2006 Joint Annual Meetings February 17-18, 2006 Concept Mapping in Algebra I Beginning Algebra FL-MAA Florida Section The Mathematical Association of America   FTYCMA Florida Two-Year College Mathematics Association

Matt Campese: Sandalwood HS Jacksonville, FL 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

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

Concept: Proposition: 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.

Retention Deficit Disorder? One of the most important factors in teaching is ascertaining what the learner already knows and teaching him accordingly. Retention Deficit Disorder? Connections?

Theory of Learning Key idea: Learners construct their own meanings for concepts and propositions from experiences over time, building their own knowledge structures. The role of the educator is to help ensure that these structures are valid.

Concept Maps: A tool to represent the structure of knowledge. A tool to facilitate learning by helping students to make the connections among concepts. A tool developed by Joseph Novak and his research group in 1972 to record the understanding of science concepts learned by students over an extended period of time.

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. Mention that this was a unique understanding of education and was contrary to the Piagetian theory that was popular at that time. Showed he was a maverick in learning theory Former professor of Cornell university

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

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.

How matter is put together

Still talking about matter, but more in molecular structure and knows the more formal terms, and is making connections to knowledge he knew in Grade 2. He shows a better understanding of the early concepts that he knew in grade 2 expanded on concepts. Novak study found that making connections early made…

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 Connection to our project connections made early improved scores…alg 1 gatekeeper There is some evidence that learning concept mapping increases students ability to solve problems longitudinal study

The IHMC, Institute for Human and Machine Cognition is a research institute located in Pensacola and associated with the University of West Florida. 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. Free for educators used in business for training

IHMC – A University Affiliated Research Institute http://ihmc.us   Cmap tools home page hot buttons      IHMC – A University Affiliated Research Institute http://ihmc.us  

FREE!!!!!!!

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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, and that CMap tools can be used to facilitate the introduction of concept mapping into the mathematics classroom.