So I spent 12 years working as an Engineer - designing packaging equipment, doing projects, managing people -- high level responsibility - pay matched. And guess what? I never did matrices - not one single one. Yet it is a requirement for high school now in most Algebra 2 courses? Does that make your typical Algebra 2 student better that they know Cramer's rule? Or are we (teachers) just making ourselves feel good by having students pump and dump (memorize and forget) one more thing.
Don't get me wrong - I think it has a place in high school - PreCalculus, a class for students who want a STEM career but if I have to really make students understand matrices in Algebra 2- that will take at least 5 class periods - nearly 3% of my year.
I can teach about stocks and its math, loans or how to use math to solve open ended problems - but that takes time. So.... how valuable are matrices? Because choices need to be made, and as a group we are picking matrices.
So are matrices more important than stocks (401k 403b anyone?) or loans (buying a house and car is a little more common than matrices)? The point is we have a limited commodity - time!
There is simply not enough time. And if I hear one more expert answer my question of how we are supposed to do it all - say "When you have a unified K-12 curriculum it will happen." - I may seriously crap myself.
I love matrices- there is really vision for programming and problem solving with Cramer'r Rule. Looking for patterns - using to simplify repetitive problems - but if you do it in 5 days in Algebra 2 do you make it to the level of discovery and struggle students need for growth as learners?
I keep thinking the experts forgot we have only 180 days when planning my curriculum - which I lose at least 15 a year to trips, etc. (and those trips need to happen). So in 165 days in 4 years I have to teach and lead student's discovery of math's interconnections and uses - a standard every few days. Ugh.
Now common core haters should not be smiling - we need a national set of standards and math does need multiple solutions not just memorization of algorithms. We just need to make sure what was published in 2010 is not written in stone. We need to allow for creativity and paradigm shifting thoughts -- they should be reviewed and revised every few years. That is real progress.
When I was in industry my simple goal was slow constant sustainable growth - I never said lets be 15% better next year. We moved for 2-3% growth year after year - and once you do that you get long term amazing results. There is too much change too quickly - half the initiatives I have seen in my limited time of 9 years never got the chance to work - not enough time or belief by anyone that they would work.
So there - projects or matrices -- it is really the question of how we make problem solvers.