How to help students understand high school geometry?

How to help students understand high school geometry?

We already see that the measures to take should happen before high school. The best approach involves changing how math and especially geometry is taught BEFORE high school. Some points to consider are:

Ø  Improve geometry teaching in the elementary and middle school so that students' van Hiele levels are brought up to at least to the level of abstract/relational.

Ø  Include more justifications, informal proofs, and "why" questions in geometry teaching during elementary and middle school.

Ø  In general, make students think, reason, and use their brain in different educational tasks (not just math).

How to help students to develop understanding of a geometry concept

Ø  When studying a concept, show correct AND incorrect examples, and in different ways or representations (rotate the pictures upside down etc!). Students are asked to distinguish between correct and incorrect examples. This will help prevent misconceptions.
 

Ø  Aks students to draw correct and incorrect examples of a geometry concept. For example, ask them to draw parallel lines and lines that are not parallel. Tying in with this, ask them to draw a parallelogram and a quadrilateral that is not a parallelogram.
 

Ø  Tying in with the previous point, you can ask the students to provide a definition for a concept. This can get them to thinking about which properties in the definition are really necessary and which are not. For example, ask them to define an "equilateral triangle".
 

Ø  Allow the students to experiment, investigate, and play with geometrical ideas and figures. For this you could use manipulatives, lots of drawing, and computer programs.

Ø  Have each student make his/her own geometry concepts notebook, with examples, nonexamples, definitions and other notes or pictures.