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define select identify

Cognitive Levels of Mathematical Understanding. Basic Knowledge – Characterizing Action Verbs. define select identify. state know. Procedures – Characterizing Action Verbs. demonstrate simplify evaluate approximate verify. determine solve calculate use

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define select identify

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  1. Cognitive Levels of Mathematical Understanding Basic Knowledge – Characterizing Action Verbs • define • select • identify • state • know Procedures – Characterizing Action Verbs • demonstrate • simplify • evaluate • approximate • verify • determine • solve • calculate • use • substitute

  2. Cognitive Levels of Mathematical Understanding Conceptual Understanding – Characterizing Action Verbs • compare • contrast • create • distinguish • recognize • model Problem Solving – Characterizing Action Verbs • adapt • connect • synthesize • formulate • design • prove • derive • justify • hypothsize

  3. Compare and contrast: • How are … alike? How are… different? • Given a condition, predict forward: • What would happen if…? • Will this ever happen? • Analyze a connection/relationship: • When will… be (larger, equal to, exactly twice..) compared to…? • When will… be as big (as small) as possible? • Explore… (done with a mathematical objective in mind) • Make a conjecture… (about something) • What do you notice about…? • Is it the same for…?

  4. Generalize/make conjectures: • When does… work? • Under what conditions does… behave this way? • Describe how to find…? • Is this always true? • Justify/ prove mathematically • Why does… work? Will it always work? • Consider assumptions inherent in the problem: • What will happen if the assumptions are changed? • …suppose the triangle is not a right triangle…? • Interpret information, make/justify conclusions: • This … will make… happen because… • What does this tell you about…. • Based on your exploration….

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