Nancy Anderson, EdD
Mathematics Teacher ~ Author ~ Consultant
Q: Is speed important in learning mathematics?
A: When talking about speed, it is important to address two separate areas: (a) the time it takes a learner to learn a new concept and (b) the time it takes a learner to solve a problem.
(a) The rate at which a learner comes to understand an idea in math is NOT related to the depth at which he or she understands that idea. For educators, this means abandoning the idea that the students who "get it" the fastest are the ones who understand a particular concept the best. For students, this means developing patience with one's own learning and not being deterred by those who appear to be working faster.
(b) The time it takes a learner to solve a problem is NOT an accurate indicator of how much that learner knows about the embedded mathematics. A math problem is only a problem if the learner reads the problem and thinks, "I'm not sure what to do here?" (If a student reads the problem and knows exactly what to do, it's not a problem, it's an exercise.) If a student takes a long time to solve a problem, it is entirely possible that the student is practicing invaluable habits of mind. For example, the student might be using "guess and check" and studying each guess to make increasingly more refined guesses. The student could be taking her or his time to truly understand the problem before digging in - a hallmark trait of effective problem solvers. On the other hand, the student could be taking a long time to solve the problem because they are struggling to recall or apply more basic math skills. Although there is not a linear relationship between skills and more complex mathematics, it is also true that our working memories are limited. As such, the more basic skill work that occupies a student's working memory, the less room she or he might have to focus on more sophisticated aspects of the problem (Bransford, Brown, & Cocking, 2000). But we don't know which of these is the case - whether their speed reflects depth of understanding or need for additional support - without looking at the student's work and discussing her or his ideas. But using speed as a proxy measure for this type of analysis -- and tagging fast as good - should always be avoided.