y = Mx + b = (delta y/delta x) x + b
Mean anything to you? Me neither. A former colleague I worked with at the high school posted on Facebook that she was helping her nephew with a homework assignment and this formula was needed. Smart lady that she is, she came up with the formula but in the comments she stated that she hadn't needed it twenty years.
I was putting some quick sketches on the board with my class recently and not a single one of them new what an extension line was. One of them got the dimension line but she's planning on becoming an engineer so I wouldn't consider her typical of the students I normally get.
By looking at these two things together, I wonder why in the hell do we stress teaching an algebraic formula that a highly educated chemistry teacher hasn't ever used in her career or since having left the classroom but omit simple drafting skills that most everyone could profit from. Most of my students are not at all familiar with 3 view orthographic projection, isometric or oblique drawings, meaning they can't interpret simple sketches or shop drawings, let alone any type of blueprint like they would encounter in a welding or machine shop.
I think it's time to go back to some of the old ways and come up with the "tracks" or whatever you want to call it like they used to do. Offer some type of shop math and business math as well as geometry, algebra and what we called Senior Math when I was in high school. Only roughly 25% of Indiana residents have a four year degree - a few years ago we were ranked 46th in the nation, in fact. I'm not sure what the number is now but that's not necessarily a bad thing. In the past if you wanted to be a machinist, welder, pipefitter, etc., you received your training on the job or through an apprenticeship program. No degree required, good job, decent benefits, live happily ever after. Granted, industry has changed but I keep reading and hearing about jobs going unfilled because employers can't find qualified help. Seems to me at least part of the equation would be change the offerings in the schools.
I learned some board drafting when I was in junior high. I remember making some simple developments and learning how to properly draw lines of different weight such as object vs center lines. Proper lettering practice was taught as well. While I had both beginning and advanced algebra in high school, most of my career I've used mostly simple arithmetic, right angle geometry and a bit of trig. Algebra, not so much. In fact it's almost the end of February and I haven't used any yet this year. I should probably keep my eyes peeled for an opportunity to use it in my day to day activities and report back when that happens. I wouldn't hold my breath, however.
If I wasn't such an old dude, I'd start my own charter school and then we would do some drafting board work, add and subtract some fractions and then make all kinds of things both beautiful and practical.