1. Assessment

2. 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)

3. 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)

4. 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”)

5. 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

6. Probes?  AIMSweb ~ www.aimsweb.com www.aimsweb.com  Intervention Central ~ www.interventioncentral.org www.interventioncentral.org  GRAPH RESULTS!!!  Computer  By hand

7. State Measures  http://community.learnnc.org/dpi/math/arc hives/instructional_resources/index.php http://community.learnnc.org/dpi/math/arc hives/instructional_resources/index.php http://community.learnnc.org/dpi/math/arc hives/instructional_resources/index.php

8. Error Analysis

9. 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

10. Error Types Fact Error Component Skill Error Strategy Error

11. 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

12. 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)

13. 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

14. 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.

15. Strategy Error Student does not know the sequence of steps to solve the problem type

16. Strategy Error Remediation Reteach the strategy ~ –Using a highly structured presentation