Q: What is the role of "practice" in learning math?

A: When thinking about the role of practice in learning, it is important to consider when, what, and how we ask students to practice. Students should only practice a skill if they can associate it with its underlying concepts.  If a learner practices a skill to the point of automaticity but does not understand its related concepts, it can be very difficult for the learner to develop such understanding later (Brown, Roediger, & McDaniel, 2014). Practice should support the goal of developing a mathematical tool kit instead of aiming to automitize just one particular skill and applying that skill by rote (Brown, Roediger, & McDaniel, 2014; Hattie & Yates, 2014; Schwarz, 2016).  This means that when students practice, they should be practicing the decision-making skills involving in knowing when to apply one skill over another.  Take, for example, whole-number subtraction. Learners should practice recognizing when interpreting subtraction as missing addend (e.g., 312 - 280 = 280 + ? = 312) yields a much faster answer than interpreting the computation as take away (e.g., 312 - 3).  In the middle grades, learner should practice using the form of an equation as a tool for solving it (e.g., realizing that 2(x + 3) = 2x + 6 has infinite solutions) rather than learning to apply just one procedure by rote.  Finally, it may be beneficial for learners to practice more than just one skill at a time (Brown, Roediger, & McDaniel, 2014; Carey, 2015). Although we all have strong memories of repeating one skill over and over again until we'd mastered it, recent research suggests that this is not what's most beneficial.  Instead, it is better for learners to practice more than just one skill at a time. This type of mixed practice develops awareness of the characteristics that define a particular class of problems.  In turn, this awareness can lead to both retention of skill and the all-important learning trait of transfer.

And one final note... people often rely on analogous reasoning to advocate for repeated and regular practice in math class. They argue that just like throwing a football over and over again helps a football player and playing the same piece of music repeatedly helps a musician, so too does drill help a math student do math. I would offer a word of caution here and remind these advocates that behaviorism was rejected as a learning science because larning [x] does not always involve the same processes - or practice strategies - as learning [y]. If we are interested in helping students learn math well, we are always better off looking within the field of math ed research instead of beyond.

Nancy Anderson, EdD

Mathematics Teacher ~ Author ~ Consultant