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Foundations for Success: The Final Report of the National Mathematics Advisory Panel
by National Mathematics Advisory Panel · 2008 · 1 reading card
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Foundations for Success: The Final Report of the National Mathematics Advisory Panel · 2008
If they cannot draw the situation they have not understood it — a formula over a misunderstanding gets the right answer by accident.
The report read the literature and said what neither camp wanted to hear: both are half right. A child still counting on fingers at twelve cannot follow a multi-step argument, because calculation consumes all their working memory. And a child who knows the tables perfectly but cannot draw the situation solves no new problem. What you do at home, on three floors. Floor one, automation, until fourth grade: addition and subtraction to twenty, then the times tables, five minutes a day with spaced repetition — ask, wait three seconds, if nothing comes give the answer and return to it in two days. Floor two, representation, all the time: every problem gets drawn before it gets calculated. If they cannot draw the situation they have not understood it, and a formula applied over a misunderstanding gives a right answer by accident. Floor three, fractions, in grades four to six: the report names them explicitly as the gate to algebra, and algebra is the gate to everything else. A child who does not master fractions will fail mathematics in secondary school, tutoring or no tutoring. Working rules: an error is discussed, not erased — you ask "how did you get here"; you never say "I was bad at maths too", because it is the most efficient sentence of surrender in the language; tutoring that redoes the homework does not repair the foundation, and if the foundation is missing you go back two years, not forward.
“Computational fluency, conceptual understanding and problem-solving ability are not alternatives to choose between. They support one another and must be developed together.”