Schwan Smith, M., and Stein, M.K. (1998). Selecting and creating mathematical tasks: From research to practice. Mathematics Teaching in the Middle School, 3(5), 344-350.
This article stresses the importance of thoughtfully selecting/assigning/creating mathematical tasks for students. The tasks presented to students should facilitate the intended learning, and to be sure that happens, teachers need to pay close attention to the level of cognitive demand tasks will potentially place on students. Low demand tasks may help students learn math facts and develop procedural fluency, but tasks with greater complexity and even procedural ambiguity have the potential to engage students in high level reasoning and connection-making.
It would be very interesting to have the "Task Sort" discussing with my own math department.
- Here's an example of a low-level task from my precalculus class:
Rewrite | pi - sqrt(5) | without the absolute value symbol.
- Here's an example of a high-level task from precalculus from one of our problem solving days:
A line tangent to a circle is a line that intersects a circle at one point and is perpendicular to the radius at the point of intersection.
The line 2x-3y=-11 is tangent to a circle at (2, 5).
The line 3x+2y=29 is tangent to the same circle at (7, 4).
Find the standard form equation of the circle.