On learning more math than it first appears you “need”
From a comment here
When I have students who suggest that they’ll never use the basic algebra I teach them, I first ask them a question: when will they use the material they learned in biology in their lives? When will they use what they learned in their history class in their careers? What percent of the things they learned in school will they directly use in the workplace?
Then I explain one of my philosophies about math classes. The fact of the matter is that most people don’t retain all of the math that they’ve ever learned. For someone in a developmental math course it might be something like 50%. For a grad student, it might be something like 80% (as a former math grad student, I can tell you that I retained significantly less than that). So if we need someone to be very comfortable with arithmetic to function in society, stopping at the end of arithmetic won’t be enough for them to retain it. They’ll need a bit more in order to retain everything.
Since math does build on itself, we can start teaching these students algebra. In using algebra, students will be challenged to use their arithmetic skills in many different ways, forcing them to actually own arithmetic. It will give them the practice of not only performing arithmetic, but also knowing when it’s appropriate to use different operations.
Finally, the problem solving and even logic skills one employs in an algebra class are really a dimension higher than that in an arithmetic class. Being introduced to a different way of thinking (using variables to represent unknown quantities, as well as using symbolic manipulation) is immensely helpful in any sort of problem solving arena, whether or not it involves math. Everyone needs problem solving skills: if jobs didn’t require them, everything would be run 100% by computers.
After explaining this to the few argumentative students I get, they generally stop complaining. And they’re art students. Sure, they might not ever need to solve an optimization problem involving a system of inequalities, but learning how to do it reinforces many of the more basic skills they will use and improves the problem solving skills they will need.