Forging Connections

This site supports the NSF project on Technology-Rich Units for Future Secondary Teachers: Forging Dynamic Connections Between Geometry and Functions, which is part of the NSF's program on Improving Undergraduate STEM Education (IUSE).

Unit 1: Understanding Geometric Transformations as Functions

  1. Identify Functions: Students distinguish independent from dependent variables, describe the behavior of dependent variables as they drag the independent variable, distinguish between functions and non-functions, and arrive at their own definition of function.
  2. Identify Families: Students drag variables to solve “Which one is different” puzzles involving four functions, three of which are from the same family. They begin by comparing the shapes of traces left by the variables, analyze the relationship between the traced shapes and the rate of change of the variables, and learn to distinguish functions based on rate of change. Students have their first encounter with function notation, as a way of indicating which dependent variable is related to which independent variable.
  3. Reflect Family: (Draft Form) Students construct, investigate, and formalize the reflect family, accomplishing objectives similar to those described above for the Rotate Family (which is more fully developed).
  4. Rotate Family: Students create rotate functions, formulate informal descriptions of the rate of change that distinguishes rotate functions, use function notation, and restrict the domain of a rotate function to observe the corresponding range. Students perform physical and virtual function dances, they solve puzzles requiring them to rotate one shape to superpose it upon another congruent shape, and they compose two rotations and figure out how to adjust the second rotation to turn the composition into an identity function. Students play a video game in which they're given three of the four elements of a rotate function (independent variable, center of rotation, angle of rotation, dependent variable), and their job is to find the value or location of the missing element.
  5. Dilate, Translate, and Glide Reflect Families: (Not yet available) Students work in small groups to construct, analyze, and formalize their understanding of these function families. Each group specializes in one family, and they share their results (including a choreographed dance) with other groups.