Mental Modeling Workshop

1. Mental Modeling Workshop Mental Modeling in Theory and Practice

2. Theories of learning in science Social Cultural Social Learning Vygotsky Social Linguistic Piaget Individual Learning Model-basedCo-construction Conceptual Change Science Education Student Preconceptions Model-based Learning ScienceStudies Psychologyof Mental Models, Analogy, Imagery T. Kuhn (Rea-Ramirez et al., 2008)

3. Limitations of Conceptual Change and Social Learning Theories Limitations of Conceptual Change Theories • Cognitive methods may be insufficient for desired conceptual changebecause they fail to take into consideration motivational factors, the role of social learning, and the context of learning • The theory emphasizes big changes that occurred quickly and lead to replacement rather than modification • The theory is underdeveloped as it describes/provides conditions for learning and effects of learning but not a satisfactory set of learning mechanisms Limitations of Social Learning Theories • The theory is very broad and often lacks empirical support and specificity: What exactly gets internalized and under what circumstances? How does the process work? • What impact may social strategies themselves have on persistent misconceptions? (Rea-Ramirez et al., 2008)

4. Mental Modeling Theory A response to gaps in Conceptual Change Theories and Social Learning Theories • Emerged from research into “informal reasoning” which examines alternatives to formal logic to describe thinking • Influenced by critical philosophers of history of science such as Kuhn who emphasized processes that create science products rather than the products themselves • In mental modeling theory, people build mental models: structural analogues of real world or imagined situations • Examples of models: images of atoms, molecules, the human circulatory system, black holes, swarms of particles in a gas • The theory concentrates on intermediate processes in the conceptual change (Rea-Ramirez et al., 2008)

5. Modeling Instruction and Student Motivation • Cyril O. Houle conducted one of the most famous studies on what motivates learners. He identified three subgroups to categorize motivational styles. • (1) Goal-oriented learners use education to accomplish clear-cut objectives. • (2) Activity-oriented (social) learners take part mainly because of the social contact. Houle wrote, ``Their selection of any activity was essentially based on the amount and kind of human relationships it would yield." • (3) Learning-oriented learners seek knowledge for its own sake. ``For the most part, they are avid readers and have been since childhood.... and they choose jobs and make other decisions in life in terms of the potential for growth which they offer.“ http://www.learnativity.com/motivation.html

6. Four types of knowledge used in science (Rea-Ramirez et al., 2008)

7. Mental Model Definition Mental model is: an internal representation, which acts out as a structural analogue of situations or processes and that serves to explain and predict the physical world behavior(Greca & Moreira, 2002) Mental model has: • spatial configuration of identifiable kinds of things • (a few) principles of how system works and • (certain) predictive power (diSessa, 2002) (diSessa, 2002a, 2002b); (Greca & Moreira, 2002)

8. Evaluating Model • Models are judged by their predictive and explanatory power. The same criteria applies in science and (ideally) for everyday life "theories" • To evaluate a particular model, scientists ask: • Can the model explain all the observations? • Can the model be used to predict the behavior of the system if it is manipulated in a specific way? • Is the model consistent with other ideas we have about how the world works and with other models in science? • In judging models, scientists don’t ask whether a particular model is "right". They ask whether a model is "acceptable". And acceptability is based on a model’s ability to do the three things outlined above. • Moreover, more than one model may be an acceptable explanation for the same phenomenon. Example: Light • What about student’s criteria? http://ncisla.wceruw.org/muse/

9. Model Evolution • Small model revisions may be motivated by using one or more episodes of dissatisfaction • Number of needed revisions may depend on the distance between the initial model and the target model • The model evolution process may involve creation of increasingly sophisticated models until reaching the target model • The resulting sequence of intermediate mental models is also called a “learning pathway”. Preconceptions Alternative conceptions and models Useful conceptions and models Natural reasoning skills Target model Mn Expert Consensus Model Intermediate Model M1 Intermediate Model M2 (Rea-Ramirez et al., 2008)

