Discovery learning is an inquiry-based, constructivist learning theory that takes place in problem solving situations where the learner draws on his or her own past experience and existing knowledge to discover facts and relationships and new truths to be learned.
Discovery learning encourages students to actively use their intuition, imagination, and creativity.
Bruner puts forward a learning theories that consists of three representational stages:-
> students who learn addition and subtraction using things,
e.g base ten blocks, woods, stone, beads etc
b) Iconic stage (2-4years old) ---------------> image
> students use paper and pencil to solve problem. they are able to visualize image
e.g solve 234+674
c) Symbol stage (5-7years old) ---------------> symbol
> students are able to use symbol for abstract.
According to Bruner, learning begins with an action that involves touching, emotion and manipulation.
THE PRINCIPLES OR THEOREMS OF LEARNING MATHEMATICS
construction principle
Better for a student to learn a new concept in mathematics is to construct his own presentation. The teacher presents examples and the students work with the examples until they discover the interrelationships.
e.g teacher introduce the concept of gradient by giving formula. teacher ask students what they found after discovering the formula. students should realize some basic characteristics about gradient :::::::::D--two parallel lines have same gradient
:::::::::D--horizontal line has zero gradient
:::::::::D--positive & negative gradient
notation principle
notation used in teaching should be suitable with intellectual development stage. For example, brackets should used when teaching primary school......
e.g 2+(3x5)=17 e.g use of ( X ) and ( . ) in multiplication
contrast & variation principle
most of the mathematical concepts are easy to understand if they are compared with other concepts.
> multiplication & division
> differentiation & integration
> intersection set & union set
every mathematical concept, principle and skill is connected to other concepts, principles & skills
e.g concept of gradient of a straight line
- tangent of the curve at a certain point
-derivative of dy/dx
-continuous function
-graphs of increasing & decreasing functions
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