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Use and Abuse of Equality in Solving Physics Problems

Use and Abuse of Equality in Solving Physics Problems. Jorge Ballester (jballest@emporia.edu) Emporia State University. Preliminary Questions. Why do we do this ? Does it confuse students?. Meaning of “=“. “this=that” means “this” represents the same value as “that”.

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Use and Abuse of Equality in Solving Physics Problems

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  1. Use and Abuse of Equality in Solving Physics Problems Jorge Ballester (jballest@emporia.edu) Emporia State University

  2. Preliminary Questions • Why do we do this? • Does it confuse students?

  3. Meaning of “=“ • “this=that” means “this” represents the same value as “that”. • Binary equivalence relation between “this” and “that” • “this=that” is either True or False.

  4. Properties of “=“ • Reflexivity: A=A. • Symmetry: if A=B then B=A.(not true of inequalities) • Transitivity: if A=B and B=C then A=C.(basis for substitution)

  5. Operational vs. Relational Understanding of Equality • Knuth, Alibali, Hattikudur, McNeil and Stephens, “Importance of Equal Sign Understanding in the Middle Grades” (2008) • Operational: 2(4+8)=24 • Relational:

  6. Use and Abuse • Use (operational)

  7. Use and Abuse • Use (operational)

  8. Use and Abuse • Use (operational)

  9. Use and Abuse • Use (operational) • Abuse (operational & relational?)

  10. Use and Abuse • Use (operational) • Abuse (operational & relational?)

  11. Use and Abuse • Use (operational) • Abuse (operational & relational?)

  12. Use and Abuse • Use (operational) • Abuse (operational & relational?) (?)

  13. Use and Abuse • Use (operational) • Abuse (operational & relational?) (?)

  14. Inclined Plane Problem • Newton’s 2ndLaw

  15. Inclined Plane Problem • Newton’s 2ndLaw

  16. E-field Outside a Charged Sphere • Gauss’s Law

  17. E-field Outside a Charged Sphere • Gauss’s Law

  18. Free Fall • Law of Conservation of Energy

  19. Free Fall • Law of Conservation of Energy • Substitution

  20. Free Fall • Law of Conservation of Energy • Substitution • Simplification

  21. Hypothesis • Some laws/equations (e.g. Newton’s 2nd) suggest an operational interpretation. • Some laws/equations (e.g. Conservation of Energy) suggest a relational interpretation.

  22. Concluding Suggestions • State general law • Use substitution explicitly • Avoid multiple =‘s except in an explicitly operational context.

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