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 = ? = ? = ? = ? SYMBOLIC MODE = ? x 6 = ? 2 + ? = 7 5 x ? = 45 ICONIC MODE 3 x 5 = ?

TEACHING POSITIONAL NOTATION Array of Beads - Concrete Representation Color Coded Labels - Intermediate Step Superimposed Labels 1 2 7

ADDITION WITH CARRYING Color Coded Squares - Intermediate Step Short cut Algorithm

USING CONCRETE MATERIALS TO TEACH THE UNDERLYING STRUCTURE OF QUADRATIC EQUATIONS Example: (2x + 1) (x + 2) XX1 X 1 1 X2X2 X2X2 X X X 2X 2 + 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)