Students’ understanding of area: combining practical and mathematical knowledge with a real-world task
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Concept of Area, Real-World Context, Practical Knowledge, High School Mathematics EducationResumo
Real-world contexts in mathematics could be used as learning situations that allow students to combine their mathematical and contextual knowledge. This study explores what mathematical and contextual knowledge 15 eighth-graders brought to a packing task. Students worked on the task for three 45-minute periods of class. The classroom teacher led the implementation of the task, and the author, as participant-observer, was a supplemental guide. Students solved the task in different ways: applying the area formula, computing volume, and iterating an area unit. The analysis of students’ written work, audio recordings, and researcher’s field notes informed that students used their mathematical knowledge first, and after the teacher asked them about the context of the task, students started using their contextual knowledge. Students experienced disequilibrium when realizing that the formula for area gave them an answer that was inadequate for the context of the task. A discussion about the meaning of the context and the formula for area emerged. This study illuminates how tasks involving real-world contexts and the teacher’s role create opportunities for students to combine their contextual and mathematical knowledge. This article contributes to discussions about the use of real-world tasks in mathematics classrooms and their interaction with students’ knowledge.
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