Guided Discovery:  A Balanced Pedagogical Approach

February 25, 2019

Elementary math teachers frequently fall into one of two categories - Traditional Proceduralists or Discovery-based Constructivists.   The former believes in teacher-led instruction and can be stigmatized as inflexible, while the latter facilitates student-inquiry and is considered progressive.  Both pedagogical methods evoke strong support and criticism, but pitting the philosophies against each other is a false choice.

Teacher-led instruction can conjure thoughts of dull procedural lectures, passive student learning, and massed practice, while progressive lessons are commonly associated with students handling manipulatives, moving freely about the classroom, and rarely – if ever - practicing basic skills.  Both stereotypes can be true, but neither is wholly accurate.  Teacher-led lessons can be dynamic, and students can make mathematical discoveries during whole-group instruction.  Sadly, an approach that balances the best of traditional and constructivist teaching has not gained enough traction in American schools.

Presenting mathematics as a series of rules and mnemonics to be memorized cheapens the subject.  Conceptual understanding, curiosity, and alternative strategies – tenants of constructivist lessons - are all integral to learning math, but can be useless without an instructor guiding the process.  It’s foolish to think that second graders will discover efficient subtraction algorithms simply by giving them base-ten blocks, and few fourth graders will accurately add unlike fractions through paper folding explorations.  Although some students might succeed using these approaches, the vast majority will not.  When children don’t discover skills by exploring, teachers need to explicitly teach the concepts.

This reality is not an indictment of instructor skill or any child’s natural intelligence. Many 20th century physicians never completed Calculus, not because they weren’t intellectually capable of mastering it, but because they were never required to learn it.  Archimedes - widely considered one of the greatest mathematicians in human history - died not understanding the decimal system, because it wasn’t widely taught and used during the era in which he lived.

These examples spotlight a truth that many educators ignore:  Mathematical learning works differently than other subjects.  Math is a skill-based, cumulative discipline, and most students have trouble advancing their knowledge without instructional guidance.  Therefore, great math instruction provides a mix of exploratory opportunities, explicit instruction, and deliberate, focused practice.

Over the past generation, teaching methodology has swung from one extreme to another, hurting mathematics education in the process.  It is time for educators to center this swinging pendulum.  Today’s best elementary math teachers are neither rigid traditionalists nor unchained constructivists.  Instead, their lessons work analogously to a trekking expedition.  The travelers will enjoy the journey and reach their destination, but it’s impossible – or at the very least inefficient - without their leader’s guidance. This Guided Discovery approach incorporates skill work, discussion, and manipulatives through teacher-led instruction.  All children are given opportunities to make mathematical discoveries, but also receive direct instruction.