IREM

From 2011 to 2016 I was part of the mathematics/physics working group of the IREM of Franche-Comté, together with Sasana BARATA, Thierry CLAD, Stéphane VERJUX and Jean-Marie VIGOUREUX. We designed the activities presented below, ran two training courses for secondary-school teachers, and published the following article. The teaching material is in French.

Publication

• Four solaire et parabole, APMEP no. 521, pp. 572-581, pdf.

Acoustics (upper secondary)

The document below studies the acoustic properties of certain buildings using mathematics and Descartes’ laws. Presented at the 2014 training course, this activity comes with GeoGebra files illustrating the topic (7 documents).

• Presentation: acoustics ( .ppt )
• GeoGebra:
  1. ellipse ( .ggb )
  2. ellipse ( .ggb )
  3. Descartes’ law of reflection ( .ggb )
  4. architecture ellipse ( .ggb )
  5. elliptical dioptre ( .ggb )
  6. Descartes’ law of refraction ( .ggb )
  7. Fermat ( .ggb )

Formation of a layer of ice on the surface of a lake (upper secondary)

We study how a layer of ice forms on the surface of a pond and how its thickness evolves over time. Two teaching approaches are proposed, one from physics and one from mathematics. This activity was presented at the 2014 training course.

• Teaching material for physics:
  1. Student worksheet ( .pdf )
  2. Curves: ice formation ( .xls )
  3. Presentation: ice formation ( .ppt )
• Teaching material for mathematics:
  1. Algorithm: ice formation ( .pdf )
  2. Presentation: ice and mathematics ( .pptx )
  3. Mathematical solution ( .pdf )

Do materials do mathematics? (upper secondary)

Conic sections turn up almost everywhere in nature — in the motion of celestial bodies across the sky, for instance. Here we set out to find them in the microscopic structure of certain materials. The presentation comes with a video that helps visualise the mathematical construction of conics. This study was presented at the 2014 training course.

• Video on conic sections: https://www.youtube.com/watch?v=GDHNoQHQmtQ
• Do materials do mathematics? ( .pdf )

The parable of joy (upper secondary)

The activity below studies the intersection between one group of people fleeing a fire in a circular pattern and another group trying to find the survivors, moving in a straight line. Also presented at the 2014 training course, it is a more playful restatement, for pupils, of what was observed in the study of materials above.

• Documents:
  1. The trees of joy ( .docx , .pdf )
  2. Curves ( .ggb )

The parabola and optics (upper secondary)

This activity builds the parabola and studies its mathematical properties starting from its optical properties. GeoGebra files complete the activity and illustrate the topic (7 documents). It was presented at the 2013 training course.

• Documents:
  1. Student ( .pdf )
  2. Teacher ( .doc , .odt )
  3. Analytical solution ( .pdf )
• GeoGebra:
  1. curve HH’ ( .ggb )
  2. Descartes ( .ggb )
  3. tangent ( .ggb )

Musical sounds (upper secondary, science stream)

The documents below present some properties of musical sounds through a slide deck and an Excel file on Fourier series. GeoGebra files complete the activity and illustrate the topic (11 documents). It was presented at the 2013 training course.

• Documents:
  1. Teacher ( .doc )
  2. Presentation ( .ppt , .pdf )
  3. Wave on a string ( .avi )
  4. Waves and Fourier coefficients ( .xls )
• Wave demonstrator:
  1. Crossing waves ( .avi )
  2. Fixed end ( .avi )
  3. Free end ( .avi )
• GeoGebra:
  1. Wave and delay 1 ( .ggb )
  2. Wave and delay 2 ( .ggb )
  3. Wave and string ( .ggb )
  4. Crossing waves + ( .ggb )
  5. Crossing waves − ( .ggb )
  6. Wave–sine ( .ggb )
  7. Standing waves ( .ggb )
  8. String–Fourier ( .ggb )

Fourier series (upper secondary)

The following activity is an introduction to sinusoidal functions and Fourier series. GeoGebra files complete the activity and illustrate the topic (7 documents). It was presented at the 2013 training course.

• Documents:
  1. Teacher ( .pdf )
  2. Presentation on applications in physics ( .pdf , .pptx )
  3. Activity on periodic phenomena ( .pdf , .docx )
• GeoGebra:
  1. Periodic activity ( .ggb )
  2. Fourier and cosine ( .ggb )
  3. Fourier and sine ( .ggb )