Geometric Investigation and the Battle vs. Time

We recently finished up our first unit in geometry class, which includes an introduction to angles.  The last lesson we cover exposes students to the concepts of linear pair and vertical angles.

The Vertical Angles Theorem is one of the easiest for students to investigate using dynamic software.  There are a number of activities available for students to "discover" the theorem by exploring the relationships between the angles.  (Math Warehouse and GeoGebra to name a few.)

In our 1:1 setup, we prefer to use Geometer's Sketchpad to do our geometric investigations.  We have come to learn that it takes time to teach students how to navigate around the GSP5 software.  The dilemma we continually face is 'how much time to do we allocate to letting students struggle through the investigative discovery' vs. 'we can demonstrate this concept to the class in a matter of minutes'.

For example, it takes Jarrod or myself about 35 seconds to build a sketch that allows students to see the Vertical Angles Theorem (see diagram below).  Another two minutes of class discussion as we manipulate the points is really all the time needed for students to get a strong understanding of the theorem.

The Battle vs. Time is one that teachers continually struggle with.  It's hard to know when it's right to allow students the opportunity to struggle with the technology available to us.