Reflections on Practice: Selecting and Creating Mathematical Tasks: From Research to Practice

What features of a mathematics classroom really make a difference in how students come to view mathematics and what they ultimately learn? Is it whether students are working in small groups? Is it whether students are using manipulalives? Is it the nature of the mathematical tasks that are given to students? Research conducted in the QUASAR project, a five-year study of mathematics education reform in urban middle schools (Silver and Stein 1996). offers some insight into these questions. From 1990 through 1995, data were collected about many aspects of reform teaching, including the use of small groups; the tool that were available for student use, for example, manipulatives and calculators; and the nature of the mathematics tasks. A major finding of this research to date, as described in the article by Stein and Smith in the January 1998 issue of Mathematics Teaching in the Middle School , is that the highest learning gains on a mathematicsperformance assessment were related to the extent to which tasks were et up and implemented in ways that engaged students in high levels of cognitive thinking and reasoning (Stein and Lane 1996). This finding supports the position that the nature of the tasks to which students are exposed detennines what students learn (NCTM 1991), and it also leads to many questions that should be considered by middle school teachers.