I started my last two master's classes last night (!!). Since the classes consist largely of teachers, we usually end up having some pretty interesting discussions about teaching approaches to translating the master's-level content to secondary education.
The first professor of the evening (analytic geometry, although the class looks like it's going to get into some fairly wide-ranging content) posed a good question: Are we teaching geometry any differently than we did 40 years ago when he took it in the 10th grade? Or had it introduced to him the 5th grade? Same question for the other core math subjects.
We know that we're being assessed more rigorously and supposedly being held more accountable. I can't speak for math teachers outside of the States (although I'd especially like to hear from my international readers tomorrow), but I know that we're supposed to be using all of the data from the countless standardized tests to which we now teach to drive instruction.
However, my professor pointed out that as he has worked with both primary and secondary math teachers over the years (his area of specialization is math instruction, aside from a love of linear algebra), the fundamental way in which we teach mathematics hasn't changed much.
We don't teach formal proof for most kids, we drill kids less on basic arithmetic, and we spend a lot of time accommodating special needs, but have we figured out a better way to help kids understand math? I'm inclined to agree with my professor.
We've integrated technology to varying degrees and with varying degrees of success. However, we still basically cover the same content at the same times, though perhaps with less rigor. My grandfather dropped out of school in the 8th grade to take over the family farm, but was still vastly more capable of balancing his books than the majority of students I see in the 9th and 10th grades. To be fair, my classes are heavily loaded with inclusion students, but I wouldn't want most of them balancing my checkbook, let alone keeping records for a business.
Forgive the rant that seems to be building here, but I'm frustrated. We put men on the moon 40 years ago, every student has a graphing calculator with more processing power than the computer I used in college, the students are tested up the wazoo and teachers are evaluated until they don't have time to teach. Yet the biggest complaint from professors who teach undergraduate math is that students lack fundamental understanding of conic sections, functions, and basic calculus. Students struggle to relate geometry with trigonometry and periodic functions with the real world. I had to cut a third of the curriculum in my physics class to backfill the necessary math.
Where are we going wrong, folks? How can we use all of the technology and data at our hands to teach kids better? Share any innovative approaches you have below and let us know what's working and what isn't.