10. Constructive Modeling CyclesGeneration, Evaluation, Modification (GEM) Left: GEM cycle derived from expert particles that illustrates a cyclical process of hypothesis generation, rational and empirical testing, and modification or rejection Model Generation MajorProblems Model Evaluation Minor Problems Model Modification (Rea-Ramirez et al., 2008)

11. Suggested Procedure for Constructing a Curriculum by Mary Rea-Ramirez The complete curriculum includes • the final target • target models • intermediate models (as necessary) • strategies that would be used to support revision cycles of the model Before the start, curriculum developer should be familiar with preconceived mental models and important misconceptions and difficulties that students experience with the topic (Rea-Ramirez, 2008)

12. Suggested Procedure for Constructing a Model-based Curriculum by Mary Rea-Ramirez • Identify the final target concept based on national/state science standards • Adjust the target concept according to the available time • Identify targets models that are inherent to achieving the final target concept • Determine how will know when and whether students have mastered the target. Plan to document (for yourself and for the student) how their model has changed during instruction. Document stumbling blocks, persistent misconceptions and other difficulties in the process. • Analyze students preconceived ideas and mental models to determine intermediate steps and intermediate models as needed • Design diverse strategies that build on various learning styles to guide students through learning pathway and to provide multiple ways of supporting criticism and revision cycles. (Rea-Ramirez, 2008)

13. Inquiry is NOT enough • From: Matt Greenwolfe <matt_greenwolfe@CARYACADEMY.ORG> • Subject: concrete vs. abstract • To: MODELING@ASU.EDU • Recall from the original modeling paper in AJP that modeling started when Malcolm Well's students failed the FCI, despite his hands-on inquiry approach that he assumed to be effective. ... • What did Malcolm add to his course after realizing that inquiry was not enough - *multiple* representations including abstract symbols, whiteboard-mediated discourse, coherent story lines, and most importantly an emphasis on building and using models that boiled the subject down into a small number of fundamental ideas. • We all know from our experience that students require a great deal of instruction, guidance and repeated practice to learn how to extract a model from their hands-on experience, and unless they extract the model, they will not be able to transfer their knowledge in the deployment phase.

14. Watch the step - Hybrids • Hybrid mental models: robust and elaborate but not always self consistent. • Present major threat to standardized test validity

15. Mental models of Earth Mixed ModelState Initial model Target model Hybrid Models

16. Model States Pure Model 1 State Pure Model 2 State Mixed ModelState Hybrid Model State Instance1 Instance2

17. MetaphorMental Models and Model states Horse Hybrid = Mule Donkey A mule = hybrid of a donkey + a horse. A horse –64 chromosomesA donkey – 62 chromosomesA mule – 63 chromosomes Image from: http://www.luckythreeranch.com/muletrainer/mulefact.asp (Hrepic et al., 2002, 2005)

18. Model States Features related to both models or neither one Features related to Model 1 only Features related to Model 2 only x NoModelState Pure Model 1 State Pure Model 2 State Mixed Model State Hybrid Model State x x x x Context1 x x x x x x x x x x x x Context2 x x x x x x x (Hrepic et al., 2002, 2005)

19. 4 basic models - mechanisms of propagation WaveModelScientifically Accepted Model (+) Ear Born Sound Propagating Air Hybrid Models Dependent Entity Independent EntityDominant AlternativeModel (Hrepic et al., 2002, 2005)

20. Making more sense of data ? ? Mental model: “dependent entity” mental model of sound propagation according to which sound propagates better in a denser medium. Factual knowledge: {T1}sound travels faster through the water than through the air. Experiences: {T2}sound can pass on the other side of the wall. {T3} sound is better heard through two cans connected by the tight string than through the air alone (which is less dense). {T4}sound diminishes on the other side of the wall. The student resolved the problem so that the contradictory experience was revised.

