Conceptual tasks

A conceptual task is intended by the task's designer to be achievable by applying only conceptual knowledge, and not by applying procedural knowledge. Moreover, students may not achieve a task by applying the knowledge that the task was designed to tap. When used on a post-test, conceptual tasks provide one important way of measuring transfer and thus robust learning. In contrast, procedural tasks would be part of a normal post-test that measures learning that may or may not be robust.

Rittle-Johnson & Siegler (1998, pg. 77) distinguish procedural from conceptual knowledge as follows: "We define conceptual knowledge as understanding of the principles that govern the domain and interrelations between pieces of knowledge in the domain (although this knowledge does not need to be explicit). In the literature this type of knowledge is referred to as understanding or principled knowledge. We define procedural as action sequences for solving problems. In the literature this type of knowledge is sometimes referred to as skills, algorithms or strategies."

Examples:

• Given a Chinese tone and/or character, generate its English translation
• Given a transformation of an equation, indicate whether the distributive, associative or commutative law justifies the transformation.
• Ask a beginning chemistry student to explain the term "valence" using Bohr's model of the atom.
• Given a physical situation, such as a baseball flying straight up after being thrown by a person, ask the student what forces are acting on the moving object.

Non-examples:

• Given an algebraic equation with a single occurrence of the unknown, solve it.

Borderline examples:

• Given 5+3, indicate that the answer is 8. For advanced learners, this is done by retrieving a fact, which is a kind of low level concept. For beginning learners, this is done by a counting strategy, so the task taps procedural knowledge.

Rittle-Johnson, B. & Siegler, R. S. (1998) The relation between conceptual and procedural knowledge in learning mathematics. In C. Donlan (Ed.) The Development of Mathematical Skills. East Sussex, UK: Psychology Press.