Teaching Mathematics in the Context of Meaning and Application

Marilyn Burns (1992) explores the tension that teachers face between teaching "what to do" versus "what to do and why." She poses the question "why is the practice of teaching the procedures of mathematics detached from meaning and applications of these procedures so pervasive in schools?" There are a host of reasons that support the emphasis on teaching procedures, and these reasons have to be considered and understood by school improvement teams before any widespread change in this practice will occur. But let's explore some of the reasons for teaching arithmetic in the context of meaning and application, of teaching the "why" as well as the "what to do" in mathematics. According to Burns (1992), these reasons are important to consider:

When you understand why, your understanding and skills can be applied more easily to new tasks.
Learning the meaning in arithmetic procedures makes them easier to remember.
Learning to reason is a goal effective in itself and leads to the continued support of learning.

Burns describes that "the true measure of the failure of teaching only the `what to do' is the feeling of mathematical incompetence and negativity toward mathematics experienced by so many otherwise highly educated people. This rejection of mathematics, sadly so common, is a clear indication that something is very wrong. It is not possible to appreciate something you do not truly understand, and the charge to teachers is a crucial one -- to teach mathematics so that children are encouraged to make sense out of all they learn to do."(p.151-152)

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