Learning Science and Mathematics Concepts, Models, Representations and Talk Colleen Megowan
Jan 12, 2016
Learning Science and Mathematics
Concepts, Models, Representations and Talk
Colleen Megowan
Warning!Powerpoint lecture slide deck
Don’t try this at home…
…or in your own classroom
Learning Science and Mathematics: Concepts, Models, Representations and Talk
Thesis: Conceptual structures and spatial representations are encoded via separate cognitive pathways. Students who make the effort to encode linguistic inputs spatially, have an advantage when reasoning. The use of whiteboards for collaborative problem solving facilitates this spatial encoding activity.
Theoretical Framework: Situated, Embodied, Distributed Cognition, Modeling, Cognitive Linguistics
Conclusions: There are three parallel dimensions of modeling and whiteboard mediated cognition are contextual, distributed, structuring
Implications: Classroom culture and teacher expectations about
•how students collaborate to represent what they are thinking about
•how they talk with each other
•what they talk about
•and who has the floor in classroom discourse
have a significant impact on students’ cognition in physics and mathematics
Introduction
Teaching and learning science and mathematics is not easy--naïve beliefs are tenacious
Modeling instruction works better than many approaches, but when and under what conditions?
What is a model?A representation of structure in a material system
Systemic structure Geometric structure Object structure Temporal structure Interaction structure
A model is a mental representation of a real thing
What is modeling?
Modeling is the activity of
building elaborating & testing
applying
conceptual models
What is Modeling Instruction? A scientific theory of instruction to guide
both research and practice Interactive engagement Rooted in cognitive science as well as
everyday thinking and learning Model-based epistemology
How to do modeling instruction—in physics or any other subject:The Modeling Cycle Model construction Model elaboration and testing Model application
Theoretical Framework
What is cognition? Cognition is situated – semantic frame v. context Cognition is culturally mediated Cognition is embodied Cognition is distributed Cognition is metaphorically framed
How is knowledge structured?
Schema theories of cognition Information processing theories of cognition Embodied cognition
Modeling Theory
Mental Models vs. Conceptual Models
Mental models subjective the private constructions of an individual
Conceptual models Objective Structure is mapped onto symbols that can
activate the mental models of others
Cognition and ModelingCognition – the construction and manipulation of private mental models
Cognitive linguistics tells us that language does not refer directly to the physical world but rather to mental models and their components
Three Worlds• Physical world – real things and processes• Mental world – personal knowledge, subjective
mental models• Conceptual world – scientific knowledge, objective
conceptual models
What should we pay attention to develop our modeling skills?
Student-centered discourse and collaborative construction of representations around a set of tasks designed to help them identify, characterize, and practice applying fundamental relationships
The use of conceptual models as an organizing principle
Where can we look for clues to student thinking?
Classroom discourse The construction and sharing of
representations
What does it buy me to use this approach?
Listening strategies Questioning strategies Optimizing strategies
Optimizing discourse Optimizing the use of spatial representation Optimizing participation and collaboration
What is the culture in the learning environment?
Conventional schooling Modeling physics
The modeling cycle What is a model? Discourse in the modeling physics classroom
A question of motivation – to engage or not to engage?
Cognition and Learning in Modeling instruction
Learning as a group process
Distributed cognition Conceptual blending Communication and Learning
Reference frames The theory of representational modularity
The role of the whiteboard in discourse
The question:
How do students’ conversations around the white-boarded representations they co-construct shape their thinking about space, time and interactions?
To get at this, you must first answer another question:
How do you get students to talk to each other about space, time and interactions?
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What have I found out?
• That it’s not about teaching—it’s about learning
• That good teaching entails observing how students exteriorize their thinking, to learn (in real time) how individual students think
• That good learning environments are designed
Unexpected influence:
The “culture of schooling” Students’ models of schooling Teachers’ models of schooling
The default culture of the classroom
Answers the key to success
The classroom economy success is rewarded with points
Procedures Knowing how v. knowing why
Boundaries Stay within the lines
The teacher controls “the floor”
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Colleen’s Assertions:
With respect to whiteboarding…
• Classroom culture matters • Tasks matter • Expectations matter• Inscriptions matter• Who’s got the floor matters • Tool use matters • Shared spatial representations matter