The importance of immediate feedback

Ever wonder why your old math textbooks had the odd-problem answers in the back of the book?  Or why flash cards can be so helpful?  Or why educational computer games and digital learning are so effective?

A big part of the answer is immediate feedback.  When a child is learning multiplication facts, for example, the use of flash cards or electronic math drills allows him to form a question (What is 5x6?), put forth an answer (um...35?) and verify its correctness (no: 5x6=30) within seconds. The initial uncertainty in the brain actually forms a "hole" to fill or a connection for the brain to attach the information to. With enough repetition, the correct facts are cemented in the child's memory.

A screenshot from the free online math drill at mathsisfun.

Sometimes a learner doesn't recognize what he does and doesn't understand.  In this case, working through a problem and getting immediate feedback is critical to efficient learning.  Case in point, I am currently taking an online math course myself.  The homework assignments in this course are set up so that when an answer is submitted, I am immediately informed as to whether my answer is correct.  If it is, hooray, my procedure was good.  If not, then I have the immediate opportunity to find my error and fix it while the problem is still fresh in my mind.  More than once I have hit "submit," thinking I had worked the problem correctly, only to find I had not.  Other times, I am unsure whether I have done something right, and am pleased to find that I have.  Either way, the immediate feedback allows me to remember the correct procedure much better than the delay of a day or even a week as we used to do in the old days of turning in homework on paper.

Which explains those odd answers in the back of the book: when students are working independently, it does no good for them to do the work if they are doing it wrong.  As I used to tell my classroom students, "Show your work as you do each problem, but then check your answers. If it's wrong, redo it until you get it right!"

So whether your child is practicing math facts or doing homework, make sure he has access to quick feedback.  Maybe this means checking the back of a book, or trade-and-grade the next day in class.  If you are homeschooling, maybe it means giving your child the answer key to check his own work when he is finished each day, or in some cases, sitting beside a new learner to help her catch errors as soon as she makes them.   The sooner the feedback, the faster the learning.