Physics in the Mathematics Curriculum Summary

Tuesday, July 2, 2002

Training in PCMI Website by Suzanne 1:00 - 1:30 in computer lab (how to log on, what's on site, update personal biography, access daily journal, how to access and post to PCMI site)

Continued discussion of our purpose:

  • Discussed existing mission statement on the PCMI website. How will we adjust this?
  • Yesterday's statement: Using physics as a context to present and study the concept of function (linear, quadratic, logarithmic, inverse, power, etc.)
  • Other ideas: seeing mathematics through the lens of physics.
  • Helping students overcome common misunderstandings by using the lens of physical activities to focus their thinking.
  • Activities we suggest and develop should be dense in mathematics, open- ended in nature, and should include the physics background needed by teachers to students to really understand the physical concepts involved in the activity.
  • Perhaps we should brainstorm on areas in which students typically have troubles, and used this as a focus of what we select to develop activities on. Don't just limit ourselves to trouble areas; the physical activities can be used just as well to reinforce, expand, and apply mathematical concepts previously learned.
  • Idea: physics and science teachers often complain students cannot solve literal equations (equations that don't involve x and y).

Swinging an Open Tube in the Air
Mathematical Concept: Step Functions, (number of revolutions per second versus tone).
Demonstration of wave introduction for students: students stand shoulder to shoulder with hand on shoulder. Show longitudinal and transverse waves and different wave speeds.

  1. Swing the tube at various speeds. How many modes are possible with your tube?
  2. Swing the tube to create the first tone consistently. Time 10 revolutions. How many revolutions/sec?
  3. Repeat step 2 for each different mode of your tube?
  4. Gather data from all groups.
  5. Plot pitch as a function of frequency.

Tomorrow, we plan to brainstorm other ideas, then fully develop these activities through the next two weeks.

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IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540
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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.