1. Four families discussing their everyday uses of math
Project and Outcomes Description:
Professors Pea and Goldman and their NSF-funded team at Stanford University have discovered new insights about the nature of mathematical activities and learning opportunities at home in family life. This is important because of the oft-observed difficulties for many students of becoming engaged in mathematics or bridging their everyday knowledge productively into school. We have studied 20 diverse families that include middle schoolers (74 participants, including 38 children), and identified the diverse contexts that serve as locations for their cultural practices of mathematics use and learning. Mathematical activities are widespread in daily life–arts & crafts, events planning, budgeting & finance, cooking, games, hobbies, home improvement, keeping in touch, music, school homework, shopping, sports, time management, travel, and adult work at home. We established inter-rater reliability for definitions of 20 different types of mathematics employed in these activities (e.g., algebra; data analysis; decimals; fractions; proportional reasoning).
From analyses of over 300 different mathematical problems described, we find that family mathematics varies considerably from the structure of school mathematics: (1) Problems emerge out of motivated needs and are resolved adaptively with division of labor and uses of tools and distributed resources; (2) Complex interacting values, such as minimizing effort–but also cost and error–guide problem solving processes and outcomes; (3) Satisficing rather than optimal solutions are commonplace; (4) Multiple kinds of mathematics are used at once, interwoven for the needs at hand (e.g., measurement, arithmetic, geometry, proportional reasoning), rather than single topics within a subject as in school.
These results have important implications for mathematics education. It will be important to systematically explore home-school connections to find new design opportunities for bridging home-based funds of knowledge and formal learning environments. We need to develop and research pedagogical models that can productively leverage learners’ experiences with these features of mathematics out of school.