Examining the use of non-routine problems to supplement instruction in secondary mathematics classes: Case study findings

“In the three decades since the 1980 publication of An Agenda for Action, the National Council of Teachers of Mathematics (NCTM) has consistently advocated a coherent prekindergarten through grade 12 mathematics curriculum focused on mathematical problem solving” (NCTM, 2009, p. xi). Despite a call for secondary mathematics students to be involved daily in the kind of problem-solving work that focuses on reasoning and sense making, that is not what is typically seen when U.S. classrooms are observed. Instead, the students are given tasks requiring only lower-order thinking skills, such as memorizing algorithms and practicing them in numerous similar numerical and word problems. Possible causes for the discrepancy have been offered: textbooks lacking in non-routine problem solving tasks; testing associated with the No Child Left Behind legislation and the pressure to “teach to the test;” a model of teaching so ingrained that it is extremely resistant to change. Could there be other factors involved? This descriptive case study examined the beliefs and teaching practice of 27 secondary mathematics teachers regarding non-routine problem solving in the context of national reform standards. Of interest in this study were the participants collectively, as this group was homogeneous in terms of demonstrating a high degree of professionalism, an interest in instructional innovation, and an appreciation for the value of problem solving in mathematics teaching. For that reason this intrinsic study used questionnaire data to select a subsample of participants whose responses indicated teaching practice most consistent with the reforms, as well as familiarity and agreement with proposed national mathematics standards (NCTM, 2000). Case studies with this group of 5 participants elaborated on the questionnaire with semi-structured interviews used to explore the complexity of factors that comprised their instructional choices