Objectives
Vertical changes act on outputs (more intuitive), while horizontal changes act on inputs (less intuitive). This asymmetry is central to why students mix up stretch/compression effects and assign their own logic to translations. This activity focuses on dilations through an extremely powerful tool: “Points by Coordinates”. This simple tool is designed to help students get over the cognitive chasm!
Vocabulary
- Dilation
- Dilation from the x axis (towards / away)
- Dilation from the y axis (towards / away)
- Dilation factor
About the Lesson
Horizontal changes feel “backwards” because they act on inputs, dilations exacerbate this cognitive challenge leading students to stay at a rule-following level rather than understanding the underlying process. Multiple representations and dynamic technology can help students bridge the gap. A powerful tool was introduced to TI-Nspire “Point by Coordinates”, specifically designed to address these cognitive challenges for students. This activity uses this feature to help address issues around understanding of dilations.