2013 Conference Proceedings - University of Nevada, Las Vegas

elied on additive strategies for all problem types, while the students in the later years usedmethods more appropriate to the problem. In the intervening years, however, the students tendedto use strategies that were genetic hybridizations of previous approaches, trying multiplestrategies and adapting as needed to deal with the specific numbers in a problem.Agostino, Johnson, and Pascual-Leone (2010) studied whether children approach differenttypes of single-step and multiple-step multiplicative reasoning problems (scalar, array,combinatorial, or proportion) with different strategies. The researchers applied cognitivepsychology principles that describe the general information processing skills being used as eitherrelated to inhibition, updating, shifting or mental attention capacity. While these are largelyinternal processes, relating to how the various executive functions are used, inhibition is relatedto a person’s ability to stifle immediate responses to environmental cues in order to provide theother functions time to operate. All four components have been shown to relate to mathematicalability. Shifting refers to one’s ability to jump easily between sets of information or problemtasks; this ability seems crucial if one is to enact a hybridization of existing strategies. Moresignificantly, the authors show that age mediates the degree to which all of four factors play arole in problem solving, showing the evolution of children’s multiplicative thinking over time.Throughout GLP, the environment plays a crucial role in providing problem solvers access tothe problem, access to other ideas about the problem and feedback about their solutions. This cancome in the form of interpersonal communication, as it did for Joy (Trowell, 2012) where suchexperiences help the problem solver shift from “getting an answer” to “learning how to solveproblems.” Joy describes her process interviews, referring to changing strategies and falling backon previous approaches just to try something different, demonstrating clearly her attempts tomutate and hybridize strategies. Her view of mathematics and problem solving as very personalis a clear expression of the unique evolutionary path that each learner will generate in theabsence of a single, universal law of what constitutes a “best solution strategy” similar to theway organisms develop uniquely from one another based on countless contingent events inevolutionary time.ConclusionsA genetic learning approach, then, provides insight into the dynamics of learning, and hencecan guide teachers’ approaches to formative assessment and designing classroom learningenvironments. Taking a GLP approach to formative assessment requires teachers to look beyondProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 195