“ Sail Back to the Palm Beaches ” FCTM 2005 October 21, 2005 CONCEPT MAPPING IN ALGEBRA I

1. “Sail Back to the Palm Beaches”FCTM 2005 October 21, 2005CONCEPT MAPPINGINALGEBRA I

2. Presented by: Matt Campese: Sandalwood HS Jacksonville, FL campesem@educationcentral.org Della Caldwell: Allen D. Nease HS St. Augustine, FL caldwed@stjohns.k12.fl.us

3. Theory of Knowledge: All knowledge is constructed by human beings. All knowledge is built up from Concepts and Propositions

4. Concept: A perception or an idea about events or objects, or records of events or objects. Concepts can be designated by names or labels. Proposition: Two or more concepts combined to form a statement about the relationship of the concepts.

5. David Ausubel (1968): If I had to reduce all of educational psychology to just one principle I would say this: The most important single factor influencing learning is what the learner already knows. Ascertain this and teach him accordingly. Retention Deficit Disorder? Connections?

6. Theory of Learning Key idea: Learners constructtheir ownmeaningsfor concepts andpropositions from experiencesover time, buildingtheir ownknowledgestructures. The role of the educator is to help ensure that these structures are valid.

7. Concept Maps: A tool to represent the structure of knowledge. A tool to facilitate Learning. A tool developed by Joseph Novak and his research group in 1972 to represent the knowledge of students prior to and after instruction.

8. A twelve-year longitudinal • study of children’s learning: • Children received audio-tutorial instruction in • basic science concepts in grades one and two. • Children were interviewed periodically in • grades one through twelve. • Concept maps were drawn from interviews • to represent the children’s understanding of • various concepts and their connections.

9. Learning Denny, a six year old, is asked to draw a map that shows his understanding of 8 common concepts Concepts: Water Solid River Vapor Steam Ice Liquid Gas Evaporate Denny’s knowledge does not include a meaning for vapor

10. Learning Concepts: Water Solid River Vapor Steam Ice Liquid Gas Evaporate We can easily teach Denny the meaning of “vapor” and a new concept, “evaporate”, by showing how they relate to his current knowledge.

13. High school physics students who make concept maps outperform students in traditional classes High school physics students who make concept maps outperform students in traditional classes High school physics students who make concept maps outperform students in traditional classes

14. The IHMC, Institute for Human and Machine Cognition is an active group of business professors, consultants and mavericks such as Joseph Novak seeking to find ways to create “intelligent enterprises.” In an effort to use concept maps in education the group at IHMC developed an extremely versatile software package called CMap Tools. Schools in Europe and South America are using the CMap Tools to bring concept mapping into the classroom as an effective learning strategy.

19. Since 1460 we have had textbooks to help teachers and students learn. Today we are using computers, internet resources, and guided classroom and field experiences to educate in ways never before possible. We think that concept mapping is another tool Mathematics teachers can use to enhance student learning. BUT What is a concept map? How can it be used in Algebra I ???????