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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? • 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 • 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 • 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
Probes? • AIMSweb ~ www.aimsweb.com • Intervention Central ~ www.interventioncentral.org • GRAPH RESULTS!!! • Computer • By hand
State Measures • http://community.learnnc.org/dpi/math/archives/instructional_resources/index.php
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 • Fact Error • Component Skill Error • Strategy 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 • 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 • 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 • 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 • Student does not know the sequence of steps to solve the problem type
Strategy Error Remediation • Reteach the strategy ~ • Using a highly structured presentation