Hans Kammer, Berner Maturitätsschule für Erwachsene, CH-3012 Berne, Switzerland

1. Physics Experiments for Mathematical Education Hans Kammer, Berner Maturitätsschule für Erwachsene, CH-3012 Berne, Switzerland

2. Motivation for dealing with empiric Data in mathematical Education • real world experiments engage students • application in a practical field stimulates more • than „grey theory“ alone • well selected applications show beginners the • enormous practical importance of mathematics • managing great data volumes is a modern • everyday application of mathematics (=>meteorology) • working with practical experiments from physics, • biology, sports etc. shows the interdisciplinar • character of mathematics • and first of all: calculator methods are simple!

3. Evaluation of experimental Data: Procedure • measuring physical data with sensors and calculator • guessing the mathematical function describing these • data • fitting optically the measured data with this • function varying its parameters with sliders or • fitting by regression with a (limited) set of built • in standard functions.

4. What should you learn for your instruction? • Handling of at least one sensor e.g. Temperature • Data Acquisition with the TI-NspireCAS Handheld • Calculator and Computer Software: • Spreadsheet and Scatterplot in Graphs-Application • Enter a Function and fitting it to the measured data • by settings ist parameters with sliders • automatic Data Regression with built in standard • function • Expanding the Regression Technique with • Parameters/Sliders

5. Subjects • The Problem of Heating and Cooling: • Newton‘s Law • Harmonic Oscillations of a Pendulum • Force Platform • and more in the workshops …

6. The Problem of Heating and Cooling: Newton‘s Law

7. The Problem of Heating and Cooling: Newton‘s Law Experimental Setup

8. The Problem of Heating and Cooling: Newton‘s Law

9. The Problem of Heating and Cooling: Newton‘s Law

10. The Problem of Heating and Cooling: Newton‘s Law

11. The Problem of Heating and Cooling: Newton‘s Law

12. The Problem of Heating and Cooling: Newton‘s Law

13. The Problem of Heating and Cooling: Newton‘s Law

14. The Problem of Heating and Cooling: Newton‘s Law

15. The Problem of Heating and Cooling: Newton‘s Law Calculation: Finite Difference Equation (Spreadsheet)

16. The Problem of Heating and Cooling: Newton‘s Law Calculation: Finite Difference Equation (Graph)

17. The Problem of Heating and Cooling: Newton‘s Law Measurement: Response Time of an EasyTemp Sensor

18. The Problem of Heating and Cooling: Newton‘s Law Measurement: Response Time („Optical Fitting“)

19. The Problem of Heating and Cooling: Newton‘s Law Evaporation Heat of Pentane: Exponential Regression

20. The Problem of Heating and Cooling: Newton‘s Law Evaporation Heat of Pentane or Acetone: Experimental Setup

21. The Problem of Heating and Cooling: Newton‘s Law Evaporation Heat of Pentane ( ): Regression Graph

22. Harmonic Oscillations of a Pendulum Calculations:

23. Harmonic Oscillations of a Pendulum Construction

24. Workshop: Pendulum Experimental Setup

25. Harmonic Oscillations of a Pendulum Sensors: Distance (ulrasonic, contactless), Acceleration

26. Harmonic Oscillations of a Pendulum Measurement: Distance, Graph

27. Harmonic Oscillations of a Pendulum Measurement: Distance, Spreadsheet, Regression

28. Harmonic Oscillations of a Pendulum Measurement: Velocity, Calculated from distance data

29. Harmonic Oscillations of a Pendulum Measurement: Acceleration, Calculated from velocity

30. Force Plate (Clinic, Biomechanical Research, Sports) 3-d Professional Force Platform for Gait and Balance Analysis (Kistler 9285BA, piezoelectric)

31. Force Plate (Kistler 9285 BA) Force Measurements and Photograhic/Cinematographic Recording of the Contact Surface from below

32. Force Plate Clinical Motion- and Gait-Analysis (Rehabilitation and prothesis enhancement, Kistler)

33. Force Plate Gait Parameters: Forces vs. time (Kistler)

34. Force Plate Motion and Gait Analysis (Kistler)

35. Force Plate Take off Forces in Performace Diagnostics (Kistler)

36. Force Plate Strain Gages instead of Piezoelectric Sensors (Vernier)

37. Force Plate School Application: Newton‘s Law

38. Force Plate Take off Forces during a Jump from the force plate (Vernier, Nspire)

39. Force Plate Take off Forces: Calculation of Jumping height (Vernier)

40. Force Plate Jump from the Force Plate: Data Analysis (Vernier, Nspire)

41. And many other applications from natural and environmental sciences, sports, medicine …

42. Thank you for your attention

45. Physics Experiments for Mathematical Education: Workshop Hans Kammer, Berner Maturitätsschule für Erwachsene, CH-3012 Berne, Switzerland

46. Subjects • Discharging a Capacior with a Resistance • Evaporation Heat of Pentane • Pendulum: Distance and Acceleration • R-L-C-Oscillator (Oscillating Circuit) • Faradays Law of Induction • Electric Characteristics (Diode, Bulb) • Force Platform

47. Workshop: Discharging a Capacitor Charging and Discharging Circuit

48. Workshop: Discharging a Capacitor Capacitor, Resistor and 9-Volt Battery

49. Workshop: Discharging a Capacitor EasyLink Interface and Voltage Probe

50. Workshop: Discharging a Capacitor Nspire Discharging Scatter-Plot and Regression-Graph