GUIDED EXPLORATION

Concrete methods that make learning

more concrete

Discovery methods that make learning

more active

Inductive methods

that make the learning

task more familiar

BRUNER’S THEORY OF COGNITIVE DEVELOPMENT:

MODES OF REPRESENTATION

Enactive Representation - using actions to represent information, dominant mode of representation in the sensori-motor period (0 to 2 yrs), “thought is action”

Iconic Representation - using visualization to represent information, dominant mode of representation during the preschool years, Piaget’s conservation tasks are good examples

Symbolic Representation - using language or other symbols to represent information, middle childhood and beyond

CLASSIC STUDY: BRUNER’S SCREENING STUDY

Participants: 5 to 8 year old children who clearly failed the conservation of liquid substance task.

Step 1: Screen is placed in front of the beakers before the liquid is poured.

CLASSIC STUDY: BRUNER’S SCREENING STUDY

Step 2: Blue liquid is poured from one of the tall beakers to the wide beaker.

Step 3: Child is asked whether the liquid is still the same amount.

Results: When children do not have the misleading visual information, they say “It’s the same, you only poured it”

DIFFERENT MODES OF REPRESENTATION

2 + 3 = ?

4 + 7 = ?

4 - 2 = ?

5 - 3 = ?

SYMBOLIC MODE

9 + 7 = ? 12+ 24 32

- 175 x 6 = ?

2 + ? = 75 x ? = 45

ICONIC MODE3 x 5 = ?

TEACHING POSITIONAL NOTATION

Array of Beads - Concrete Representation

Color Coded Labels - Intermediate Step

1 0 0 2 0 7

Superimposed Labels

1 2 7

ADDITION WITH CARRYING

Color Coded Squares - Intermediate Step

100 10 10

100

+

Short cutAlgorithm

1

2 4 6

+ 1 2 7

3 7 3

10 10

10 10

1 1 1

1 1 1

1 1 1

1 1 1

1

1 1 1101010

10 10 10

10

100 100

100

100

USING CONCRETE MATERIALS TO TEACH THE UNDERLYING STRUCTURE OF QUADRATIC

EQUATIONS

Example: (2x + 1) (x + 2)

X X 1

X

1

1

X2 X2

X

X

X

2X2 + 5X + 2

X

X

1

1

IMPLICATIONS OF CONCRETE METHODS

• Research findings are mixed on the usefulness of concrete materials

• Students must also reflect on the underlying principle, perhaps through discussions with peers

• Once a learner grasps a concept, then introduce drill & practice to ensure increased efficiency

• Computer simulation programs are a good way to help students build “situation models” (e.g., ant problem)