> > Do we really need a full year of geometry, anyway? >
I ask somewhat facetiously the following: suppose we had three years of geometry and one year of algebra in the curriculum, would not the question "Do we really need a full year of algebra, anyway?" be appropriate.
Yes, we need a full year of geometry, but we need a full year of geometry and not some year wasted without mathematics. We need more years of investigations using thought and fewer years of learning meaningless algorithmic processes that are more easily forgotten than learned. We need years of having students learn to think through a probem, to understand, and to develop rather than to mimic. Do we need a full year of geometry? Yes, and more. Let's not bail out the students, let's not make their lives easy, but rather let's get inside their heads and rumage around, expunging the inert while getting them to begin generating fruitful thoughts.
If I had a choice of having students study 3 years of geometry and only 1 of algebra as opposed to the present, I would have guessed heaven had arrived on the wings of a TI-92.