Problem solving as an instructional method: The use of open problems in technology problem solving instruction

Abstract

Problem solving is not only an instructional goal, but also an instructional method. As an instructional method it can be used to build new mathematical knowledge, to solve problems that arise in mathematics and in other contexts, to apply and adapt a variety of problem-solving strategies, and to monitor and reflect on the mathematical problem-solving processes. However, depicting complexity of thinking and learning processes in such environments offers challenges to researchers. A possible solution may be through multiple perspective. On one exemplary problem this instructional method will be demonstrated in a technological context including then behaviors, dispositions and knowledge observed as a result of problem solving investigations in a technological context. These are discussed from three different perspectives – students’, lecturer’s and researcher’s offering a rich portrait of a problem solving mathematical activity in a technological context. Implications for mathematics instruction at the secondary and tertiary level will be given at the end of report.