Why do we use different levels of cognitive demand when creating tasks?
 

“Our focus on mathematical tasks is built on the idea that the tasks used in the classroom form the basis for students' learning (Doyle 1988). Tasks that ask students to perform a memorized procedure in a routine manner lead to one type of opportunity for student thinking; tasks that require students to think conceptually and that stimulate students to make connections lead to a different set of opportunities for student thinking (Stein & Smith, 1998, p. 269)." Using mathematical tasks that vary in difficulty are essential when differentiating classroom learning because it allows for students to move to the next level of understanding and provides the teacher with the opportunity to go more in-depth with their lessons while also covering the breadth of the curriculum.

 

It is important to note that each level of cognitive demand is associated with an intent for assessment, so a teacher would not give a student a high cognitive demand task with the intent of looking for an answer to a standard algorithm problem and vice versa. These tasks are in place to help "be more responsive to, and supportive of, students' attempts to reason and make sense of mathematics (Stein & Smith, 1998, p. 275)." "In particular, results from Stein and Lane (1996) suggest the importance of starting with high-level, cognitively complex tasks if the ultimate goal is to have students develop the capacity to think, reason, and problem solve (Smith & Stein, 1998, p. 344)." However, something that is also important to acknowledge is that teachers do not always agree on the degree of difficulty for tasks, especially for tasks within the Procedures without Connections and Procedures with Connections categories because the level of intensity is really dependent on the students' depth of understanding and knowledge of mathematical concepts.

 

This is valuable in the classroom not only for students but also for teachers. In research done by Margaret Smith and Mary Stein, teachers also found it to be a reflective tool for their lessons. “In our work, we have seen how the mathematics Tasks Framework can give teachers insight into the evolution of their own lessons. After teachers learned about the framework, they began to use it as a lens for reflecting on their own instruction and as a shared language for discussing instruction with their colleagues (Stein & Smith, 1998, p. 271).” Using this framework is especialy effective if done in cooperation with other teachers because they are able to give a fresh perspective on the difficulty of the task you are creating.