I hear people talk a lot about the importance of context in mathematics....usually, I think, for all the wrong reasons. There is a common misconception that if we show students how they can "use math" that they will find it more enjoyable and see the value in learning it in school. I'm pretty sure the problem isn't that students really want to know how this stuff is valuable in usage. The problem, I think, is that when the subject is relegated to procedures/facts/tricks it often disrupts the way a student naturally thinks.
By it's very name, this approach implies that we are "applying" something. Usually, there is a mathematical topic presented and then problems are selected in which students have to apply what they have learned to solve these problems. Sometimes, the problem might come first and then topics are presented (as facts) to provide students with the "tools" necessary to solve a problem ("necessitating" content). The focus here is on math as a tool to solve a problem. The assumption is that the mathematics exists before, and inspires, the problem.
Doing math is an act of creation by students. Usually, there is a problem/task/situation that requires students to think in the form of reflective abstraction
. Mathematical "facts" arise as generalizations students make by looking for patterns and consistencies. These facts might, then, be explored in the abstract. The focus here is on problems as an entry to creating mathematics. The assumption is that the problem exists before, and inspires, some
mathematics (I say "some" because although that may be anticipated by the teacher, it is ultimately defined by the students).
As I see it, yes, context is important but not to show students how they can use math. The context is important to show students how their mathematics is a natural extension of how they think and live in the world. Constance Kamii
says it best:"Most math educators think about verbal problems (word problems) as applications of computational 'skills,' rather than as the beginning point that eventually leads to generalized computation, without content, context, or practical purpose."
Kamii, C. (1985). Young children reinvent arithmetic: Implications of Piaget's theory. New York, NY: Teachers College Press.