Idk how they're teaching the quadratic formula nowadays, but when it was taught to me it was taught as a fact to be used later on. The problem solving and critical thinking time could have been spent on working through and coming up with it
>Idk how they're teaching the quadratic formula nowadays, but when it was taught to me it was taught as a fact to be used later on.
I find it hard to believe that anyone could actually say that and believe it. In what scenario would a person that is not actively working in a STEM field (and frankly even then) ever need to solve a quadratic equation by hand? When most kids can barely handle using the formula on it's own I don't think deriving it is going to add any value to anyone other than already advanced students.
I believe that's false. It's easier to understand something if it's tied together and built on other things you already know. Simply being handed a formula and told to use it does neither of those thing.
As you said, what good is being given a formula and told to use it for problem solving if you can barely understand it. Instead do the problem solving to derive the equation.
Not sure this makes sense pedagogically. I would challenge you to try this in a classroom of average middle schoolers and see how it goes. I don't think you grasp the difficulties here.
But the length of the real proof is beside the point. We teach them about 1 and 2 before going to 1+1=2. And when we do go to 1+1=2, we show it to them using objects and counting. We don't simply tell "here's the function for addition, just put numbers into to to solve problems".
And it is used later on, probably every day until you graduate. Most people probably won't use it at their jobs, but things that are useful during your studies are useful period.
