1 A Modeling Approach to Science Teaching Nicholas Park Greenhill School

A Private Universe We go through life collecting memories, and organizing them into mental models, or schema. Our memory depends on connections; new inputs which do not fit in an existing schema tend to be “forgotten.” It takes a very discrepant phenomenon to motivate a change in existing schemata. We go through life collecting memories, and organizing them into mental models, or schema. Our memory depends on connections; new inputs which do not fit in an existing schema tend to be “forgotten.” It takes a very discrepant phenomenon to motivate a change in existing schemata. 2

Science and Modeling Scientists construct and use shared models to describe, explain, predict and control physical sytems.  By making this process explicit, we help students to Revise their mental schemata (models) in the light of experimental evidence and collaborative discourse Understand the scientific process Scientists construct and use shared models to describe, explain, predict and control physical sytems.  By making this process explicit, we help students to Revise their mental schemata (models) in the light of experimental evidence and collaborative discourse Understand the scientific process 3

4 What Do We Mean by Model?  Essential and non-essential elements of a physical system or process are identified  Models are used to represent the structure underlying the essential elements  Essential and non-essential elements of a physical system or process are identified  Models are used to represent the structure underlying the essential elements

5 Why Models?  Models are basic units of knowledge  A few basic models are used again and again with only minor modifications.  Students DO work from mental models – the question is which model it will be:  A shared, rigorous model with explicit experimental support?  An inconsistently applied, private model based on miscellaneous experiences.  Models are basic units of knowledge  A few basic models are used again and again with only minor modifications.  Students DO work from mental models – the question is which model it will be:  A shared, rigorous model with explicit experimental support?  An inconsistently applied, private model based on miscellaneous experiences.

What about problem solving?  The problem with problem-solving  Students come to see problems and their answers as the units of knowledge.  Students fail to see common elements in novel problems. “But we never did a problem like this!”  Models as basic units of knowledge  A few basic models are used again and again with only minor modifications.  Students identify or create a model and make inferences from the model to produce a solution.  The problem with problem-solving  Students come to see problems and their answers as the units of knowledge.  Students fail to see common elements in novel problems. “But we never did a problem like this!”  Models as basic units of knowledge  A few basic models are used again and again with only minor modifications.  Students identify or create a model and make inferences from the model to produce a solution.

7 What doesn’t work  Presentation of facts and skills, with the assumption that students will see the underlying structure in the content.  They systematically miss the point of what we tell them.  They do not have the same “schema” associated with key ideas/words that we have.  Students passively listen while T works  Presentation of facts and skills, with the assumption that students will see the underlying structure in the content.  They systematically miss the point of what we tell them.  They do not have the same “schema” associated with key ideas/words that we have.  Students passively listen while T works

8 What works Interactive engagement Student discourse & articulation Cognitive scaffolding Multiple representational tools Consensus-based model building Explicit hierarchal organization of ideas and concepts into models Interactive engagement Student discourse & articulation Cognitive scaffolding Multiple representational tools Consensus-based model building Explicit hierarchal organization of ideas and concepts into models

9  Construct and use scientific models to describe, to explain, to predict and to control physical phenomena.  Model physical objects and processes using diagrammatic, graphical and algebraic representations.  Recognize a small set of models as the content core.  Evaluate scientific models through comparison with empirical data.  View modeling as the procedural core of scientific knowledge  Construct and use scientific models to describe, to explain, to predict and to control physical phenomena.  Model physical objects and processes using diagrammatic, graphical and algebraic representations.  Recognize a small set of models as the content core.  Evaluate scientific models through comparison with empirical data.  View modeling as the procedural core of scientific knowledge The Modeling Method

10 How to Teach it? constructivist vs transmissionist cooperative inquiry vs lecture/demonstration student-centered vs teacher-centered student-centered vs teacher-centered active engagement vs passive reception student activity vs teacher demonstration student activity vs teacher demonstration student articulation vs teacher presentation lab-based vs textbook-based lab-based vs textbook-based

THE MODELING CYCLE 11

I - Model Development  Students in cooperative groups  design and perform experiments.  formulate functional relationship between variables.  evaluate “fit” to data.  Post-lab analysis  whiteboard presentation of student findings  multiple representations  justification of conclusions  Students in cooperative groups  design and perform experiments.  formulate functional relationship between variables.  evaluate “fit” to data.  Post-lab analysis  whiteboard presentation of student findings  multiple representations  justification of conclusions

II - Model Deployment  In post-lab discussion, the instructor  brings closure to the experiment.  fleshes out details of the model, relating common features of various representations.  helps students to abstract the model from the context in which it was developed.  In post-lab discussion, the instructor  brings closure to the experiment.  fleshes out details of the model, relating common features of various representations.  helps students to abstract the model from the context in which it was developed.

II - Model Deployment  In deployment activities, students articulate their understanding in oral presentations. are guided by instructor's questions: » Why did you do that? » How do you know that? learn to apply model to variety of related situations. » identify system composition » accurately represent its structure

15 Modeling in a Nutshell  Through carefully guided discourse, students construct shared models, using various representations, to describe shared experiences with physical systems and processes.  Let the students do the talking  Ask, “How do you know that?”  Require diagrams and representations whenever possible  Through carefully guided discourse, students construct shared models, using various representations, to describe shared experiences with physical systems and processes.  Let the students do the talking  Ask, “How do you know that?”  Require diagrams and representations whenever possible

CHEMISTRY A Closer Look: 16

17 Algorithms vs Understanding What does it mean when students can solve stoichiometry problems, but cannot answer the following? Nitrogen gas and hydrogen gas react to form ammonia gas by the reaction N H 2  2 NH 3 The box at right shows a mixture of nitrogen and hydrogen molecules before the reaction begins. Which of the boxes below correctly shows what the reaction mixture would look like after the reaction was complete?

