Memorization and Learning

Share Cognitive Science Implications for Teaching Mathematics

In many education circles “memorization” is a dirty word; but bear with me.  I am strongly opposed to mindlessly memorizing the steps of an algorithm for the purpose of solving a class of problems.   However, I will argue for carefully guided memorization which will produce very effective learning of concepts.  I will also argue that instruction based on this knowledge of those concepts must teach students to solve problems

Math teachers will espouse understanding as opposed to memorization and then will assign enough exercises, all of the same type, to encourage memorization of a solving process.  Students quickly come to believe that mathematics is a large collection of miscellaneous facts and procedures all to be memorized.

Dr. Robert H. Lewis, Professor of Mathematics at Fordham University correctly, and sarcastically, observes: “It is the unconsciously held delusion that mathematics is a set of rules and formulas that have been worked out by God knows who for God knows why, and the student’s duty is to memorize all this stuff.”

The point is that a great deal of what passes for studying mathematics is memorization, but it is memorization of the wrong thing.  Memorization is important in the study of mathematics, but we must be careful to memorize only those items that will be beneficial to our learning and understanding.

Let’s begin by looking at a few definitions related to learning and memorization.

Definition: Memory is the physiological organs or clustered neural networks in the brain for retaining and retrieving information.

Definition: Memorization is a cognitive process of the brain that encodes, retains, retrieves, and decodes information in long-term memory. (Adapted from Yingxu Wang)

Definition: According to Richard E. Mayer as well as Susan A. Ambrose et al. Learning is a change in knowledge attributable to experience. Knowledge includes facts, procedures, concepts, strategies, and beliefs (compare with Bloom’s Taxonomy).

Definition: A learner’s knowledge consists of those facts, procedures, concepts, strategies, and beliefs that are stored in long-term memory and can be recalled from long-term memory.  That is, a learner’s knowledge consists of memorized facts, procedures, concepts, strategies, and beliefs.

Definition: To learn a subject means to acquire knowledge about that subject and to have that knowledge available for recall from memory for application to future activities and problems.

It follows from the above basic definitions (memorization & to learn) that learning is memorization and memorization is learning.  Learning and memorization are equivalent concepts.  The smart thing to do is to memorize the essential items and employ abstraction, generalization, deductive reasoning, creativity, and critical thinking to solve problems with those memorized facts.

In short, memorization and learning involve getting something into long-term memory and getting it out of long-term memory.  Contrary to popular belief, getting information into long-term memory is the easier of the two. 

The more effective learner is the learner who practices retrieval in such a manner that retrieval paths are strengthened.

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