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Diagnosing Student Errors

Diagnosing Student Errors. Jan. 25, 2007. Diagnosing Errors. Two Principles from NCTM Equity “all students can learn For us: teach students at the appropriate levels Assessment “assessment supports mathematical learning”

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Diagnosing Student Errors

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  1. Diagnosing Student Errors Jan. 25, 2007

  2. Diagnosing Errors • Two Principles from NCTM • Equity • “all students can learn • For us: teach students at the appropriate levels • Assessment • “assessment supports mathematical learning” • For us: assessment should align with content, instructional practices, students’ appropriate levels

  3. Common Errors • Overgeneralizing (p. 18-20 in Ashlock) Sum: number to the right of the equals sign • 6 + 3 = 9 • 7 – 5 = 5 • Overspecializing (pp. 20-21) 100.36 + 12.57 turned into 100.36 + 125.70 Altitude of a triangle • Misuse of algorithms Subtraction: errors carrying and regrouping

  4. Dealing with Errors • Self-assessment • What does self-assessment mean? • Examples of self-assessment?

  5. Dealing with Errors • Self-assessment • Have students show work • Included showing and checking work as a task component • During the Hexagon taskhow did you show and check your work? • What about other students?

  6. Dealing with Errors • Self-assessment • Check-off sheet

  7. Getting at students’ thinking • Interviewing • Questions and follow-up questions • Writing • Math journals, reflections • Writing as a task component • Peer conversation • Have students explain their process and solution to each other

  8. Getting at students’ thinking • Developing students’ metacognition • Cognition means “thinking” • “meta” means “thinking about” • In a nutshell we’re trying to get students to: • think about their thinking

  9. Getting at students’ thinking • Interviewing (p. 27): Types of questions

  10. Getting at students’ thinking • Interviewing (p. 27) • Other than the questions listed there, what other questions could you also ask?

  11. Other ways to diagnose • Graphic organizers • Simple form (p. 30) • Flow charts- thoughts on these? • Informal note taking • Clipboard and index cards • Names on the bottom • Flip the cards up, jot down notes

  12. Other ways to diagnose • Informal Observations • What signs should you look for? • Frequent strugglers • Finished early • oFf-task • Frustrated

  13. Getting at students’ thinking Rate the likelihood of being able to do each of these daily during mathematics class. • Interviewing each student • Questioning the whole class for understanding • Interviewing 2 students who are struggling • Facilitating students’ self-assessment • Questioning and posing 1-2 follow-up questions while they complete tasks • Interviewing a small group of students while the rest of the class completes tasks • Jotting down notes on students as they work on tasks • Taking a small group of four students to correct misconceptions that they have

  14. So here’s a task… • Your class is collecting pencils for underprivileged children. You need 15 more in order to have 100 pencils. Kiri, Shannon, and Latoya bring in pencils. Each of them brings between three and ten pencils. The four of them bring 15 pencils total. How many pencils does each bring? • Find other answers. • How did you approach this problem? http://www.arcytech.org/java/integers/

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