18 How Do You Know?  All students know the formula for water is H 2 O.  Very few are able to cite any evidence for why we believe this to be the case.  All students know the formula for water is H 2 O.  Very few are able to cite any evidence for why we believe this to be the case.

19 Do They Really Have an Atomic View of Matter? Before we investigate the inner workings of the atom, let’s make sure they really believe in atoms.  Students can state the Law of Conservation of Mass, but they will claim that mass is “lost” in some reactions.  When asked to represent matter at sub- microscopic level, many sketch matter using a continuous model. Before we investigate the inner workings of the atom, let’s make sure they really believe in atoms.  Students can state the Law of Conservation of Mass, but they will claim that mass is “lost” in some reactions.  When asked to represent matter at sub- microscopic level, many sketch matter using a continuous model.

20 Where’s the Evidence? Why teach a model of the inner workings of the atom without examining any of the evidence?  Students “know” the atom has a nucleus surrounded by electrons, but cannot use this model to account for electrical interactions.  Why disconnect the Bohr model of the atom from the effort to understand the hydrogen line spectrum? Why teach a model of the inner workings of the atom without examining any of the evidence?  Students “know” the atom has a nucleus surrounded by electrons, but cannot use this model to account for electrical interactions.  Why disconnect the Bohr model of the atom from the effort to understand the hydrogen line spectrum?

21 Uncovering Chemistry Examine matter from outside-in instead of from inside-out  Observable Phenomena  Model  Students learn to trust scientific thinking, not just teacher/textbook authority  Organize content around a meaningful ‘Story of Matter’ Examine matter from outside-in instead of from inside-out  Observable Phenomena  Model  Students learn to trust scientific thinking, not just teacher/textbook authority  Organize content around a meaningful ‘Story of Matter’

Sample Cycle: Density  Prerequisite activities  Define volume by “counting cubes,” and validate the formulas learned in math.  Define mass as amount of matter, measured using a balance.  Develop law of conservation of mass – through a lab with physical and chemical changes  Prerequisite activities  Define volume by “counting cubes,” and validate the formulas learned in math.  Define mass as amount of matter, measured using a balance.  Develop law of conservation of mass – through a lab with physical and chemical changes

Sample Cycle: Density  Density Lab and Follow-up  Question: What is the relationship between the mass of a solid and its volume?  Density Lab and Follow-up  Question: What is the relationship between the mass of a solid and its volume?

“Even if students correctly say ‘mass per unit volume’ rather than ‘mass per volume’ in interpreting M/V, there is no conclusive assurance that they really understand the meaning. Some do, but others have merely memorized the locution. It is important to lead all students into giving simple interpretation in everyday language before accepting a regular use of ‘per.’ Many students do not know what the word ‘ratio’ means. Those having difficulty with reasoning and interpretation should always be asked, at an early stage, for the meaning of the word if they, the text, or the teacher invoke it.” A Arons, Teaching Introductory Physics, John Wiley & Sons, “Even if students correctly say ‘mass per unit volume’ rather than ‘mass per volume’ in interpreting M/V, there is no conclusive assurance that they really understand the meaning. Some do, but others have merely memorized the locution. It is important to lead all students into giving simple interpretation in everyday language before accepting a regular use of ‘per.’ Many students do not know what the word ‘ratio’ means. Those having difficulty with reasoning and interpretation should always be asked, at an early stage, for the meaning of the word if they, the text, or the teacher invoke it.” A Arons, Teaching Introductory Physics, John Wiley & Sons,

 In worksheet 3 students make comparisons of the mass, volume and density of pairs of objects based on particle representations.  Worksheet 4 further reinforces the notion that the slope of a graph has physical meaning.  The first quiz requires students to determine the slope and perform standard calculations involving density.  In next activity: Density of a gas, students determine the density of carbon dioxide. The fact that the value is 3 orders of magnitude smaller than that of liquids and solids sets the stage for the discussion of an atomic model of matter that accounts for this difference.  In worksheet 3 students make comparisons of the mass, volume and density of pairs of objects based on particle representations.  Worksheet 4 further reinforces the notion that the slope of a graph has physical meaning.  The first quiz requires students to determine the slope and perform standard calculations involving density.  In next activity: Density of a gas, students determine the density of carbon dioxide. The fact that the value is 3 orders of magnitude smaller than that of liquids and solids sets the stage for the discussion of an atomic model of matter that accounts for this difference. 25

26 Recap: What works Interactive engagement Student discourse & articulation Cognitive scaffolding Multiple representational tools Consensus-based model building Explicit hierarchal organization of ideas and concepts into models Interactive engagement Student discourse & articulation Cognitive scaffolding Multiple representational tools Consensus-based model building Explicit hierarchal organization of ideas and concepts into models

For more information Local workshops next summer (hopefully!) in physics, chemistry, and physical science. Modeling curricula do an excellent job sequencing the curriculum to provide a good storyline and to facilitate model construction and deployment. Elements of the modeling approach can be adapted to any curriculum. I am happy to provide advice, resources, or assistance. Local workshops next summer (hopefully!) in physics, chemistry, and physical science. Modeling curricula do an excellent job sequencing the curriculum to provide a good storyline and to facilitate model construction and deployment. Elements of the modeling approach can be adapted to any curriculum. I am happy to provide advice, resources, or assistance.