Summer 2012. Copyright (c) 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved....
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Summer 2012. Copyright (c) 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. All names and data used in this presentation are fictitious. AIMSweb Administering & Scoring Math Concepts & Applications (M-CAP)
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AIMSwebAdministering & Scoring
Math Concepts & Applications (M-CAP)
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Copyright Notice
AIMSweb: Administering & Scoring Math Concepts & Applications (M-CAP)
Copyright © 2012 NCS Pearson, Inc. All rights reserved.
Warning: No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the copyright owner.
Pearson, PsychCorp, AIMSweb and the PSI logo are trademarks in the U.S. and/or other countries of Pearson Education, Inc., or its affiliate(s). Produced in the United States of America.
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M-CAP Practice
Exercises
This Module is designed to accompany
AIMSweb® Web-Based
Software
Overview M-CAP Assessment
Training Session
and
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Purpose of M-CAP • M-CAP is a brief, standardized measure of general mathematics problem-solving
skills for students in grades 2 through 8 with national norms for grades 2 through 12.
Test Name Area AssessedTest
ArrangementsWhat is Scored
M-CAPGeneral Math
Problem Solving Skills
Individual, Small Group, or
Large Group
Number of Correct Items
5
• Purpose: Used to quickly screen and monitor mathematics progress• Alignments:
• NCTM: Domains that are consistent with the 2006 recommendations of the National Council of Teachers of Mathematics (NCTM) regarding curriculum focal points for grades PreK–8 (NCTM, 2006).
• Common Core: Instructional Links report aligned to Common Core (Fall 2012)
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M-CAP Domains by Grade
Consistent with the 2006 recommendations of the National Council of Teachers of Mathematics (NCTM) regarding curriculum focal points for grades PreK–8 (NCTM, 2006).
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NCTM Curriculum Focal Points by Grade
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An Overview of M-CAP Test Development
• Facts about M-CAP:– Developed by professional test developers and math experts.
– Customer input was also gathered throughout development of
M-CAP
– Items are based on grade-level and domain-specific criteria
– Approximately 11,200 items were developed and field tested before being selected for publication.
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An Overview of M-CAP Test Development
• Facts about M-CAP (cont’d):
– Item placement on each anchor probe was based on increasing item difficulty
– probes were designed to be of similar difficulty per grade level
– To ensure the sensitivity and maximize the amount of data collected from at-risk learners, easier items were generally placed at the beginning of each probe and more difficult items followed
– Additionally, skills are presented in a similar order, frequency, and sequence across each probe and grade level
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Sample Grade 2 M-CAP
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Sample Grade 5 M-CAP
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M-CAP
Administration is flexible and can include:
Individual Administration
Small Group Administration
Whole Class Administration
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Suggested Universal Screening Timelines
(Grade 1)Fall
(Grade 1)Winter
(Grade 1)Spring
(Grade 2)Fall
(Grade 2) Winter
(Grade 2)Spring
(Grade 3+) Fall
(Grade 3+)Winter
(Grade 3+) Spring
M-CAP M-CAP M-CAP M-CAP M-CAP M-CAP
8 min(Individual or group)
8 min(Individual or group)
8 min(Individual or group)
Grade 3-6:8 min
(Individual or group)
Grade 3-6:8 min
(Individual or group)
Grade 3-6:
8 min(Individual or group)
Grade 7+:10 min
(Individual or group)
Grade 7+:10 min
(Individual or group)
Grade 7+:10 min
(Individual or group)
M-COMP M-COMP M-COMP M-COMP M-COMP M-COMP M-COMP M-COMP M-COMP
8 min 8 min 8 min 8 min 8 min 8 min 8 min 8 min 8 min
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Student Copies• 2-4 pages (or duplex copy),
one copy per student.
Examiner Copy• Scoring key
Paper/Pencil Administration: Prepare the AIMSweb® M-CAP Test
Before Testing
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Additional tools needed
Digital Stopwatch (or Timer) preferred
List of Studentsto be Tested (Optional)
Printed Directions
Before Testing
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Obtain the Necessary Test MaterialsDuring Universal Screening you will use a different probe for fall, winter and spring sessions.
MEASURE FALL WINTER SPRING
M-CAP PROBE #1 PROBE #2 PROBE #3
M-COMP PROBE #1 PROBE #2 PROBE #3
You do NOT need to give 3 probes and take the median for any of the M-COMP or M-CAP measures. They are all one probe each per Universal Screening window.
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Setting up the Assessment Environment
• Give a backup probe in the case an assessment is “spoiled.”
Examples: o For Universal Screening,
use an alternate progress monitor probe.
o For progress monitoring use an alternate progress monitoring probe.
• Ensure child is alert and well for testing
• Remove or cover visual aids in the room that could provide assistance
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Before TestingThe M-CAP and M-COMP measures are both Standardized Tests. You must:
o Administer M-CAP and M-COMP the same way, each time.
o Adhere to the exact standardized directions at ALL times.
o Remember for 8 minutes (or 10 minutes, depending on the measure and grade level) it’s about testing, not teaching. Do not teach or correct the student.
o Avoid Practice Effects: Do not allow students to pre-read, use the probes for practice, or use the probes for review after testing, etc.
o Prepare to proctor the assessment carefully.
o No rulers, guides, or other manipulatives are to be used during Universal Screening.
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Before Testing
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More on Standard Procedures:
• As stated previously, M–CAP & M-COMP are standardized tests.
• To make valid normative (national, state, district, or school) decisions, all directions must be followed carefully.
