I gave a student a pop quiz on percent change – find discount and tax – after she completed independent practice on this objective. The student followed the steps very well, as you can see in the photo (I added the ink later) up to the very end. At that point she added the tax to 6 for a total cost of $9.36 – good deal for an $80 coat!
This is hardly uncommon if not typical in education both at the secondary and post-secondary level. The focus is largely on steps and not concept building. I asked her follow up questions (as opposed to telling her what to do to fix it) to flesh out the concept. “What did you do first and why?” “What does discount mean?” “What did you do here (pointing to the 6/100 part)?” “What do you pay the cashier?” She was confused because she wasn’t thinking real life situation but got caught in the weeds of the math steps.
What often happens is that students give up when pressed to think. I often have students tell me “can’t you just tell me the answer?” and “you’re the teacher, you’re supposed to teach me.” I respond “Yes, I can show you and I already taught you; now it’s your turn.”