Will we really forget what we just “learned”?
Yes. We repeatedly have to review for recall to learn for the long term. We must do this because unless we use the new material a lot and in special ways we will simply forget it. This was learned by Ebbinghouse early last century and has been confirmed repeatedly.
Students will have “learned math” only when they are proficient in understanding concepts, procedures, can reason precisely and can formulate and solve problems appropriate to their grade level as defined by the California Math Content Standards. Mastery learning means having fixed the material in your mind so as to exercise that skill fluently.
And that means the long term recall of mentally well-integrated concepts, facts, procedures and connections – i.e., all that we really know of mathematics and what we can do with it.
We know that we forget. We also know that rote learning & cramming don’t work except for the very short term S.o, what to do about remembering for the long term?
The answer is repeated review for recall mastery on a very special spaced practice schedule. And that takes special discipline – deliberate practice, deep practice to ensure fluent recall.
Look at the chart above. To retain newly learned information we must first mentally integrate the material into prior knowledge and then review it within the first few hours of first exposure. After that we need to practice repeated recall attempts – each to mastery – at special spaced repetition intervals.
What else does cognitive science teach?
Cognitive science also tells us that effective learning occurs when working repeatedly to remember just failed recall items. This is working “at the edge” – on the hard parts of what must be studied.
This is why master teachers use repeated quizzing to help students first grasp it short term and then retain it for the long term.
Good students repeatedly self-quiz until “they really get it” – understanding and fluent recall. This is moving beyond failing and just giving up.
Students need to assign themselves daily practice to: review and recall math concepts; the meaning of symbols; problem types & solution schema; worked-out examples. Only then should solving mixed-cumulative problem sets be attempted.
Does such practice need guidance?
Such “deep” or “deliberate” practice for understanding and fluent recall is very hard mental work and needs real encouragement and guidance.