2013 Conference Proceedings - University of Nevada, Las Vegas

connections are connections or relationships of mathematical ideas and representations fromtasks within and across mathematical domains and curricular areas. Moreover, makingconnections is the core of mathematical understanding. As Hiebert and Carpenter explained:The mathematics is understood if its mental representation is part of a network ofrepresentations. The degree of understanding is determined by the number andstrength of its connections. A mathematical idea, procedure, or fact is understoodthoroughly if it is linked to existing networks with stronger or more numerousconnections (p. 67).While potential benefits of early algebra and mathematical connections are widely reportedin literature, there is scarcity of research on classroom activities that show how teachers mayrealize these benefits and on how early algebra is a tool for mathematical connections. Thepurpose of this study is to contribute to research on creating classroom contexts for supportingstudents’ development of mathematical reasoning as recommended by Proulx and Berdnaz(2009). This paper addresses this research gap by reporting how elementary school teachersmade mathematical connections in their early algebra classes, thereby supporting students’beginning understanding of algebra, and understanding of other mathematical domains.Theoretical PerspectiveGreeno’s (1998) situative learning perspective informs this study. This perspective viewslearning as individuals’ construction of knowledge as they participate in communities ofpractice. Individuals’ constructed knowledge is a tool for and a product of participation incommunities. Since “individual mental structures certainly change as part of this learning”(Sawyer & Greeno, 2009; p.364), knowledge is transferrable from one community of practice toanother. That is, students’ impoverished understanding of algebraic ideas may reflect aspects ofthe communities in which they participated. “Situative approaches provide analyses focused oncoordination of actions of individuals with each other and with material and informationalsystems” (Anderson, Greeno, Reder & Simon, 2000; p.12). A more specific methodologicalimplication from this perspective is a focus on constraints and affordances of activity systems(Greeno, 2003). Affordances are aspects of an activity system that participants may use to reachtheir goals. Constraints structure the interaction between participants of a community andaffordances. Based on this framework, the situative research question for the current study is:What are the affordances and constraints for supporting understanding of mathematicalProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 180