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Assessment. National Research Council (2001). “students need to be efficient and accurate in performing basic computation with whole numbers” (p. 121)

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National research council 2001
National Research Council (2001)

  • “students need to be efficient and accurate in performing basic computation with whole numbers” (p. 121)

  • students must learn to “use an algorithm for computation with multi-digit numbers because it is an important part of developing mathematical proficiency” (p.7)


Assess these skills
Assess these skills?

  • Curriculum-Based Measurement

    • Developed more than 25 years ago (Stan Deno)

    • Reliable & valid way of assessing student progress in the basic skill areas

    • CBM-Probes ~ narrow-band tests ~ are simple to administer and score & sensitive to improvement & time efficient

    • Science-based research (Marston, 1989; Thurber & Shinn, 2002) ~ having students write answers to grade-level computational problems for 2-4 min. is a reliable and valid outcome measure for typically achieving and those with severe problems (all fact probes are 2 minutes)


Probes
Probes

  • Correct digits

    • Older students (grades 5 & beyond) – in answer or answer & critical processes but grades 1-4 answer only

  • Standardized directions

    • “We’re going to take a 2 (or 4) -minute math test. I want you to write your answers to these math problems. Some are ___ and some are _____. Look at each one carefully before you write the answer. When I say begin, write your answer to the first problem (point) and work across the page (show). Then go to the next row. Keep doing this until I say stop. Try to work each problem. If you really don’t know how to do it, put an x through it and go to the next problem.” At the end of 2 minutes say, “Stop.”

    • Testing ~ not teaching

    • No skipping (“try to work each problem”)


Scoring guidelines
Scoring Guidelines

  • Correct digits

    • Each correct digit is underlined and counted

    • Incomplete problem ~ count correct digits

    • Xed out ~ count correct digits

    • Poor legibility & difficult to determine the number ~ count incorrect

    • Reversed but obvious ~ (3) count correct


Probes1
Probes?

  • AIMSweb ~ www.aimsweb.com

  • Intervention Central ~ www.interventioncentral.org

  • GRAPH RESULTS!!!

    • Computer

    • By hand


State measures
State Measures

  • http://community.learnnc.org/dpi/math/archives/instructional_resources/index.php



Diagnosing errors
Diagnosing Errors

  • Step 1: Analyze errors and make a hypothesis about the cause of the errors

  • Step 2: Interview student to determine cause of the error (if not obvious)

  • Step 3: Reteach

  • Step 4: Test


Error types
Error Types

  • Fact Error

  • Component Skill Error

  • Strategy Error


Fact error
Fact Error

  • Basic facts ~ 100 addition and multiplication facts formed by adding or multiplying any 2 single-digit numbers and their subtraction and division counterparts

  • Student follows the correct sequence of steps for solving the problem but misses the problem because of a basic fact error


Fact error remediation
Fact Error Remediation

  • Does the student miss a certain fact consistently?

    • If so, the remediation must involve practice on that fact

  • Does the student miss a fact inconsistently?

    • Increase incentives for accurate work (so students do not rush through work and make careless errors)


Component skill error
Component Skill Error

  • Previously taught skills that are integrated as steps in a problem-solving strategy

  • Lower grade ~ counting or symbol identification error

  • Later grades ~ wider range


Component skill error remediation
Component Skill Error Remediation

  • Is the error occurring consistently?

    • If no, don’t remedy

    • If yes, reteach the particular component skill for AT LEAST 2 consecutive days. Once the student can perform that skill with mastery, reintroduce examples of the problem type that was originally missed.


Strategy error
Strategy Error

  • Student does not know the sequence of steps to solve the problem type


Strategy error remediation
Strategy Error Remediation

  • Reteach the strategy ~

    • Using a highly structured presentation


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