Proof should be taught in geometry — I highly recommend it. But today, unfortunately, there is too much of a trend — pushed by the NCTM
and others — to take proof out of geometry and to use geometry as time to review algebra 1. Students miss a great deal of cognitive training that way, training (in how to reason and construct arguments) important for law, philosophy, writing, mathematics, and science. The ancient Greek philosopher Plato is purported to have had a sign above his school, the Academy, saying “Let no one who is not a geometer enter here ” — meaning, he wanted only people in his school who knew geometry or were capable of learning it, since the ancient Greeks knew that geometry taught reasoning, and thus could be used to prepare people for the higher rigors of philosophy.
I’d recommend you find a geometry text that has proofs in it. Students should have to learn a number of proofs, memorize some proofs, and do a plethora of proofs.
It would be a good idea to spread geometry over several years, too. Students — from even the elementary years — need a good introduction to shapes and their interrelationships before the students even get to the proofs, i.e., before they get to systematically organizing and structuring geometry. You can get some ideas from Montessori methods; here are some videos:
Circles (39 sec)
Triangles, polygons and other shapes (57 sec)
Prisms and cylinders (1 min 20 sec)
Triangles and polygons (2 min 28 sec)
Cylinders (1 min 6 sec)
Arithmetic (prep for algebra), mostly (3 min, 40 sec)
Child with cylinder blocks (1 min, 24 sec)
Excerpt from “Nurturing the Love of Learning” produced by the American Montessori Society (10 min, 5 sec)
Montessori School in Phuket (13 min, 21 sec)
In view of the value we get out of geometry, it would be highly beneficial to study formal geometry (that is, study geometry as a science using proofs) over two years or three instead of cramming it in one year and then running from it.
You can read how I generally run my geometry classes and tutoring sessions in my prior post “A Typical Geometry Class at MGTutoring
“, where I wrote up some highlights and commentary from a recent tutoring session.