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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)
  • 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
  • AIMSweb ~
  • Intervention Central ~
    • Computer
    • By hand
state measures
State Measures
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