So does a person need algebra to work in advanced vocational fields? No. It might help but it is not by any stretch a must have. After high school I went in the Navy and worked on the HVAC and refrigeration system for the ship. We had ten centrifugal chill water A/C units combined total of 2000 tons capacity. My job was maintenance and repair of those units and our refrigeration gear. While I did have to know some basic formulas it was not complex. I also had to maintain a balanced heat load throughout the ship making sure all areas got cooled dowm and how to reconfigure if they weren't. Therometers told me what I needed to know. Experience taught me what to do.
After I got out I took the two courses I mentioned. Somewhere along the way the state decided to add or supliment Math class into the courses separate from the vocational class. I already knew the needed math to do my job.
A Math instructor swore to me I could not go on a job and place a ladder against a building safely without using either pencil and paper and a measuring tape or a calculator to figure the proper angles. I asked him if he'd ever seen an extension ladder before? I told him place your feet with your toes at the base of the ladder with your feet at each side of it. Then you extend your arms straight out and grasp ladder. If you can do that and the ground is safe then the ladder is safe to climb. He being a Math teacher could not grasp that time and trades honored concept. I could not grasp his advanced math he was insisting on above and beyond what I needed. Not all Math teachers are cut out to climb ladders and not all students are cut out for advanced math courses.
Ironically during that time I enlisted for an Army NG stint as a 13-B. I hauled ammo but we had courses on reading grid maps and getting grid coordinates, azimuth, and back azimuth etc. I had that figured in a few minutes enough to where I was asked if I wanted to be a forward observer instead. I said no thanks LOL.
Some people have the gift of being able to do complex math. I am not one of those gifted. I can do functional math in my head. Grocery shopping? I don't need the calculator. I have a short cut that puts me within about 5% of my grocery budget. I've worked as a clerk before in a store that did not allow use of the cash register total keying in amount paid to give back change. We laid the amount the customer gave on top of the till drawer, counted back to customer the change from amount due to amount given. We didn't come up short and that protected both us and customer from mistakes. Many kids today pass Algebra but can't do basic math in their heads that they actually need. That should be the schools primary focus.
I'm not against advanced Math courses especially for those with the gift for it. I am against making it mandatory at a high school level for students who would be served far better in basic fundamental Math courses. For Voc/Tech students half their sophmore and all their junior and senior year should be strictly vocational courses {I recommend taking two} focused with a goal of Co-op program the senior year. My senior year of high school I was working an 8-5 full time job. Being versitle and adaptable to both your employers needs and the job market will go a long ways. I've done several skilled professions including OTR truck driving at one point.
I teach high school science, and I agree with you. My third track chemistry students are required to pass chem to graduate, but most of them are not really capable of making the connections or doing the math. It's very frustrating for them and for me. Most do their best, but it's only by 'cooking the books' that many of them pass the course. Many would be better served by a vocationally oriented course where they could learn skills that they will actually use. I don't like to pretend, but if they are working hard and truly not equipped to understand, I can't in good conscience fail 2/3 of the class. Inflexible policies put many people into situations which lead to dishonest grading and waste of time and resources.