1. TEACHING BY PROVIDING CONCRETENESS, ACTIVITY, AND FAMILIARITY
Concrete Methods,
Discovery Methods
&
Inductive Methods

2. TEACHING BY PROVIDING CONCRETENESS, ACTIVITY, AND FAMILIARITY
Desire to Learn (D2L) – Practice Discussion
Chapter 8 Group Presentation
Chapter 8 PP
Next week (Oct ): 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. 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
*Some Lab-based and Classroom-based evidence show that using meaningful methods of instruction encourage the learner to become actively engaged in the learning process with the outcome of having increased problem-solving transfer.

4. Concrete Methods

5. Concrete methods Concrete Manipulatives
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
Manipulatives are frequently utilized for concrete methods

6. 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

7. 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
Why does a concrete representation of the material to be learned influence learning?
Enactive mode –using actions to represent information- physical actions like counting on fingers in solving math problems
Iconic mode – using visualizations to represent information, picturing the statue Man Thinking by Rodin
Symbolic mode – using language or other symbols to represent information, is like knowing formulas for figuring out the area of a square
Process student may go through in the course of developing new concepts then has 3 phases
Understanding first by doing - enactive
Then by visualizing - iconic
Eventually symbolic representation -symbolic
According to this view, understanding progresses from the level of active manipulations of objects then to images which leads to symbolic representation.

8. 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

9. 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
Materials used- Some difficulty with transfer, especially when material used represent specific of objects. For example; might think that using fraction circles that look like a real pie to assist in the process of teaching fraction would ultimately facilitate building conceptual knowledge of fractions because the concrete objects being used are grounded in real world experiences- but what some research suggests is that using realistic concrete materials may actually hinder learning over using simply using circles that have been divided into parts. This is because realistic manipulatives (like the fraction circle that looks like a real pie or a pizza) convey superficial information that is irrelevant to the concept of fractions (chocolate or banana cream, pepperoni or vegetarian) , distracting the learner from the relevant information being conveyed (how fractions work).
Learning environment- just because students are using or playing with concrete manipulatives, does not necessarily mean that they will se the connection between the material and the concept being learned. Thus Student who are allowed simply engage in free play or exploration of manipulatives (and ultimately interact with them in a may that is meaningful to them personally) does not necessarily mean that they are interacting with them in a way that leads to understanding of concepts. Use geoboards as an example.
Connections between concrete objects and abstract representation- linking non-symbolic representations to abstract , symbolic representations is quite challenging. As teachers we need to make verbally explicit the link between the objects we are using and what they represent. That we are using the objects to help build new knowledge and understanding of the symbol system they represent.

10. Take Home Message Material Structured learning environment
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
Instead of using the realistic looking pie or pizza to teach fraction- use simply colored fractions circles. Allows students to focus on concept and not be distracted by irrelevant features.
Learning environment- structured activities designed to get students to explore and focus on concepts being learned.
As teachers we need to make verbally explicit the link between the objects we are using and what they represent. That we are using the objects to help build new knowledge and understanding of the symbol system they represent.

11. Discovery Methods
Students as explorers

12. 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
Origami Frogs- 3 groups
Pure discovery- give paper, no sample tell to make a frog
Guided discovery- give paper and example tell can use example to make a frog, provide hints while they attempt
Expository- Give directions for making a frog as handout.

13. 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
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.
Expository method- Quick gratification, Student has tools to use, but they don’t know how to use them

14. Inductive methods

15. 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.
Students asked to go through personal mental search of prior knowledge, relating new learning to other ideas in the learners memory. This helps activate the learner’s knowledge base providing links between new learning and what was previously learned.

16. 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

17. 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.”
A CHINESE PROVERB BY LAO TZU