GUIDED EXPLORATION Concrete methods that make learning more concrete Discovery methods that make...

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)