Tool Building: Web-based Linear Algebra Modules - Student Reactions

David E. Meel and Thomas A. Hern

Even though Transformer3D is not a fancy three-dimensional rendering program, students were still able to use it to make observations, propose conjectures, and test hypotheses. In particular, students made the following observations after working with Transformer3D:
  • "Moving individual pieces of a vector changes the position but not the shape of the transformed image".
  • "The shape of the transformation of unit circle is dependent on the matrix A and not on x".
  • "Although it's difficult to see what works with what, it was interesting to try to make the Transformation look like it was from R3 to R2. I really had to think about what I needed to change".
  • "The 3D program helped me make sure my observations from the other one were right. I could test ideas and make sure they worked although sometimes it was hard to tell when things were moving".

Having students observe how different components of the matrix A impacted the nature of the transformation was the goal of constructing Transformer3D. In addition, having the students be able to make conjectures and then examine them in multiple settings has the potential to be valuable.

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