Using Geometry with TI Technology
When students interact with dynamic geometry software, they can construct, measure, and move figures to explore properties, confirm theorems, and visualize geometric situations. Lessons using this technology allow students to create their own geometry knowledge and are also more fun than reading properties and theorems out of a textbook. Most importantly, engaging students in doing the math (not simply viewing the math) makes their learning deeper and more durable.
In the GEOMETRY GRAB BAG webinar, we took a look at Exploring A Situation, Confirming Properties, Constructing Un-mess-up-able* Figures, and Capturing Data using the geometry capabilities of TI Calculator technology (both TI-84+ family and TI-Nspire). Here is a quick overview; be sure to check the links at the bottom of the post for all the resources and the webinar replay.
A. Getting Started
Here are quick HOW-TO guides for geometry on TI-Nspire and the Cabri Geometry App on TI-84+. For many pre-made activity files, students just need to know how to grab and drag a geometric figure, then observe and reflect on the results. In a dynamic geometry environment, creating a figure such as a triangle is like creating infinitely many examples of triangles to explore, since measurements update as the figure is moved.
B. Explore A Situation
A pre-made file allows students to focus on the implications of the geometric scenario, rather than on construction details. Instructions for linking devices and transferring files are included in the webinar materials.
Lines & Transversals asks students to compare and contrast situations when something is true or not true. Targeted questions on the student lab sheet help clarify angle pairs that are sometimes OR always congruent and supplementary.
Triangle Midsegments is a nice exploration to “get your feet wet” with constructing and measuring. I like to ask students “what do you want to measure?” to give them control of the investigation. The most important step of the activity is to DRAG AND OBSERVE; how do the measurements change? Provide a template for students to record sketches, measurements and conjectures, to hold them accountable for mathematical thinking.
Area Formulas in TI-Nspire is a great visualization to help students gain understanding of area relationships. I ask my students: “Why does it work?” and “Can you explain it another way?”
C. Confirming Properties
The dynamic geometry activity can help students discover properties and confirm them with measurements and calculations. This can lead to justification and formal proof if desired in your curriculum objectives.
The Pythagorean Theorem can be visualized by building squares on the sides of a right triangle. The Converse helps students determine if a triangle is acute, right, or obtuse.
Coordinate Reflections takes advantage of the coordinate plane that “lives within” each geometry page in Cabri Jr. and TI-Nspire. Students can explore many properties of transformations besides the changes to coordinates.
D. Constructing Figures
There is an important distinction between drawing and constructing figures in dynamic geometry environments. When a figure is accurately constructed — sometimes called “un-mess-up-able”– it is guaranteed to retain its specific properties no matter how it is dragged on the screen. If a figure is merely drawn to look like a particular diagram (for example, drawing a “right” triangle without using the perpendicular tool), its properties won’t stay valid as the figure is manipulated.
Parallelogram Properties has students first constructing a parallelogram, then measuring its parts to find out important properties. You can extend the learning to other types of quadrilaterals or explore less common theorems with the power of dynamic geometry, allowing even struggling students to go beyond the basic topics.
E. Capture Carnival
Data capture is a huge asset within TI-Nspire. Once variables are defined, values can be captured manually or automatically. Then students can create a scatterplot, develop an algebraic model, or perform regressions as desired. If you are using Cabri Jr. on the TI-84+ family, you can still collect data by hand, then store in the Stat Lists for further examination.
Chords in Circles is an example of a geometric figure that generates an interesting function relationship. Other data collection activities are included in the webinar materials.
F. Tips for Successful Teaching: Online & Face-To-Face
- Keep your TI-84 SmartView Emulator software or TI-Nspire Premium software on top of your working document (Word, Google Docs, Smart Notebook, etc.)
- Use screenshots frequently so students can keep up and catch up. Annotate these for asynchronous students.
- Use color and motion to highlight ideas and address misconceptions directly.
- Think about what preliminaries are important for your students to be successful: needed definitions, labels on points (or not), dragging points before taking down data, reminders to “make different kinds of triangles,” etc.
- Provide templates for students to RECORD observations and REFLECT on the geometry concepts.
- SUMMARIZE the results for the class, either yourself or by students, since this ensures that important math concepts don’t get lost in the technology activity, and it helps make the learning more durable.
Using dynamic geometry technology has greatly enhanced my geometry teaching! Dive into these resources to see what the power of geometry technology can do for your students.
Notes and Resources:
This webinar was based on two prior blog posts on the T3Learns Blog:
*The term “Un-mess-up-able Figure” is from the CME Project’s Geometry textbook published by Pearson (2009: Cuoco, et. al.), and is defined as: A figure that remains unchanged when you move one point or other part of the figure.