Math and Early Numeracy

Transcription

1 P O W E R E D B Y E D F O R M A T I O N PRACTICE EXERCISES Practice Exercises AIMSweb GENERAL OUTCOME MEASURES (GOMs) Math and Early Numeracy Edformation Inc Flying Cloud Drive, Suite 204 Eden Prairie, MN P: (952) (888) F: (952) edformation Inc. All rights reserved. No part of this book may be reproduced or transmitted in any form by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher.

2 Practice Exercise 1 Practice Exercise 1 Scoring Key Practice Exercises 36 AIMSweb Training Workbook

3 Practice Exercise 1 A copy of the Accuracy of Implementation Rating Scale (AIRS) for Math-CBM is in the Appendix of the AIMSweb Workbook, Administration and Scoring of Mathematics Computation Curriculum-Based Measurement (M-CBM) and Math Fact Probes for Use with AIMSweb. P r a c tic e Practice Exercise 2 E x e r c is e s A copy of the Accuracy of Implementation Rating Scale (AIRS) for Math-CBM is in the Appendix of the AIMSweb Workbook, Administration and Scoring of Mathematics Computation Curriculum-Based Measurement (M-CBM) and Math Fact Probes for Use with AIMSweb. AIMSweb Training Workbook

4 Practice Exercise 2 Practice Exercise 2 Scoring Key Practice Exercises 38 AIMSweb Training Workbook

5 Practice Exercise 3 Practice Exercises 40 AIMSweb Training Workbook

6 Practice Exercise 3 Scoring Key Practice Exercises AIMSweb Training Workbook 41

7 Practice Exercise 3 A copy of the Accuracy of Implementation Rating Scale (AIRS) for Math-CBM is in the Appendix of the AIMSweb Workbook, Administration and Scoring of Mathematics Computation Curriculum-Based Measurement (M-CBM) and Math Fact Probes for Use with AIMSweb. P r a c tic e Practice Exercise 4 E x e r c is e s A copy of the Accuracy of Implementation Rating Scale (AIRS) for Math-CBM is in the Appendix of the AIMSweb Workbook, Administration and Scoring of Mathematics Computation Curriculum-Based Measurement (M-CBM) and Math Fact Probes for Use with AIMSweb. AIMSweb Training Workbook

8 Practice Exercise 4 Practice Exercise 4 Scoring Key Practice Exercises AIMSweb Training Workbook 43

9 Practice Exercise 5: Score for ANSWER ONLY Practice Exercises AIMSweb Training Workbook 45

10 Practice Exercise 5 Scoring Key for ANSWER ONLY Practice Exercises 46 AIMSweb Training Workbook

11 Practice Exercise 5 A copy of the Accuracy of Implementation Rating Scale (AIRS) for Math-CBM is in the Appendix of the AIMSweb Workbook, Administration and Scoring of Mathematics Computation Curriculum-Based Measurement (M-CBM) and Math Fact Probes for Use with AIMSweb. P r a c tic e Practice Exercise 6 E x e r c is e s A copy of the Accuracy of Implementation Rating Scale (AIRS) for Math-CBM is in the Appendix of the AIMSweb Workbook, Administration and Scoring of Mathematics Computation Curriculum-Based Measurement (M-CBM) and Math Fact Probes for Use with AIMSweb. AIMSweb Training Workbook

12 Practice Exercise 6: Score for ANSWER ONLY Practice Exercises 48 AIMSweb Training Workbook

13 Practice Exercise 6 Scoring Key for ANSWER ONLY Practice Exercises AIMSweb Training Workbook 49

14 Practice Exercise 7: Score for ANSWER AND CRITICAL PROCESSES Practice Exercises AIMSweb Training Workbook 51

15 Practice Exercise 7 Scoring Key for ANSWER AND CRITICAL PROCESSES Practice Exercises 52 AIMSweb Training Workbook

16 Practice Exercise 7 A copy of the Accuracy of Implementation Rating Scale (AIRS) for Math-CBM is in the Appendix of the AIMSweb Workbook, Administration and Scoring of Mathematics Computation Curriculum-Based Measurement (M-CBM) and Math Fact Probes for Use with AIMSweb. P r a c tic e Practice Exercise 8 E x e r c is e s A copy of the Accuracy of Implementation Rating Scale (AIRS) for Math-CBM is in the Appendix of the AIMSweb Workbook, Administration and Scoring of Mathematics Computation Curriculum-Based Measurement (M-CBM) and Math Fact Probes for Use with AIMSweb. AIMSweb Training Workbook

17 Practice Exercise 8: Score for ANSWER ONLY Practice Exercise 8 Scoring Key for ANSWER ONLY Practice Exercises 54 AIMSweb Training Workbook

