TEACHING BY PROVIDING
CONCRETENESS, ACTIVITY, AND
FAMILIARITY
Concrete Methods,
Discovery Methods
&
Inductive Methods
TEACHING BY PROVIDING CONCRETENESS,
ACTIVITY, AND FAMILIARITY
 Desire to Learn (D2L) – Practice Discussion
 Chapter 8 Group Presentation
 Chapter 8 PP
Next week (Oct. 18-22): You must post your current
issue PowerPoint by Monday, Oct. 18th, run your
discussion through Thursday, Oct. 21st and
summarize the discussion on Friday, Oct. 22nd. You
must post on at least 3 other discussions but feel
free to post more than 3 if you are interested.
3 Techniques to provide meaningful instruction



Concrete Materials – make the learning task more
concrete
Discovery Activities – make the learner more active in
the learning task
Inductive Sequencing –make the learning task more
familiar by having the learner use prior knowledge
Concrete Methods
Concrete methods
 Goal: Making ideas more concrete in a learner’s
mind by relating the problem (abstract concept) to
concrete objects
Concrete
Manipulatives
Physical objects students move and
rearrange that facilitate understanding of
the concept being taught
Concrete Materials Common in Teaching
Math and Science
 Examples in Math:
 Base 10 blocks (called Dienes Blocks in book)
 Tangrams
 Geoboards
 Play money
 Montessori Materials – example from book




Using beads to represent 1s, 10s and 100s
Progress to expanded notation using colored labels
Progress to standard notation using superimposed labels
Standard notation
Bruner’s Theory of Cognitive Development (1964)
 Three modes of representing information used in
learning a new skill
Enactive mode – using actions
Iconic mode – using visualization
Symbolic mode – using language or other
symbols
 3 phase course of conceptual development
Concrete Manipulatives in Mathematics
--Bundles of sticks in math (Brownell,1935;Brownell and Moser,1945) The use of manipulatives in teaching was first
systematically tested in the 1930’s

Brownell and Moser (1949)


Two 3rd grade groups were taught to solve two-digit subtraction
problems
One group by the standard method and the other using concrete
manipulatives
Found:
Both groups could solve problems like those used during
instruction
 The advantage of meaningful learning comes when the child is
asked to transfer that knowledge to a new situation.
 Concrete manipulatives group performed better in learning to
solve different problems

Controversy Found in Recent Research
 Use of Concrete Materials alone does not
guarantee successful acquisition of concepts
 Factors of influence
 Wrong type of material- manipulatives that hinder learning
of abstract concepts
 Structure of learning environment that doesn’t support
learning from concrete materials
 Failing to connect the concrete materials to the abstract
representations
Take Home Message
 Material
 Select material that is simple representations of concepts to
be taught.
 Structured learning environment
 Do not allow students to “play” or “free explore” concrete
materials prior to instruction of how to use them in relation
to the concept being taught.
 Make explicit how concrete material are physical
representations of the symbolic system
Discovery Methods
STUDENTS AS EXPLORERS
Discovery Methods
 Goal: students become active in the learning
process as they work to discover the rules for
solving the problem without being instructed
 Three kinds of discovery methods
 Pure discovery- student independently discover method for
solving problem with minimal teacher guidance.
 Guided discovery- student discover method for solving
problem with teacher guidance (hints and/or directions)
 Expository- student are explicitly told how to solve the
problem
Do Discovery Methods lead to Learning?

Immediate Retention



Long-term Retention



Guided discovery better than both pure discovery and expository
Lowest for pure discovery- suggesting learning wasn’t meaningful
Teaching for transfer: Ability of the student to transfer
information from what they have learned to a new situation



Equal for guided discovery and expository
Lowest for pure discovery- suggesting less learning occurs
Guided discovery better than both pure discovery and expository
Lowest for pure discovery-
Implications

Extra processing required by students under direction found in
guided discovery method leads student to retain more information
and transfer that information to novel learning situations.
Inductive methods
Inductive Methods
 Goal: making the learning task more familiar by
having the learner use prior knowledge

Inductive Reasoning: ability to abstract a general rule
or principle based upon a specific example or
instantiation.
Inductive methods
 Inductive Method- the rule is given only after the
learner has induced the underlying framework for
the rule.
 Example: Area = Base x Height
 Rather than giving the formula allow students to
attempt various methods for solve problems first
then introduce the rule later.
 Findings: Improves long-term retention and
increases transfer
“GIVE A
MAN A
FISH; FEED
HIM FOR A
DAY.
TEACH A
MAN TO
FISH; FEED
HIM FOR A
LIFETIME.”
A CHINESE PROVERB BY LAO
TZU