Teaching geometric constructions has always been a challenge. The rules are easy enough - compass, straightedge, no measuring. But for the teacher the challenges come quickly. How to actually demonstrate them in class? How will the students remember the steps when trying it themselves? What happens when they do the homework?

- Compasses and straightedge on a whiteboard or overhead projector.
- Software such as Geometers Sketchpad (GSP) or GeoGebra.

The Math Open Reference website offers a third option. In the chapter devoted to constructions (here), there are most of the Euclidean constructions taught in high school. Each one can be stepped through one step at a time, or be let to free run all the way through. Each one also has written instructions for those who prefer that.

Using a projector you can show each construction step by step while you discuss it with the class. The compass actually looks and acts like a compass, and it can draw partial arcs just the like the real one. The straightedge and pencil looks real also.

Fig 1. Freeze-frame of the angle bisection construction.

"The lesson was a huge success. Displaying your construction animations
greatly increased student understanding, motivation and 10x more
efficient. Also they can always visit your site themselves if they
wish."

The next problem arises when the students try to do it themselves. They have to rely on memory to redo what they saw a few minutes ago in class. This memory is typically not very good. Not until they have done it themselves a few times will they really retain it. The ultimate goal of course is to get to the point where the visual aid is no longer needed and they can perform the constructions in a test unaided. Using Math Open Reference, they can bring it up on a computer and follow along with the animations, pausing between steps. This leads to a high degree of success and hastens the time when they can do it unaided.

Some teachers do this in a computer lab setting while they walk around looking over shoulders to find the students who need some extra help. Teachers report that this activity is very engaging. According to Roy Chancellor, a math teacher in Scottsdale Arizona:

"Animated constructions are absolutely indispensable for guiding the
students at their own pace. It would be next to impossible to teach
these constructions in whole-group format. The students were engaged
throughout the lab."

Because the Math Open Reference animations are freely accessible on the web without any special downloads or software, they can again see the step-by-step animations and practice at their own pace until they get it down. They are seeing the exact same animations they saw at school.

Software like GSP is less useful here because:

- The student has probably not purchased it.
- The sketches do not show how they can be produced using real drawing instruments.

Again, Roy Chancellor:

"In my HS geometry class, we're doing a unit on properties of
triangles, such as circumcenter, incenter, centroid, and orthocenter.
After learning various theorems about these special locations, my
students used your construction pages to create each one. After making
the constructions, they used measuring tools to verify each of the
theorems from earlier in the week. It was an excellent way to connect
the book knowledge to something they created."

*John Page is a software designer living in California's Silicon Valley.
He is the author of the free online geometry textbook Math Open Reference. *

Send a message to John Page

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