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 dont ask whether a
  particular model is "right". They ask whether a
  model is "acceptable". And acceptability is based
  on a models 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 students criteria?

http//ncisla.wceruw.org/muse/
9
Model Evolution
Preconceptions Alternative conceptions and
models Useful conceptions and models Natural
reasoning skills
Target model Mn
Expert Consensus Model
Intermediate Model M1
Intermediate Model M2

• 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.

(Rea-Ramirez et al., 2008)
10
Constructive Modeling CyclesGeneration,
Evaluation, Modification (GEM)
Model Generation

• Left GEM cycle derived from expert particles
  that illustrates a cyclical process of hypothesis
  generation, rational and empirical testing, and
  modification or rejection

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 .ORG
• Subject concrete vs. abstract
• To MODELING_at_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 Model State
Hybrid Models
Target model
Initial model
16
Model States
Mixed Model State
Hybrid Model State
Pure Model 2 State
Pure Model 1 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/mulefac
t.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
Mixed Model State
Hybrid Model State
Pure Model 2 State
Pure Model 1 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
Wave ModelScientifically Accepted Model
() Ear Born Sound
Propagating Air
Hybrid Models
Dependent Entity
Independent Entity Dominant Alternative Model
(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.
• Students are engaged in interpreting real 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
  modelsand evidence to support those modelswith
  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 modelvF

v
2v1
v1
t
t1
v

• Newtonian modelaF

2v1
v1
t
t1

• Hybrid modelaF and vF incorporated in the
  same answer

v
2v1
v1
t
t1
(Hrepic et al., 2002, 2005)
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