Creativity, flexibility, adaptivity, and strategy use in mathematics

Flexible and adaptive use of strategies and representations in mathematics education

“…As already mentioned above, the part of this issue dealing with adaptive use of strategies concludes with a commentary article by Selter (2009), wherein he discusses the different contributions against the background of the existing theories and points to new directions for future research.…”

Profiles of Cognitive Flexibility in Arithmetic Reasoning: A Cross-Country Comparison of German and American Elementary Students

“…In a similar vein, Verschaffel, Luwel, Torbeyns, and Van Dooren (2009) prefer a distinction between "flexibility," to describe the use of multiple strategies, and "adaptivity," for the actual selection of appropriate strategy choices. In this vein, Selter (2009) extended the idea of "adaptivity" to creatively develop and select for use an "appropriate strategy." In marked contrast, another group of researchers has contended that flexibility consists of choosing among different strategies simply on the basis of the characteristics "… wherein strategy flexibility is conceived as selecting the strategy that brings the child most quickly to an accurate answer to the problem" (Torbeyns et al, 2009, p. 583).…”

“…Critical to the effective use of mental strategies is cognitive flexibility, an attitude of mind that is both adaptive and agile. In this context, the past decade has seen significant gains in our understanding of mental processes that contribute to or make up mental flexibility (Grüßing, Schwabe, Heinze, & Lipowsky, 2013;RathgebSchnierer & Green, 2013;Selter, 2009;Threlfall, 2009). In addition, new approaches have been invented for conducting empirical research on mentally flexible strategies and procedures (Rathgeb-Schnierer & Green, 2013Threlfall, 2009;Torbeyns, De Smedt, Ghesquière, & Verschaffel, 2009).…”

Teaching and Learning About Whole Numbers in Primary School

“…This has led to multiple and sometimes inconsistent perspectives on the concept (Star and Newton 2009). These varying definitions have resulted in different ways of operationalizing the concept (see, for example, Verschaffel et al 2009;Torbeyns et al 2009a;Selter 2009;Threlfall 2002; Rathgeb-Schnierer and Green 2013). There has been some consensus among all the definitions on the idea that flexibility in mental calculation includes two central features: the knowledge of different solution methods and the ability to adapt them appropriately when solving a problem.…”

“…Recent studies reported in the field of flexible mental calculation reflect not only different interests and aims, but also different definitions of flexibility, which influence both the research methods used and data interpretation. These various definitions of flexibility also lead to different emphases in teaching, with the aim of promoting flexibility in mental calculation (Selter 2009;Threlfall 2009). According to Threlfall, "The assumption that it is all a matter of strategic choice will lead to very different conclusions about appropriate action from the perspective that presumes the importance of conceptual understanding and thinks of some kind of calculating as 'zeroing in' on solutions" (2009, p. 552).…”