What matters when choosing tasks for students?

“Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.”  -Stein, Smith, Henningsen, & Silver, 2000

What are we doing today?

One of the biggest decisions we make as teachers is choosing the tasks our students will work on during class.  We use tasks from textbooks and the Internet.  We borrow tasks from colleagues or design our own.   No matter where the tasks originate from, the nature of tasks we select affects our students’ ideas about what it means to do mathematics.  Different tasks provide different opportunities for students to learn mathematics.

One way to think about how to select a task is by looking at the cognitive demand required by it.   Cognitive demand refers to the type of student thinking required to solve the task.   A group of researchers developed different categories of cognitive demands found in mathematical tasks.

Low-level cognitive demand tasks can be solved by memorization or by using procedures that don’t have meaning for students.  High-level tasks engage students in using procedures with attention to the reasoning behind them or in what they label “doing mathematics”–making conjectures, justifying, and interpreting.

After studying over 500 tasks in middle schools, the researchers found that the greatest gains in student achievement occurred in classrooms where teachers used high-level tasks and the cognitive demand of the task was maintained as students worked on the tasks.   It was also noted that although many tasks started out requiring high cognitive demands, the demands of the tasks often decreased as they were implemented in classrooms.

Of course, there is a lot more to think about when selecting tasks.  How do the tasks build on what your students already know?  How do the tasks engage students?   What particular mathematical concepts are fostered by the task?  But considering the level of thinking you want to foster in your students is a good place to start.

Want to know more?   Check out the research below.

Stein, M. K., & Lane, S.  (1996).  Instructional tasks and the development of student capacity to think and reason:  An analysis of the relationship between teaching and learning in a reform mathematics project.  Educational Research and Evaluation, 2(1), 50 – 80.

Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. Teachers College Press, 1234 Amsterdam Avenue, New York, NY 10027.