| > Which aspects of algebra do the students have the most trouble understanding? The basic concepts of variables and functions. I can't stress enough that most of your high school facebook friends posting these memes are doing so non-ironically: https://www.google.com/search?q=math+was+great+until+they+ad... Which, I guess, means "everything". But really getting over that first conceptual hurdle is the hardest part. After that, it's a lot more hand-holding through exercises/practice than trying to surmount a fundamental conceptual barrier. > What are some good examples of tables, graphs, and functions the students need to interpret? Tables and ratios and rates of change abound in the trades. Especially anything related to electricity or water. You really need at least a conceptual understanding of variables and functions to understand a lot of the material. Also, most tradesmen will want to run their own business at some point (that's where the money is), and tables/graphs/functions abound. If you're struggling with college algebra, odds are good that you're uncomfortable: 1. interpolating values from a table (1/16 : x, 2/16 : y, ..., 1: z; oh no, I need to know the value for 3/32 and it's not on the table!), 2. evaluating a function at a point ("the equation tells me xs from ys and zs, but I need zs from xs and ys!"). Pick a trade and (1) and (2) are fundamentally necessary skills. Smart phone calculators obviate this some-what, but it's still important to have at least a conceptual understanding even if the mechanical skill of doing the math atrophies. Otherwise you won't even know how to use the calculator properly. See this all the time. The money thing in particular is super important, though. I do a lot of example problems that basically boil down to "if your fixed cost is $X and the equipment needs to be replaced every 2 years, and if you charge $Y, will you make a profit? What is the smallest value of Y that will make a profit? Etc." Students really struggle with this sort of thing, especially if you throw in seasonal variable with fixed debt payments ("how much do I need to make in the summer months to cover the loan payments in the winter months?"). Questions like this are at the heart of college algebra. Like, would not be surprising if lots of small businesses fail because the owner doesn't do the work of making sure the unit economics can cover amortized costs, and then end up defaulting on their loan. TBH even gig economy participants need to be able to do the more basic stuff from college algebra... |