21. A MODELING METHODfor high school physics instruction • The modeling approach organizes the course content around a small number of basic models, such as the "harmonic oscillator" and the "particle subject to a constant force." • These models describe basic patterns which appear ubiquitously in physical phenomena. • Students become familiar with the structure and versatility of the models by employing them in a variety of situations. • This includes applications to explain or predict physical phenomena as well as to design and interpret experiments. • It also includes the construction of more complex models by modification of the basic models. • by Malcolm Wells, David Hestenes, Gregg Swackhamer (American Journal of Physics, July 1995. Online at modeling.asu.edu)

22. Using a particular model Pre Instruction; Calculus based; University; NY Inconsistently Consistently N = 100 (Hrepic et al., 2002, 2005)

23. Using a particular model Mid Instruction; Calculus based; University; NY Inconsistently Consistently N = 96

24. Using a particular model Post Instruction; Calculus based; University; NY Inconsistently Consistently N = 95

25. Movements of particles of the medium Pre Instruction; Calculus based; University; NY (+) Random Travel (+) Travel Away From The source Vibration on the Spot N = 100

26. Movements of particles of the medium Mid Instruction; Calculus based; University; NY (+) Random Travel (+) Travel Away From The source Vibration on the Spot N = 96

27. Movements of particles of the medium Post Instruction; Calculus based; University; NY (+) Random Travel (+) Travel Away From The source Vibration on the Spot N = 95

28. Model states Pre Instruction; Calculus based; University; NY Mixed Any Pure Other Mixed Entity Pure Wave Mixed Ear-Wave N = 100

29. Model states Mid Instruction; Calculus based; University; NY Mixed Any Pure Other Mixed Entity Pure Wave Mixed Ear-Wave N = 96

30. Model states Post Instruction; Calculus based; University; NY Mixed Any Pure Other Mixed Entity Pure Wave Mixed Ear-Wave N = 95

31. Writing modeling curriculum: Guiding Questions from Kathy Harper at OSU 1) What is your model? 2) What is your story line? (Along this line - no pun intended - some units have one model that gets applied to a number of different situations, but doesn't really change much, whereas other units start with one model and refine it one or more times.) 3) What observations/experiences are your students going to make/have to lead them to construct the model you want them to build? 4) Is your model descriptive (e.g. kinematics) or causal (e.g. dynamics)? (This question isn't as necessary with all the topics.) 5) Do your deployment activities force the students to invoke the model? 6) Do your activities extend the model to where you want it to go? (In other words, are the deployment activities rehashings of what has already been done, or do they apply the model to new situations?)Q6 was added by Doug Forrest, a peer leader for the second Modeling Workshop. (Jane Jackson, Personal Communication, 2008)

32. Ideas for model building instructional strategies by Melvin Steinberg • Conceptual dissatisfaction: discrepant events (surprising observations) and discrepant questions (should be used when discrepant events are not available to provoke the student dissatisfaction with the existing student model) • If possible, find and build on an analog domain where students already have a runnable mental model. Foster discussion of similarities and differences between target and analog models. • Observational constraints: hands on experiments to provide observations that constrain model building in a productive direction • Representation in dynamic imagery: choose experimental investigations not to confirm a principle but to enable students to run mental simulations • Imagery enhancement: color coding, blocks, arrows. Symbols used should be simple and schematic in a to support mental representations as well as those on paper • Gradual model modification: making small step modifications to make building of complex models doable for beginning students (Steinberg, 2008)

33. The Modeling for Understanding in Science (MUSE) project • Teaching Strategies • The teacher assumes the role of co-inquirer in the classroom, engaging the students in scientific inquiry and invigorating their investigations through questions and class discussions. • Instruction emphasizes students’ use of scientific models to understand, illustrate, and explain key scientific ideas and data. • The teacher continuously assesses students’ understanding to determine the direction of instruction. Through iterative, ongoing assessment of individuals and groups, the teacher gives students constructive feedback to direct their learning. • Assessment is authentic. Teachers apply proven assessment tools (check lists and rubrics) to evaluate student learning through a variety of tasks: student journals, homework assignments, written exams or quizzes, oral exams, and group posters and presentations. http://ncisla.wceruw.org/muse/teaching/index.html

