A set-oriented perspective (Lockwood, 2014) is a way of thinking about counting problems that emphasizes the importance of reasoning about the set of outcomes being counted. Research has shown that solving counting problems correctly can be difficult for students at all levels, and mathematics educators have sought to identify strategies and interventions to help students reason conceptually about combinatorial tasks. We suggest some aspects that need to be accounted for in the design of tasks, searching to support a deeper understanding of the formulas for combinations, and we offer some thoughts on possible details that may be added to Lockwood's model. Yet, a strong relationship seems to exist between counting processes and the formulas/expressions that translate the answers to the tasks. The results corroborate the relationships described in Lockwood's model. Data were collected through direct observation, videotaped lessons and several documents. Students worked in challenging and contextualized tasks in an inquiry-based teaching approach.
Supported on the premises of Realistic Mathematics Education and on Lockwood's model for students' combinatorial thinking. Whether it’s a Windows, Mac, iOS or Android operating system, you will still be able to bookmark this website.In this paper, we share the results of a teaching experiment involving a class of thirty-one 12 th graders (17-18 years-old), in northern Portugal, for 12 lessons of 90 minutes each, aimed at engaging them in the guided reinvention of the formulas for the basic combinatorial operations, focusing on combinations.
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