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