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. Experimental Setup

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

15. 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. Calculations: Harmonic Oscillations of a Pendulum

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

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

34. 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

51. Workshop: Discharging a Capacitor Charging and Discharging Circuit

52. Workshop: Evaporation Heat of Pentane Preparation of the Temperature Probe

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

54. Workshop: Evaporation Heat of Pentane Optical Fit

55. Workshop: Evaporation Heat of Pentane Regression

56. Workshop: Pendulum Motion and Acceleration Sensors

57. Workshop: Pendulum Measurement Procedure

58. Workshop: Pendulum Experimental Setup

59. Workshop: Pendulum Measurement Scatter-Plot, Spreadsheet

60. Workshop: Oscillating Circuit Starting and Oscillating Circuit

61. Workshop: Oscillating Circuit Experimental Setup

62. Workshop: Oscillating Circuit Nspire Voltage Measurement (EasyLink)

63. Workshop: Faraday’sLaw of Induction

64. Workshop: Law of Induction Measurement: Voltage Probe and EasyLink

65. Workshop: Law of Induction Measurement: 50 Hz R-C-Ripple Filter (if necessary)

66. Workshop: Law of Induction Experimental Setup

67. Workshop: Law of Induction Measurement: Voltage Surge (Coil 23’000 Turns)

68. Workshop: Law of Induction Oscillating Magnet (turn by 90° for Measurement)

69. Workshop: Law of Induction Oscillating Magnet: Experimental Setup

70. Workshop: Law of Induction Oscillating Magnet (Coil with 23’000 turns) 2 Oscillating Modes

71. Workshop: Characteristics (Bulb. Diode LED) Measuring Circuit: With 2 Nspires and 2 Voltage Probes

72. Workshop: Characteristics Measuring: Characteristics of an ideal and a real Bulb

73. Workshop: Characteristics Measuring: Characteristics of a LED (GaAS/GaP)

74. Workshop: Force Plate Measuring: Vernier Force Platfrm (with Strain Gauges)

75. Workshop: Force Plate Measuring: Nspire F vs. t Graph

76. Workshop: Force Plate Calculations: Integral (Trapezoidal Rule)

77. Thank you for your attention