1. Learning Science and Mathematics Concepts, Models, Representations and Talk Colleen Megowan

2. Warning! Powerpoint lecture slide deck Don’t try this at home… …or in your own classroom

3. 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

4. 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?

5. 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

6. What is modeling? Modeling is the activity of building elaborating & testing applying conceptual models

7. 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

8. How to do modeling instruction— in physics or any other subject: The Modeling Cycle Model construction Model elaboration and testing Model application

9. 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

10. How is knowledge structured? Schema theories of cognition Information processing theories of cognition Embodied cognition

11. Modeling Theory

12. 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

13. Cognition and Modeling Cognition – 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

14. 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

15. Where can we look for clues to student thinking? Classroom discourse The construction and sharing of representations

16. 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

17. 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

18. 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

19. The question: How do students’ conversations around the white-boarded representations they co- construct shape their thinking about space, time and interactions?

20. 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?

21. 21 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

22. Unexpected influence: The “culture of schooling”  Students’ models of schooling  Teachers’ models of schooling

23. 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” 42

24. 24 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