Treffer: A Study of Grade Two Students Solving a Non-Routine Problem with Access to Manipulatives

Mathematical problem solving remains a struggle for many students today (Celebioglu et al., 2010; Englard, 2010; Gavaz et al., 2021; N. H. Lee et al., 2014; Yeo, 2011). Though intervention studies have reported measured impact on improving students' problem-solving abilities (Gavaz et al., 2021; Gidalevich & Kramarski, 2019; N. H. Lee et al., 2014), few studies examine how learners would approach a non-routine problem without learning problem-solving strategies in school (Celebioglu et al., 2010; Saygili, 2017; Yazgan, 2015; Yeo, 2011). The latter would complement instruction related to strategies by making known the entry point of young problem solvers. In this study, 10 Grade Two students in a neighborhood primary school in Singapore were individually engaged in solving a non-routine problem with access to manipulatives. Based on their mathematics instructional history in school, the students have not been introduced to the relevant problem-solving strategies related to the task. The study examines how the students approach and solve the problem. Findings revealed that all the ten students were able to solve the problem with eight of them using manipulatives to help them. The study recommends that prior to classroom teaching, teachers can invite students to share their problem-solving methods and demonstrate how formal notations can capture these mathematically. Appropriate manipulatives should also be made accessible during problem-solving lessons.

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