Dear Outstanding Educator,
I don’t know if this is true but I remember reading somewhere that to lock in a math concept into long-term memory, a student needs to practice 5-6 times correctly. Otherwise, the student will have locked into long-term memory the wrong way to solve a problem. I also remember reading that it takes 12-15 additional practice exercises to unlearn the wrong way and relearn the correct approach.
A sports coach wants to train her athletes by observing their performance and making corrections as soon as she notices a disconnect. She’d rather they practice under supervision until they’ve demonstrated consistent competency before they practice independently.
Ideally, you would have each student practice a problem and then receive immediate feedback and corrective instruction if they got the problem wrong. There are some good online platforms that provide such instant feedback and correction and I’ve seen them successfully implemented in lower ability-level classrooms.
“Flipping the classroom” is another option, where students watch teacher recorded lessons at home and then class time is used for discussion and practice.
The above options assume that the school has both the budget and infrastructure, to support such 21st Century learning, and/or that students have computers and internet at home.
What if we just give them the answers? I give my students homework so they can practice. If I gave them the answers with the assignments and graded them the answer would that be more effective?
Wolfram Alpha and the PhotoMath app can provide answers to pretty much any textbook problem, so if students want to shortchange their education by copying from the internet the answers to their homework, it will happen.
I think one thing that might be helpful is to make sure your students have good examples in their notes before assigning the homework. If they miscopied a step in the example, they will be 100% correct in solving the homework incorrectly.
Beyond that, I think each class of students will react differently to having the answers in front of them. For some, providing the answers removes the need to struggle with a challenging problem, shortchanging their problem solving skills development. For others, especially those students who lack smartphones and internet at home, it can be a lifeline to avoiding the spiral of practicing the wrong way to solve.