|Students must learn mathematics with
understanding, actively building new knowledge from experience and prior
Research has solidly
established the importance of conceptual understanding in becoming proficient in
a subject. When students understand mathematics, they are able to use their
knowledge flexibly. They combine factual knowledge, procedural facility, and
conceptual understanding in powerful ways.
Learning the "basics"
is important; however, students who memorize facts or procedures without
understanding often are not sure when or how to use what they know. In contrast,
conceptual understanding enables students to deal with novel problems and
settings. They can solve problems that they have not encountered before.
understanding also helps students become autonomous learners. Students learn
more and better when they take control of their own learning. When challenged
with appropriately chosen tasks, students can become confident in their ability
to tackle difficult problems, eager to figure things out on their own, flexible
in exploring mathematical ideas, and willing to persevere when tasks are
Students of all ages
bring to mathematics class a considerable knowledge base on which to build.
School experiences should not inhibit students' natural inclination to
understand by suggesting that mathematics is a body of knowledge that can be
mastered only by a few.