18 Practice Exercise 9: Score for ANSWER AND CRITICAL PROCESSES Practice Exercise 9 Scoring Key for ANSWER AND CRITICAL PROCESSES Practice Exercises 56 AIMSweb Training Workbook

19 Practice Exercise 9 A copy of the Accuracy of Implementation Rating Scale (AIRS) for Math-CBM is in the Appendix of the AIMSweb Workbook, Administration and Scoring of Mathematics Computation Curriculum-Based Measurement (M-CBM) and Math Fact Probes for Use with AIMSweb. P r a c tic e Practice Exercise 10 E x e r c is e s A copy of the Accuracy of Implementation Rating Scale (AIRS) for Math-CBM is in the Appendix of the AIMSweb Workbook, Administration and Scoring of Mathematics Computation Curriculum-Based Measurement (M-CBM) and Math Fact Probes for Use with AIMSweb. AIMSweb Training Workbook

20 Practice Exercise 10: Score for ANSWER ONLY Practice Exercises 58 AIMSweb Training Workbook

21 Practice Exercise 10 Scoring Key for ANSWER ONLY Practice Exercises AIMSweb Training Workbook 59

22 Scoring of AIMSweb Computation The number of Correct Digits (CD) that a student writes are scored and summed using one of two scoring methods. For M-CBM probes in Grades 1-4, scoring the number of CD in the answer only is the preferred method. For M-CBM probes in Grades 5-6, educators can choose to score the number of CD in the answer only or in the answer and critical processes of the answer. The former (CD in answer only) may be the preferred method when a mathematics curriculum teaches students multiple ways to solve computational problems (i.e., there is no single correct way). The latter method implies there is a common way that students learn to solve more complex computational problems and that more challenging problems are worth more in terms of outcomes and successful completion should be reflected in a higher CD score. For Math Fact Probes, only the numbers of digits in the answer are counted. General Scoring Rules Independent of Scoring Method Correct Digits - Each correct digit that a student writes is marked with an underline and counted. (2 CD Possible) (2 CD Possible) Score = 2 CD Score = 1 CD (2 CD Possible) (2 CD Possible) Score = 1 CD Score = 0 CD Scoring of AIMSweb Computation (4 CD Possible) Score = 4 CD (4 CD Possible) Score = 2 CD 18 AIMSweb Training Workbook

23 Incomplete Problems - Sometimes students don t finish a problem. Score for the number of correct digits that are written. Answer Key (4 CD Possible) Score = 2 CD (4 CD Possible) Score = 3 CD X-ed Out Problems - Sometimes students start a problem and then cross it out. Sometimes students go back and write answers for problems they have crossed out. Ignore the X and score what you see. (3 CD Possible) Score = 1 CD Answer Key Scoring of AIMSweb Computation (3 CD Possible) Score = 3 CD AIMSweb Training Workbook 19

24 Legibility and Reversed or Rotated Numbers - Sometimes trying to figure out what number the student wrote can be challenging, especially with younger students or older students with mathematics achievement problems. To make scoring efficient and reliable, we recommend attention to three rules. 1. If it is difficult to determine what the number is at all, count it wrong. 2. If the reversed number is obvious, but correct, count it as a correct digit. (2 CD Possible) Score = 2 CD (2 CD Possible) Score = 1 CD 3. If the numbers 6 or 9 are potentially rotated and the digit is currently incorrect, count it as an incorrect digit. (1 CD Possible) (1 CD Possible) Score = 0 CD Score = 0 CD Scoring of AIMSweb Computation 20 AIMSweb Training Workbook

25 Scoring Rules for Answer and Critical Processes When students Grade 5 or Grade 6 M-CBM probes are scored for the number of CDs in the answer only and critical processes, the examiner uses the answer key that details which digits are to be counted. Each problem has an assigned CD value based on what AIMSweb believes is the most conventional method of solving the computational problem. Compare how the same multi-step multiplication problem would be scored using the different methods. Answer Only 5 CD Possible Answer and Critical Processes 13 CD Possible Should the student solve the problem correctly as shown below-left, their score would be 13 CD. Although you don t need to count every digit written in a correct answer, it is important to write the number of CDs awarded to the problem next to the answer. Should the student solve the problem and not write any of the CD as shown belowright, the score would be 0 CD. (13 CD Possible) Score = 13 CD (13 CD Possible) Score = 0 CD Answer Key Scoring of AIMSweb Computation Sometimes students are so proficient in their computation that they don t show all their work. If the answer is correct as shown below-left, their score is the number of CDs possible shown in the answer key. If they do not show their work and the answer is incorrect, the examiner can only score what they see as shown below-right. Answer Key (13 CD Possible) Score = 13 CD (13 CD Possible) Score = 3 CD AIMSweb Training Workbook 21

