Memorization Versus Memory
Within the math education community, a lot of confusion surrounds the word fluency. Yet Common Core State Standards call for fluency at each grade level.
Grades 2 and 3 standards specify that students know a standard “from memory,” phrasing which may further cloud our concept of fluency.
In the Ignite Talk “There IS a Difference,” K-5 math educator Graham Fletcher explains the subtle yet powerful difference between memorization and from memory.
Many of today’s adults practiced facts using flash cards. They drilled and drilled and drilled. For some, the effort appeared successful; they could rattle off their facts within the two-minute time limit. For other learners, memorization did not happen. Instead, they arrived at the conclusion that they were simply bad at math.
Fletcher suggests we take a closer look at the definitions of “fluency” and “from memory.” He reflects on the use of “fluency” within language arts where some students “read” 120 wpm with no understanding while others read at 80 wpm and can fully explain what they just read. He notes that fast does not equal fluent.
Rather, true fluency means that students have developed efficient, accurate, and flexible ways of learning.
Efficiency - Efficiency implies that the student does not get bogged down in many steps or lose track of the logic in the strategy. An efficient strategy is one that the student can carry out easily, keeping track of sub-problems and making use of intermediate results to solve the problem.
Accuracy - Accuracy depends on several aspects of the problem-solving process, among them, careful recording, the knowledge of basic number combinations and other important number relationships, and concern for double-checking results.
Flexibility - Flexibility requires the knowledge of more than one approach to solving a particular kind of problem. Students need to be flexible and choose an appropriate strategy for solving the problem at hand. They can use one method to solve a problem and another method to double-check the results.
But if memorization doesn't promote fluency--efficient, accurate, and flexible ways of learning--what does?
Fletcher suggests that it comes down to strategy. Memorization is void of strategy while learning facts “from memory” relies on strategy. When we practice strategies—when we use them repeatedly, practicing them over and over and over—they become automatic. Fletcher says, “Automaticity of a strategy can appear to be memorization…but it’s not.” Automaticity comes through “learning, repetition, and practice,” until it’s become a natural response. A student who can efficiently solve 6 x 7 by knowing that 6 x 6 = 36 and adding one more set of 6 has a mathematical depth of understanding that the mere memorization of facts will never equal. Fletcher reflects, “A student’s ability to memorize math facts reveals nothing about their mathematical competence.”
This reminds me of a former teaching partner. One day, in a teacher training, we were discussing math fact memorization. She broke down, saying that she’d never been able to memorize her facts. Yet her mathematical abilities far exceeded mine. As a child, I excelled in fact memorization. Highly competitive, I thrived on racing through the multiplication fact sticker chart. But, like the 120 wpm child in language arts, I had no clue what I was doing. I was simply memorizing something that had no meaning, no context. As an adult working with my partner, I had no idea she didn’t have her facts memorized. Her strategies were so accurate, efficient, and flexible—so FLUENT—that she could find answers to math facts as fast as I could. Yet, in the end, memorization was all I had to fall back on, while her bank of mathematical strategies was endless.
Accurate, efficient, and flexible strategies come from memory, not from mere memorization. Students will thank us for remembering the difference!
Watch Graham Fletcher's Ignite Talk here:
This article was originally posted on February 10, 2015.