Essay On The Difference Between Productive And Unproductive Struggle

Students learn mathematics with deeper meaning when they engage in productive struggle--grappling to make sense of problems (Hiebert & Grouws, 2007). Warshauer (2014) adds that teachers can engage students in productive struggle by asking them questions instead of telling them the answers; questioning can help students organize their thoughts as they struggle to make sense of problems. Teachers should increase the cognitive load by refraining from giving students too much help when solving problems (Hiebert & Grouws).
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

Larson et al. (2012) maintain that having a productive disposition is related to persevering to solve problems. Productive disposition is defined by Kilpatrick et al. (2001) as “habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy” (p. 5). Kilpatrick et al. report that students are excited about mathematics when they first come to school but that, unfortunately, our present school system is making most students lose this disposition. They call for teachers to change their practices to make mathematics more