In this chapter, we want to review and discuss the research on how students in secondary
schools can develop the ability to solve a wide variety of complex problems. We will also
address how instruction can best develop this ability. A fundamental goal of all
instruction is to develop skills, knowledge, and abilities that transfer to tasks not
explicitly covered in the curriculum. Should instruction emphasize the particular problem
solving techniques or strategies unique to each task? Will problem solving be enhanced
by providing instruction that demonstrates or develops problem solving techniques or
strategies useful in many tasks? We are particularly interested in tasks that require
mathematical thinking (34) or higher order thinking skills (17). Throughout the chapter,
we have chosen to separate and delineate aspects of mathematics problem solving when
in fact the separations are pretty fuzzy for any of us.