EFFICIENCY ACCURACY + FLEXIBILITY COMPUTATIONAL FLUENCY Memorization or Automaticity? Memorization of basic facts usually refers to committing the results of unrelated operations to memory so that thinking is unnecessary. Isolated addition and subtractions facts are practiced one after another as if there were no relationships among them; the emphasis is on recalling the answers. Teaching facts for automaticity, in contrast relies on thinking. Answers to facts must be automatic, produced in only a few seconds; counting is not sufficient. Thinking about relationships among facts is critical. A child who thinks of 9 + 6 as 10 + 5 produces the answer of 15 quickly, but thinking, not memorization, is at the core (although over time these facts are eventually remembered). The issue here is not whether facts should eventually be memorized but how this memorization is achieved: by drill, practice, and memorization, or by focusing on relationships? Research shows that the most effective way for students to learn the basic facts is to arrange them into clusters based on relationships or thinking strategies. When relationships are the focus, there are far fewer facts to remember and big ideas like compensation, hierarchical inclusion, and part/whole relationships come into play. Also if a child forgets an answer, she has a quick way to come up with it. Finally the few facts that do need to be memorized are the doubles and combinations that make ten, because they are the basis for critical landmark strategies such as double plus or minus, making tens, using compensation, and using other known facts. |
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