Understanding#
See also: learning, solo-taxonomy
Skemp (2006) identifies two types of understanding and links them to teaching practices
-
Relational understanding; and,
knowing both what to do and why 2. Instrumental understanding
'rules without reasons'...the possession of such a rule, and the ability to use it
Examples from mathematics#
- Knowing the formula for area of a rectangle
- How to multiply fractions
- Calculate the circumference of a circle
Which is best?#
We might argue that relational understanding should be the goal. However, Skemp's that a deeper problem is when there is a mismatch between the aims of teacher/student. i.e. where one is aiming for relational and the other instrumental.
Analogy - finding your way around a new town#
The difference between knowing fixed routes between having a "map" of the town.
- Instrumental understanding - "learning an increasing number of fixed plans", plans that can get one from one point to another where the next step in the journey is dependent on the local situation
- Relational understanding - "building up a conceptual structure (schema) from which its possessor can (in principle) produce an unlimited number of plans"
heavy emphasis on scheme building - links to SOLO taxonomy
References#
Skemp, R. R. (2006). Relational Understanding and Instrumental Understanding. Mathematics Teaching in the Middle School, 12(2), 88--95.