I’m sure it is very easy for entrepreneurs and manufacturers to come up with a device – call it “hoopulator” – which a student can use in the gym to precision-shoot a basketball into the hoop. It certainly makes the job of the physical education instructors a lot easier! Why has no one even thought of inventing such a thing? Is it perhaps because it defeats the purpose of playing basketball, namely developing skills that improve bodily activity? … And if used, it makes students’ bodies lazy and unfit?
Don’t calculators and computers used at an early stage have the same effect of making the brain lazy and unfit? Is the “mental” activity involved in punching buttons of a calculator of the same kind as going through the mathematical/algebraic process mentally? Technology-driven teachers use calculators even in elementary schools in place of having the kids learn multiplication table – I’ve heard complaints from teachers that many high school students don’t know the multiplication table. Knowing multiplication table enables students to do long multiplication and division, which do to the brain what playing basketball (or any other sport) does to the body. Furthermore,
If students don’t know the multiplication table, they cannot master algebra.
So, technology persuades teachers to relegate algebraic skills to more advanced calculators!
If students don’t know algebra, they cannot master calculus.
So, differentiation, integration, and all the other necessary skills of calculus are relegated to TI-89!
If students don’t know calculus, they cannot master differential equations.
So, differential equations is relegated to computer algebra programs!
When does the brain of a student start to work mathematically? If we replace teaching our students how to understand math with how to punch buttons or press keys, will they EVER learn to THINK? Will any of these students have a chance to become a creative mathematician or scientist?