Overall, I think this is a much better way to teach math—in some sense it’s similar to removing date memorization from history classes, which I also agree with. I do have an issue with the phrase “a triangle has the same area as itself.” A more user-friendly intuition for me is “if you describe the same thing two ways, it’s still the same thing.” This seems more generalizable and also gets more directly at the point that sin(A)/a is a complete description of a triangle’s proportions.
Agreed with respect to better way to teach maths. However, noting that teaching like this requires students who want to learn like this which is almost always going to be the minority. For folks interested/enjoy this perspective, I encourage you to read A Mathematician’s Lament by Paul Lockhart.
Overall, I think this is a much better way to teach math—in some sense it’s similar to removing date memorization from history classes, which I also agree with. I do have an issue with the phrase “a triangle has the same area as itself.” A more user-friendly intuition for me is “if you describe the same thing two ways, it’s still the same thing.” This seems more generalizable and also gets more directly at the point that sin(A)/a is a complete description of a triangle’s proportions.
Agreed with respect to better way to teach maths. However, noting that teaching like this requires students who want to learn like this which is almost always going to be the minority. For folks interested/enjoy this perspective, I encourage you to read A Mathematician’s Lament by Paul Lockhart.