34. The Modeling for Understanding in Science (MUSE) project 2. Tasks & Curricular Materials • Materials include rich data sets or opportunities for students to generate their own data through observations of natural phenomena. • Studentsare engaged in interpretingreal data: organizing, seeking patterns, and attempting to explain those patterns using a scientific or explanatory model. • Students apply and sometimes revise their models when attempting to explain unfamiliar phenomena. • Individuals or groups regularly share their models—and evidence to support those models—with peers through poster sessions, presentations, or paper writing. http://ncisla.wceruw.org/muse/teaching/index.html

35. The Modeling for Understanding in Science (MUSE) project 3. Norms of Behavior & Participation • Students form a scientific community to learn about, present, and discuss explanatory models (and the empirical justification for those models)with their peers. Students collaboratively gather data, discuss, observe, and present scientific arguments for critique. • Students hone their reasoning skills through judging their own and other students’ explanatory models. Students assess models to determine whether they fit with data, have predictive power, and are consistent with other scientific models or concepts. http://ncisla.wceruw.org/muse/teaching/index.html

36. Math in Modeling • Our magnets is for lower age group - less mathematical • Developing mathematical aspects of the model - developing the rules of the game • Aristotle, Newton

37. Hybrid model in mechanics: What happens if we double the force on body moving with a constant v? • Aristotelian modelv~F v 2v1 v1 t1 t v • Newtonian modela~F 2v1 v1 t1 t • Hybrid model:a~F and v~F incorporated in the same answer v 2v1 v1 (Hrepic et al., 2002, 2005) t1 t

38. References • diSessa, A. A. (2002a). Personal Communication. • diSessa, A. A. (2002b). Why "Conceptual Ecology" Is a Good Idea. In M. Limon & L. Mason (Eds.), Reconsidering Conceptual Change: Issues in Theory and Practice (pp. 29-60). Dordrecht, Netherlands: Kluwer Academic Publishers. • Greca, I. M., & Moreira, M. A. (2002). Mental, Physical, and Mathematical Models in the Teaching and Learning of Physics. Science Education, 86(1), 106-121. • Hrepic, Z., Zollman, D., & Rebello, S. (2002). Identifying Students' Models of Sound Propagation. In S. Franklin, J. Marx & K. Cummings (Eds.), Proceedings of 2002 Physics Education Research Conference. Boise, Idaho: PERC Publishing. • Hrepic, Z., Zollman, D., & Rebello, S. (2005). Eliciting and Representing Hybrid Mental Models. In Proceedings of Annual Meeting of the National Association for Research in Science Teaching (2005). Dallas, TX. • Rea-Ramirez, M. A., Clement, J., & Nunez-Oviedo, M. C. (2008). An Instructional Model Derived from Model Construction and Criticism Theory. In J. Clement & M. C. Nunez-Oviedo (Eds.), Model Based Learning and Instruction in Science: Springer. • Rea-Ramirez, M. A. (2008). Determining Target Models and Effective Learning Pathways for Developing Understanding of Biological Topics. In J. Clement & M. C. Nunez-Oviedo (Eds.), Model Based Learning and Instruction in Science: Springer. • Steinberg, M. S. (2008). Target Model Sequence and Critical Learning Pathway for an Electricity Curriculum Based on Model Evolution. In J. Clement & M. C. Nunez-Oviedo (Eds.), Model Based Learning and Instruction in Science (pp. 79-102): Springer. • Personal communication: Kathy Harper Visiting Assistant Professor of Physics & Astronomy Denison University harperk@denison.edu 103 Olin Science Hall Granville, OH 43023