Introduction to Geometer S Sketchpad (GSP)

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Drawing vs. Constructing

Participant Handout

Introduction to Geometer’s Sketchpad (GSP)

Dynamic geometry environments (DGEs) are particular technology tools that have been used in the learning and teaching of geometry to assist students in moving beyond the specifics of a single drawing to generalizations across figures. The Geometer’s Sketchpad is one of many DGEs. Although they all are different, they do share some common features which include among others: a set of primitive elements of Euclidean geometry; the ability to construct other geometric objects using these primitive objects; the ability to act on constructed objects via transforming tools, measurement tools, and calculation tools; and the ability to explore relations among constructed objects via dragging, animation, and hiding and showing objects and measurements.

Questions to consider:

1.  What types of things were you able to do in GSP?

2.  Discuss the dependent and independent relationships of objects in GSP. How can you determine if an object is dependent or independent?

3.  Use GSP to determine the angle sum of a triangle.

4.  How would you classify the cognitive demand of the task in question 3?

5.  What other geometric properties of triangles could you have students explore using your sketch from question 3 or with a slight modification of the sketch?

Drawing versus constructing

Create a right triangle. Measure the angles and then drag a vertex to determine if the triangle always remains right.

Questions to consider:

1.  How can we create figures so that they pass a drag test (i.e. keep the properties we want it to have) and don’t break?

2.  Can you create a triangle that is a right triangle and will always be a right triangle when dragged?

Discussion of drawing versus constructing

Questions to consider:

1.  Construct the following objects:

a.  Isosceles triangle

b.  Isosceles right triangle

c.  Equilateral triangle

d.  Rectangle

e.  Square

f.  Rhombus

g.  Kite

h.  Trapezoid

i.  Isosceles trapezoid

j.  Cyclic quadrilateral

2.  In what ways is constructing in GSP similar to and different from using a compass and straightedge?

3.  Why is it important for students to understand the difference between drawing and constructing?

4.  How would you characterize the cognitive demand of the construction task? Why?

5.  How can you use GSP to have students explore properties of particular objects? Provide an example.

Adapted from: Hollebrands, K. F., & Lee, H. S. (2012). Introduction to dynamic geometry environments. In Preparing to teach mathematics with technology: An integrated approach to geometry (1-22). Dubuque: Kendall Hunt.