Content Example: Newton s Laws

1. Content Example:Newton’s Laws What does it mean to “understand” Newton’s Laws?

2. Watching Jim Minstrell Teach about Newton’s Laws of Motion What do you notice that would cause you to change your answers to some of the questions about moving objects? What did you notice that would cause you to change or add to your answers to questions about problems of practice? What did Jim Minstrell need to know in order to teach this way?

3. Why Are Newton’s Laws Considered a Great Intellectual Achievement? First Law: Every object continues in a state of rest, or of motion in a straight line at a constant speed, unless it is compelled to change that state by unbalanced forces exerted on it. Second Law: The acceleration produced by a net force on an object is directly proportional to the magnitude of the net force, is in the same direction as the net force, and is inversely proportional to the mass of the object (F = ma). Third Law: For every action there is an equal and opposite reaction. Universal Gravitation: The gravitational force between any two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them (F = Gm1m2/r2)

4. Historical Sense-making Strategies for Explaining Motion Aristotle, Ptolemy, and Aquinas Setting the stage for Galileo: Impetus theorists and Copernicus Galileo Newton

5. Aristotle, Ptolemy, and Aquinas Practical reasoning: Moving objects with simple machines, throwing,pushing, bows and arrows Narrative reasoning: Where and why do objects move Animate objects (animals) move on their own Natural motion: Inanimate objects tend toward their own spheres (earth, water, air, fire) Violent motion: Animals can impart motion to inanimate objects Heavenly objects are kept in motion by the Prime Mover Aquinas: Prime Mover is Christian God Model-based reasoning: Ptolemaic system explains motions of sun, moon, planets

6. Setting the stage for Galileo Practical reasoning: Siege engines (catapults, trebuchets, cannon); accuracy depends on direction and speed (not just personal skill) Narrative reasoning: Protestant reformation emphasizes personal God rather than distant Prime Mover Model-based reasoning: Copernicus suggests sun-centered model that fits observations better

7. Galileo Practical reasoning: Inventing better telescopes, measuring speed and direction of rolling and falling objects Narrative reasoning: Challenging Ptolemy and Aquinas: Copernicus’ model is true, not just way to calculate positions Telescopic observations of corruptible heavens Model-based reasoning: Mathematical predictions of speed of falling objects

8. Newton Practical reasoning: Mathematical predictions of trajectories (models improve practical reasoning rather than the other way around) Narrative reasoning: Anti-Trinitarian Biblical text criticism: God does not intervene in everyday events Newton’s apple: The apple and the moon are following the same laws Model-based reasoning: Newton’s Laws of motion and universal gravitation

9. Newton’s First Law Traditional wording Every object continues in a state of rest, or of motion in a straight line at a constant speed, unless it is compelled to change that state by unbalanced forces exerted on it. Contrasting Newton and Aristotle Motion doesn’t need to be explained, only changes in speed or direction (velocity). Necessity: No forces or balanced forces always mean no change in speed or direction, and vice versa.

10. Newton’s Second Law Traditional wording The acceleration produced by a net force on an object is directly proportional to the magnitude of the net force, is in the same direction as the net force, and is inversely proportional to the mass of the object (F = ma). Contrasting Newton and Aristotle Forces do not cause motion. Instead they cause acceleration, or change in speed or direction (i.e., velocity).

11. Newton’s Third Law Traditional wording For every action there is an equal and opposite reaction. Contrasting Newton and Aristotle Forces always come in pairs. When A exerts a force on B, B exerts an equal and opposite force on A. This does not mean that the forces on A or B are balanced.

12. Aristotelian and Newtonian Answers to Questions Book on the table Aristotelian: Table blocks book from falling Newtonian: Table exerts an upward force that balances the downward force of gravity Coin in the air Aristotelian: Coin’s upward flight is sustained by a “force from the hand” Newtonian: Continuing upward motion doesn’t need to be explained. Unbalanced force of gravity slows the coin down.

13. Aristotelian and Newtonian Answers to Questions (cont) Cart at constant velocity Aristotelian: Continued motion requires continued force Newtonian: Net force is 0 for motion at constant speed and direction Accelerating cart Aristotelian: Increasing motion requires increasing force Newtonian: F = ma. Constant acceleration requires a constant net force

14. Teaching Newton’s Laws to (Aristotelian) High School Students Describing motion: Focusing on speed and direction rather than destination and reason for motion Negotiating standards for what counts as evidence (“experientially real”) Extending experience: Collecting data in situations where Aristotle’s rules break down Questioning students’ narrative and practical knowledge Model-based reasoning: Finding consistent, parsimonious explanations that fit all the data Quantitative rigor: Using models to make precise, quantitative predictions

15. Watching Jim Minstrell Teach Again How does he address each of the challenges to his students’ learning with understanding?

16. Patterns in Teaching Strategies American and Japanese math teachers Carol and Jennifer Barb Neureither Jim Minstrell

17. Niels Bohr on Scientific Reasoning The task of science is both to extend our experience and reduce it to order, and this task represents various aspects, inseparably connected with each other. Only by experience itself do we come to recognize those laws which grant us a comprehensive view of the diversity of phenomena. As our knowledge becomes wider we must always be prepared, therefore, to expect alterations in the points of view best suited for the ordering of our experience.

