“It’s not complicated, faster is better!” If you believe the AT&T commercials faster is always better and for years we have taught math using that same theory! We taught procedures and gave daily timed math facts tests to ensure students would become faster and faster at “doing” math. We celebrated two things; the correct answer and arriving at it quickly or automatically. Through our efforts a small segment of our population was congratulated and made to believe they were our best and brightest. They were true mathematicians! But for a much larger group of people we proved just the opposite. The message was sent; you either were a mathematician or you weren’t.
The Common Core State Standards want to change that perception for our teachers, our students, and our population as a whole. Mathematics can be learned by all. Speed is not the end-all, be-all. The standards for mathematics stress two components: conceptual understanding and fluency.
The standards emphasize the need for fluency, which is not to be misinterpreted as speed, a great deal. Fluency, in the standards, is described as an understanding of the meaning of operations and their relationships to each other, the knowledge of number relationships, and a thorough understanding of the base ten number system. There are standards that call specifically for fluency with addition and multiplication facts and with standard algorithms, but this fluency is to come after adequate groundwork involving work with strategies and algorithms based on place value and the properties of operations has occurred.
According to William McCallum, author of the common core for math, “…being fluent in math refers to knowing how to do a calculation, whereas to know from memory means being able to produce the answer when prompted without having to do the calculation” (blog 9/4/12). On the topic of timed tests for basic facts, Marilyn Burns writes in About Teaching Mathematics, “…timed tests do not measure children’s understanding…It doesn’t ensure that students will be able to use the facts in problem-solving situations. Furthermore, it conveys to children that memorizing is the way to mathematical power, rather than learning to think and reason to figure out answers” (2000, p. 157). Accordingly, John A. Van de Walle states (2006), speed (using timed tests) “is effective only for students who are goal oriented and who can perform in pressure situations. The pressure of speed can be debilitating and provides no positive benefits.” He continues with the comment, “these timed tests should generally be avoided as they do not promote reasoned approaches to fact mastery. If there is any defensible purpose for a timed test of basic facts it may be for diagnosis – to determine which combinations are mastered and which remain to be learned. Even for diagnostic purposes there is little reason for a timed test more than once every couple of months” (pp. 95-96).
For this reason, the common core recommends that students master strategies for efficient fact retrieval prior to practicing the facts for fluency (accuracy and speed). In the end, fluency and automaticity are important. As students explore the conceptual understandings of more rigorous concepts, they need efficient methods for determining basic facts. However, fluency and speed should not be “the goal”, but one ingredient that leads to students’ success in meeting their year end math goals.
Bill McCallum: http://commoncoretools.me/author/wgmccallum/