Differentiated Instruction and Critical Thinking



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What is Mastery?

  • “Tim was so learned, that he could name a horse in nine languages; so ignorant, that he bought a cow to ride on.”
  • Ben Franklin, 1750, Poor Richard’s Almanac

Working Definition of Mastery (Wormeli)

  • Students have mastered content when they
  • demonstrate a thorough understanding as
  • evidenced by doing something substantive
  • with the content beyond merely echoing it.
  • Anyone can repeat information; it’s the
  • masterful student who can break content into
  • its component pieces, explain it and alternative
  • perspectives regarding it cogently to others,
  • and use it purposefully in new situations.

Non-mastery…

  • The student uses primarily the bounce pass in the basketball game regardless of its potential effectiveness because that’s all he knows how to do.

…and Mastery

  • The student uses a variety of basketball passes during a game, depending on the most advantageous strategy at that moment in the game.

What is the standard of excellence when it comes to tying a shoe?

  • What is the standard of excellence when it comes to tying a shoe?
  • Now describe the evaluative criteria for someone who excels beyond the standard of excellence for tying a shoe. What can they do?

Consider Gradations of Understanding and Performance from Introductory to Sophisticated

  • Introductory Level Understanding:
  • Student walks through the classroom door while wearing a heavy coat. Snow is piled on his shoulders, and he exclaims, “Brrrr!” From depiction, we can infer that it is cold outside.
  • Sophisticated level of understanding:
  • Ask students to analyze more abstract inferences about government propaganda made by Remarque in his wonderful book, All Quiet on the Western Front.

Determine the surface area of a cube.

  • Determine the surface area of a cube.
  • Determine the surface area of a rectangular prism (a rectangular box)
  • Determine the amount of wrapping paper needed for another rectangular box, keeping in mind the need to have regular places of overlapping paper so you can tape down the corners neatly
  • Determine the amount of paint needed to paint an entire Chicago skyscraper, if one can of paint covers 46 square feet, and without painting the windows, doorways, or external air vents.
  • _______________________________________________
  • Define vocabulary terms.
  • Compare vocabulary terms.
  • Use the vocabulary terms correctly.
  • Use the vocabulary terms strategically to obtain a particular result.

There’s a big difference: What are we really trying to assess?

  • “Explain the second law of thermodynamics” vs. “Which of the following situations shows the second law of thermodynamics in action?”
  • “What is the function of a kidney?” vs. “Suppose we gave a frog a diet that no impurities – fresh organic flies, no pesticides, nothing impure. Would the frog still need a kidney?”
  • “Explain Keynes’s economic theory” vs. “ Explain today’s downturn in the stock market in light of Keynes’s economic theory.”
  • From, Teaching the Large College Class, Frank Heppner, 2007, Wiley and Sons

Feedback vs Assessment

  • Feedback: Holding up a mirror to the student, showing him what they did and comparing it to the criteria for success, there’s no evaluative component or judgement
  • Assessment: Gathering data so we can make a decision
  • Greatest Impact on Student Success: Formative feedback

Be clear: We grade against standards, not routes students take or techniques teachers use to achieve those standards.

  • Be clear: We grade against standards, not routes students take or techniques teachers use to achieve those standards.
  • What does this mean we should do with class participation or discussion grades?

Assessment OF Learning

  • Still very important
  • Summative, final declaration of proficiency, literacy, mastery
  • Grades used
  • Little impact on learning from feedback

Assessment AS/FOR Learning

  • Grades rarely used, if ever
  • Marks and feedback are used
  • Share learning goals with students from the beginning
  • Make adjustments in teaching a result of formative assessment data
  • Provide descriptive feedback to students
  • Provide opportunities for student for self-and peer assessment
  • -- O’Connor, p. 98, Wormeli
  • Teacher Action
  • Result on Student Achievement
  • Just telling students # correct and incorrect
  • Negative influence on achievement
  • Increase of 16 percentile points
  • Providing explanations as to why their responses are correct or incorrect
  • Increase of 20 percentile points
  • Asking students to continue responding to an assessment until they correctly answer the items
  • Increase of 20 percentile points
  • Graphically portraying student achievement
  • Increase of 26 percentile points
  • -- Marzano, CAGTW, pgs 5-6
  • Item
  • Topic or
  • Proficiency
  • Right
  • Wrong
  • Simple Mistake?
  • 1
  • Dividing fractions
  • 2
  • Dividing Fractions
  • 3
  • Multiplying Fractions
  • 4
  • Multiplying fractions
  • 5
  • Reducing to Smplst trms
  • 6
  • Reducing to Smplst trms
  • 7
  • Reciprocals
  • 8
  • Reciprocals
  • 9
  • Reciprocals


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