Granberg (2016) distinguishes between productive struggle and unproductive struggle; the latter she explains occurs when “their struggles did not provide any useful knowledge for solving the problem” (Journal of Mathematical Behavior, p. 44). She found that the students in her study were engaged in unproductive struggle initially, and all but two were able to convert from unproductive struggle to productive struggle. These two perhaps could not tap into their previous knowledge to construct new knowledge because the problems were too challenging and outside of their zone of proximal development. Granberg concludes that teachers should discuss with their students the differences between productive and unproductive struggle.
Granberg (2016) suggests that students may not engage in productive struggle if the problems are outside of their zone of proximal development. However, some students, such as ELLs, may not engage in productive struggle not because the mathematics is outside of their zone of proximal development, but because they struggle to make sense of problems in monolingual classrooms. Murrey (2008) explains that it may be necessary to provide ELLs with access to content by scaffolding the English, but the ma...
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...otsky maintains that students learn best when they are trying to solve problems that are too challenging for them to solve on their own but possible for them to solve with appropriate supports. The National Council of Teachers of Mathematics (2014) states that it is imperative for teachers to have high expectations for all students so they provide them problems that are within this zone. They say that too often teachers have low expectations for certain students and offer these students mathematical problems below their zone of proximal development. Teachers who have low expectations for students also tend to wait less time for those students to make sense of problems and persevere to solve them (Kilpatrick et al., 2001). Therefore, it seems apparent that students will be more successful if their teachers have high expectations for their capabilities in mathematics.
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