Balanced Assessment of Mathematical Performance
Alan Bell, Hugh Burkhardt, and Malcolm Swan
The implementation of higher-order thinking in the school mathematics curriculum depends on the provision of appropriate assessment material. Teachers' natural and laudable desire to see students succeed at public examinations is bound to be reflected in their teaching. Short, closed, stereotyped examination questions are bound to encourage imitative rehearsal and practice on similar tasks in the classroom. (WYTIWYG or "What You Test Is What You Get"). Conversely, a range of high-quality tasks that assess a broader range of skills will convey messages about the nature of the desired learning activities more powerfully than any analytic description. It is hard for teachers to adopt new teaching practices, even those that offer innovative learning experiences focused on higher- level skills, if the teacher cannot see how the skills acquired will be recognized in their students.
What are higher-order skills? First, they are those general strategies and domain-specific tactics that govern the choices of lower-level technical skills and concepts used in a given activity. They enable a student to deploy mathematical knowledge and techniques effectively. They include the ability over a range of domains to generalize, represent, abstract, prove, check, generate questions, test a hypothesis, or practice a skill. They also include the ability to formulate a question in mathematical terms, or in terms appropriate for solving a problem, and to interpret a mathematical