18. Experientially Real Objects, Systems, and Phenomena

19. Development of Knowledge Extending experience: Adding to our stock of “experientially real” objects, systems, and phenomena Adding new sense experiences Adding vicarious sense experiences (e.g., pictures, video) Adding believable, experientially real data (e.g., measurements, carefully recorded observations) Reducing experience to order: Developing new and better models and theories Conceptual change: Replacing old theories with new ones that account for more data Converting previous “theories” to taken-for-granted experientially real objects, systems, phenomena (e.g., existence of objects, conservation of liquid volume)

20. What Counts as Experientially Real? Everyday judgments: Seeing (or hearing, touching, feeling) is believing Vividness and immediacy of experience Confirmation by peer group Scientific judgments: Creating data from experience Reproducibility Precision Provenance of records Confirmation by skeptical observers

21. What Counts as aGood Model or Theory? Procedural display: Whatever it takes to get a good grade Practical reasoning: Whatever it takes to get practical results (including inventing things) Narrative/metaphorical reasoning: Stories or metaphors that bring coherence to our experiences (including news, history) Model-based reasoning: Models that account for all relevant data in testable, parsimonious ways “Unbroken chain of connections” from data to models Consistency with other models and theories

23. Focus on Lesson Sequences

24. General Teaching Strategies Covering content: Telling the story with examples and expecting students to tell it back (Jennifer’s approach) Leads to narrative understanding or procedural display Learning cycles focusing on application of model-based reasoning (Carol’s approach) Inquiry cycles focusing on developing new models through reasoning about data (Minstrell’s approach) Combined inquiry and learning cycles (Japanese math teachers, Jim Minstrell, Barb Neureither)

25. Telling the Story of Science:The Pattern of School Science Science content is the scientific story of the world Students’ experiences are used to motivate students, justify content Data (experientially real by scientific standards) are separated from experiences that meet student criteria for “experientially real” Students are responsible for repeating science content, making connections or solving problems within its domain Compare with history or literature teaching: Students are expected to understand the story on its own terms; connections to students’ personal experiences are motivational “extras”

26. Common Patterns in Inquiry and Learning Cycles: The Pattern of Excellent Science Teaching Science content is model-based reasoning: Patterns provide a link between explanations and multiple experiences Students’ experiences and patterns are essential part of content Experiences meet both scientific criteria for data and student criteria for “experientially real” Students are responsible for using models to reason about multiple experiences Different from history or literature teaching: Grounding of models in experience is essential characteristic of science

27. Classroom Environments for Learning and Inquiry Cycles Personal and emotional safety for students, including moderate levels of risk and ambiguity Motivating students to learn: Expectancy times value Social norms for participation and communication

28. Learning Cycles Focusing on Application Establishing the problem: introducing new experience or helping students to see that they have not fully reduced their experiences to order Modeling: Introducing new models/theories and showing how they can be used to reason about students’ experiences Coaching: Students apply the models to other observations with scaffolding (help and support) Fading and maintenance: Students apply the models to more observations with less support

29. Inquiry Cycles:Developing Evidence-based Arguments Questions: Teacher or student suggests problems to investigate Evidence: Data: Students create or are given data that both meets scientific criteria and is experientially real to them Evidence: Patterns: Students create data displays (e.g., charts, graphs) and find patterns in data Student explanations: Students develop explanations for the patterns they have found Scientific explanations: Students compare their explanations with scientific models

30. Combined Inquiry and Learning Cycles Establishing the problem and modeling: Students develop and share patterns and models through inquiry Conclusion of modeling: Teacher reinforces key elements of appropriate student reasoning Coaching and fading: Students practice with additional examples and diminishing support Examples Japanese math lessons Barb Neureither Jim Minstrell (including episodes not on tape)

31. Learning and Inquiry Cycles Prerequisites Model or theory Set of real-world examples Pattern for students to follow in applying theory to examples Stages or activities Establishing the problem Modeling Coaching Fading Maintenance Prerequisites “Experientially real” data Pattern(s) that students will be able to see Theory or model that explains patterns Activities Questions Evidence: Data and patterns Students’ explanations Scientific explanations Communication

32. Final Questions (based on reading Minstrell’s chapter) What were the stages in the evolution of Minstrell’s teaching strategies? What were the key elements in his developing approach to each problem of practice? Content and learning goals Students and assessment Classroom environment and teaching strategies (e.g., inquiry cycle for Newton’s Second Law) Professional resources and relationships (for discussion) What commitments and habits of mind enabled Minstrell to develop his approaches?

33. Coaching on Learning and Inquiry cycles: In subject-matter groups 1. Pick one using objective from topics you discussed on for your case studies 2. Develop learning cycle to teach that objective, meeting criteria in TSMU 3. Develop inquiry cycle for the same objective 4. Compare and contrast two teaching approaches

34. Learning and Inquiry Cycles Prerequisites Model or theory Set of real-world examples Pattern for students to follow in applying theory to examples Stages or activities Establishing the problem Modeling Coaching Fading Maintenance Prerequisites “Experientially real” data Pattern(s) that students will be able to see Theory or model that explains patterns Activities Questions Evidence: Data and patterns Students’ explanations Scientific explanations Communication