Three projects at Saint Bernard School (Uncasville, CT) have tried to answer the math student’s perennial question: What do I have to learn this for?  The goal of the first project (2013-2014) was to show students in pre-calculus applications of transcendental functions and matrices. The second (2015-2016) introduced structured problem solving through Problem-Based Learning to students in Calculus I. The third (2017-2018) focused on middle school students in grades 6, 7 and 8.  Some of these activities are based on Dumpster Optics and require only inexpensive materials. Others made use of specialized items. In all cases, the mathematics is brought to the fore - what do I need to know that for?

1 Spreading Light – How does light spread as you go away from a small light bulb? (square numbers, quadratic functions, graphing). Requires only simple materials.

  1.     Single file with instructions, student handout and teacher notes Spreading_Light.pdf

2 Pinholes and Triangles – How can a pinhole make an image? (similar triangles). Requires only simple materials. Optional: making an actual pinhole camera is a more complex process but the materials are simple. Measurement with similar triangles has two alternate versions, indoors predicting and measuring image size and outdoors measuring the height of a tree.

  1.     Slides with instructions  Pinholes_and_triangles_slides.pdf   

  2.     Student handout - how a pinhole makes an image  Part_1_Pinhole_Image_Observations.pdf

  3.     Student handout - measurements of image size Measurement-Predict_Pinhole_Image_Size.pdf

  4.     Outdoor version of measurements  Measurement-How_tall_is_a_tree.pdf

Spectroscopy – What colors are given off by a glowing or reflecting source? Use interpolation to find the wavelength of the H alpha line in this quick exercise.

  1. Slides with instruction. Spectroscopy and Interpolation.pptx.pdf The spectrum can be projected as a class project, of printed for students to work on at their desks.

Projects were supported in part by SPIE, the International Society for Optics and Photonics.