26 First, compare students answers to the answer key. If the problem is incorrect, then underline any of the digits that are correct. Two examples are provided below. Answer Key (13 CD Possible) Score = 5 CD (13 CD Possible) Score = 6 CD Alignment. Sometimes students answers are not aligned correctly according to place value. If the answer is correct, ignore the alignment problem and count the digits as correct as shown below. (4 CD Possible) Score = 4 CD Answer Key If the answer is incorrect, count the digits as they appear in approximate place value as shown below, even if a place value error may seem obvious. Although this may make good diagnostic information, in many instances, the time spent trying to figure out whether the error was one of place value or due to some other cause has the potential to make scoring time consuming and less reliable. Scoring of AIMSweb Computation Answer Key (13 CD Possible) Score = 4 CD 22 AIMSweb Training Workbook

27 Practice Exercise 1: Oral Counting Count the total number of Oral Counts 2. Count the total number of errors 3. Subtract errors from total number. Correct Oral Counts O ra l A copy of the Accuracy of Implementation Rating Scale (AIRS) for Oral Counting is in the Appendix of the AIMSweb Workbook, Administration and Scoring of. C o u n tin g 16 AIMSweb Early Numeracy Measures

28 Practice Exercise 2: Oral Counting Count the total number of Oral Counts 2. Count the total number of errors 3. Subtract errors from total number. Correct Oral Counts Oral Countingi A copy of the Accuracy of Implementation Rating Scale (AIRS) for Oral Counting is in the Appendix of the AIMSweb Workbook, Administration and Scoring of AIMSweb Early Numeracy Measures 17

29 Practice Exercise 3: Number Identification Count the total number of Number Identifications 2. Count the total number of errors 3. Subtract errors from total number. Correct Number Identifications A copy of the Accuracy of Implementation Rating Scale (AIRS) for Number Identification is in the Appendix of the AIMSweb Workbook, Tests of Early Numeracy: Administration and Scoring of AIMSweb Early Numeracy Measures for Use with AIMSweb. Number Identification 22 AIMSweb Early Numeracy Measures

30 Practice Exercise 4: Number Identification Count the total number of Number Identifications 2. Count the total number of errors 3. Subtract errors from total number. Correct Number Identifications A copy of the Accuracy of Implementation Rating Scale (AIRS) for Number Identification is in the Appendix of the AIMSweb Workbook, Tests of Early Numeracy: Administration and Scoring of AIMSweb Early Numeracy Measures for Use with AIMSweb. Number Identification AIMSweb Early Numeracy Measures 23

31 Practice Exercise 5: Quantity Discrimination Count the total number of Quantity Discriminations 2. Count the total number of errors 3. Subtract errors from total number. Correct Quantity Discriminations Q u a n tity A copy of the Accuracy of Implementation Rating Scale (AIRS) for Quantity Discrimination is in the Appendix of the AIMSweb Workbook, Tests of Early Numeracy: Administration and Scoring of AIMSweb Early Numeracy Measures for Use with AIMSweb. D is c rim in a tio n AIMSweb Early Numeracy Measures 27

32 Practice Exercise 6: Quantity Discrimination Count the total number of Quantity Discriminations 2. Count the total number of errors 3. Subtract errors from total number. Correct Quantity Discriminations A copy of the Accuracy of Implementation Rating Scale (AIRS) for Quantity Discrimination is in the Appendix of the AIMSweb Workbook, Tests of Early Numeracy: Administration and Scoring of AIMSweb Early Numeracy Measures for Use with AIMSweb. Quantity Discrimination 28 AIMSweb Early Numeracy Measures

33 Practice Exercise 7: Missing Number _ 1. Count the total number of Missing Numbers 2. Count the total number of errors 3. Subtract errors from total number. Correct Missing Numbers Missing Number A copy of the Accuracy of Implementation Rating Scale (AIRS) for Missing Number is in the Appendix of the AIMSweb Workbook, Tests of Early Numeracy: Administration and Scoring of AIMSweb Early Numeracy Measures for Use with AIMSweb. 32 AIMSweb Early Numeracy Measures

34 Practice Exercise 8: Missing Number Count the total number of Missing Numbers 2. Count the total number of errors 3. Subtract errors from total number. Correct Missing Numbers A copy of the Accuracy of Implementation Rating Scale (AIRS) for Missing Number is in the Appendix of the AIMSweb Workbook, Tests of Early Numeracy: Administration and Scoring of AIMSweb Early Numeracy Measures for Use with AIMSweb. Missing Number AIMSweb Early Numeracy Measures 33