INSTRUMENTAL teaching and learning means we have a rule or procedure and we know how to apply it.
RELATIONAL teaching and learning means we have deep understand of concepts and the relationships between concepts.
Each way of teaching and learning has long and short term effects.
Examples of INSTRUMENTAL TEACHING AND LEARNING include, but are not limited to:
finding area by multiplying length by width,
algorithms for addition, subtraction, multiplication and division,
changing the sign on numbers moved from one side of the equals sign to other.
Other examples of instrumental teaching and learning can be easily found on other websites. Unfortunately, the instrumental approach to teaching and learning maths is widespread. The learning theory was that children practise the rule or procedure, and understanding will follow. Current learning research tells us that in many cases,
understanding never followed, or
incorrect understanding followed, or
if correct understanding did follow, the child did not know if it was important or related to any other parts of mathematics.
Examples of RELATIONAL TEACHING AND LEARNING include, but are not limited to:
explaining area is the amount of space a shape or surface takes up in 2 of the 3 dimensions, explaining that the 3 dimensions are up and down, left to right, front to back,
thinking additively about place value, addition and subtraction; thinking multiplicatively about place value, multiplication, division, fractions, and metric measurement, using the distributive property to multiply and divide, and relating division to fractions,
explaining that the equals sign means equality (both sides are equal) so to remove a negative number from 1 side, we add the number to both sides