Mathematical Learning

Abstract

Lehrer and Lesh review research in the psychology of mathematical learning and mathematics education through a genetic, developmental framework that reflects both cognitive and sociocultural perspectives on learning. The authors examine individual cognitive processes and sociocultural contexts that underscore mathematical thinking. Origins of mathematical learning are linked to the development of argument. The role of inscriptions, notations and symbolic patterns are reviewed as a distinct form of mathematical literacy. These ideas are applied to studies of geometry measurement that stress spatial visualization and to mathematical modeling. A final section presents implications for classroom learning and describes how to create a classroom culture that values mathematical explanation, thinking, and instructional design.

Awareness of pattern and structure in early mathematical development

“…For example, some research groups have advocated equal importance of geometric and measurement concepts that can support number concepts (van Nes, 2008), and some argue that measurement, which may incorporate geometry and spatial reasoning, can provide an alternative pathway to mathematics learning (Slovin & Dougherty, 2004;Lehrer & Lesh, 2003). Others advocate an approach to early mathematics learning focused on algebraic thinking, mathematical modelling, and data exploration that often cuts across other curriculum areas (Carraher et al, 2006).…”

Cooperative learning in mathematics: A study on the effects of the parameter of equality on academic performance. [Aprendizaje cooperativo en matemáticas: Un estudio de los efectos del parámetro de igualdad sobre el rendimiento académico]

“…These results have remained the same for every area of the educational curriculum, and very especially, for mathematics Hossain & Tarmizi, 2013;Lehrer & Lesh, 2013;Plass et al, 2013;Slavin & Lake, 2009;Suri, 2010), being this particular area of knowledge one of the most prolific in both manuals and compilations published (Davidson, 1990a;Sities & Buethe, 2010;Strebe, 2010), as well as in the different research carried out, something which has resulted in numerous research reports and hundreds of scientific and informative publications (Eisenhauer, 2007;Kagan & Kagan, 2005;Slavin et al, 2013).…”

“…The research which we have carried out derives from the widely proven premise that cooperative learning in any of its three interactive structures (collaboration, cooperation and tutoring) is superior to other classroom management strategies, and especially in the math class (Hossain & Tarmizi, 2013, Ke & Grabowski, 2007, Lehrer & Lesh, 2013, Nunnery, Chappell, & Arnold, 2013, Özsoy & Yildiz, 2004, Roseth, Johnson, & Johnson, 2008, Zakaria, Solfitri, Daud, & Abidin, 2013 for its evident influence on the generation mathematical reasoning (Booisen & Grosser, 2014). In fact, barring few studies which do not reveal differences between cooperation strategies and other types (Tracey, Madden, & Slavin, 2010), most works confirm that the cooperative organization in the math class it is indeed the teaching and learning structure which generates the best results in a highly relevant variable for this particular discipline: academic performance (Winne & Nesbit, 2010).…”

Designing Disruptions for Productive Hybridity: The Case of Walking Scale Geometry

“…The disruption invites agentive student participation in hybrid learning activity in which students otherwise may have been held accountable, implicitly or explicitly, to cultural tools (e.g., representational forms, discursive norms) determined by the teacher or curriculum. In the WSG case representational forms and practices, shown to be highly consequential for the development of mathematical reasoning (Hall & Greeno, 2008;Lehrer & Lesh, 2003), was the target of disruption.…”