Concrete Methods,Discovery Methods

&Inductive Methods

TEACHING BY PROVIDING CONCRETENESS, ACTIVITY, AND

FAMILIARITY

TEACHING BY PROVIDING CONCRETENESS, ACTIVITY, AND FAMILIARITY

Desire to Learn (D2L) – Discussion SummariesSyllabus revisionHigh Yield Learning Activity #2 – due Nov.

18thChapter 7 Feedback reviewChapter 8 Concrete, Discovery, Inductive

Methods review

For next Thursday (Tues. is election day: VOTE!)Read chapter 9; work on HYLA #2

Views of the Effects of Feedback

Behaviorist View:Response learning—

the acquisition of a new response

Reinforcement: strengthens behaviors; punishment: weakens behaviors; no cognition required

Cognitive View: Feedback is

information that you can use to interpret to make sense of the learning situation

Dependent NOT on the actual feedback but on your interpretation of the MEANING of the feedback that is important

Three Examples: One

Mr. Antonovich:

April:

Mr. Antonovich:

What is the longitude of Chicago, April?

About 40 degrees.

No, …think about it for a second… Can you help her… Jeremy?

Three Examples: Two

Ms. Salinas:

Max:

Ms. Salinas:

What is the longitude of Chicago, Max?

About 40 degrees.

No, it’s about 88 degrees west. What is its latitude, Stephanie?

Three Examples: Three

Ms. Bentley:

Sam:

Ms. Bentley:

What is the longitude of Chicago, Sam?

About 40 degrees.

No, keep in mind we are measuring degrees east and west. Chicago is which direction from Greenwich?

Example Analysis

Mr. Antonovich Gave immediate feedback, gave no further

informationMs. Salinas

Gave immediate feedback, but no information on how to correct

Ms. Bentley Gave immediate feedback with corrective

information and asks another question that then allows the student to answer successfully

Take Home Message on Feedback

Effective FeedbackIt is immediateIt is specificIt provides corrective information

for the learnerIt has a positive emotional tone

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 ManipulativesPhysical 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 materials are physical representations of the symbolic system

STUDENTS AS EXPLORERS

Discovery Methods

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 Equal for guided discovery and expository Lowest for pure discovery- suggesting less learning occurs

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 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 HeightRather 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

A CHINESE PROVERB BY LAO TZU

“GIVE A MAN A FISH; FEED HIM FOR A DAY. TEACH A MAN TO FISH; FEED HIM FOR A LIFETIME.”