• Actions that may invalidate decisions and conclusions made about student performance: • Any changes in the presentation of the probes with the exception of
enlarging the probe for visually impaired students.• Alterations of the instructions given to students, although sign language is
permitted• Inappropriate use of probes as teaching instruments. • Use of any accommodations, modifications, or supplementary aids
(e.g., rulers, calculators, templates, straight edges, etc.) with the exception of magnifiers
• Before administering a probe, it is important that the examiner become familiar with these administration directions.
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Directions
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Directions (Continued)
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During Testing
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After Testing: Scoring
• Collect tests immediately. • Scoring:
– All problems receive either full credit or no credit.
– If any part of an answer is incorrect, whether it is a one-part or multi-part question, the score for that item is 0.
– Examiners circle the score value (i.e., 1, 2, 3) for a correct answer and circle “0” for an incorrect answer.
– The total score value is then summed at the bottom of the page.
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Scoring: Awarding Points
– Least difficult items: 1 point– Medium difficulty items: 2 points– Most difficult items: 3 points
Point Values are pre-assigned.
Thus, no scorer-subjectivity.
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Scoring: Variant Answers
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• Variant Answers: The Answer Key includes the most common answers, but there may be other correct answers. Considerations include:
• Best practices
• Professional judgment
• Primary goal: Determine if the answer reflects an understanding of the task presented (e.g., a money task response indicates if the student knows how to properly express monetary amounts).
• Credit may be given for a clearly correct response conveyed in a manner other than the one indicated.
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Scoring: No Partial Scoring
All problems receive either full credit or no credit.
No credit
Full credit
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Scoring: Incomplete ItemsIf the student leaves any part of the problem incomplete or unanswered, the item receives no credit.
No credit
No credit
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Scoring: Crossed Out Items• If a student shows his or her work, but then crossed or “X-ed” out
the problem without placing the answer in the blank, the item is incorrect and no points are given.
• If the student has crossed out the problem, but ultimately placed an answer in the blank, score the item based on whether or not the answer placed in the blank is correct.
No credit No credit Full Credit
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Scoring: Legibility• If the response is hard to read, but can be determined, score the
answer as correct
No creditFull Credit
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Scoring: Reversals• If the response is reversed, but it is obvious what digit the
student intended, score as correct.
No creditFull Credit
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Scoring: Reversals• If the response is rotated, and it cannot be easily determined
what digit was intended, score as incorrect.
No credit
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Scoring: Placement of Symbols• Generally, M−CAP probes provide the appropriate symbols on
money, measurement, and time items.
– If a student also adds a symbol, and does so correctly, the item is considered correct.
– If a student adds the symbol incorrectly, or adds the wrong symbol, the item is considered incorrect.
No creditFull CreditFull Credit Full CreditFull Credit No creditNo creditNo creditNo creditFull Credit No creditFull CreditFull Credit No credit34
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Scoring: Placement of Symbols
• The improper inclusion of a symbol can also make a potentially correct answer incorrect.
• In the example shown below, the correct answer is “penny.” If a student responds with a numeric value (e.g., 0.01) or any term other than the name of the coin (e.g., cent, 1 cent), the answer is incorrect.
Full Credit No credit
0.01¢
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Scoring: Incorrect Unit of Measurement
• If a student also includes a measurement term (e.g., “ft” or “feet”) in the answer and it is in the proper placement (after the number), the inclusion does not impact scoring.
• If, however, the student includes “ft” or “feet” in the wrong location, or includes the wrong unit of measurement, the answer is incorrect.
No credit No credit
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Scoring: Clock Reading Tasks
• AIMSweb provides the proper symbol in the answer blank, yet some students may only write the complete answer (hour and minutes) in just one of the blanks, not both. Either is correct.
• In doing so, these students may or may not use the proper symbol to separate the hour and minutes. If the proper symbol is not used, the item is incorrect.
No creditFull Credit
1 30
Full Credit
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Scoring: Estimating / Rounding
• When students are asked to estimate answers, wherever possible, each item was designed so the answer is the same whether the student rounds before or after completing the problem.
• Where this was not possible, and two answers can be considered correct depending on when rounding occurred, 2 answers are provided on the Answer Key.
(Answers should not be rounded and are incorrect unless the item expressly requests that action.)
Full Credit
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Scoring: Reducing / Simplifying
• Unless the item expressly asks students to reduce/simplify a fraction, it is not required for a correct answer.
• Many students reduce/simplify fractions without being asked. If the calculation is correct, the answer is correct so long as it is in either the original form, or lowest form.
(The Answer Key provides both the initial fraction produced by working the problem and the lowest form possible of that fraction, as needed.) Either answer is correct.
• Every possible reduction/simplification between the original fraction and lowest form are not considered correct.
If the student reduces/simplifies the answer, the reduction/simplification must be in the lowest possible form to receive credit.
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Scoring: Reducing / Simplifying
Full CreditFull Credit
No Credit40
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Scoring: Converting
Full Credit
In items that ask the students to sequence numbers that include mixed numbers and decimals, either from greatest to least or least to greatest, students are expected to correctly sequence them in the number formatpresented.
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Scoring: ConvertingIf students decide to reduce/simplify the fractions and convert the mixed numbers to decimals:
• Full Credit: Whenever reductions/simplification and conversions are calculated and sequenced correctly
• No Credit: If the student makes an error in reduction/simplification or conversion, whether or not the final sequencing is correct based on the incorrect conversion
Full Credit No Credit
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Scoring: Calculate Score
1. Compare the student answers to the correct answers on the scoring template.
2. Add the total number of points earned.
3. Enter scores in AIMSweb
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M-CAP Practice Exercises
1. Your Trainer will read aloud the administration and scoring directions for M-CAP.
2. Next, “pretend” this test was administered to you and/or students in the room. (Thus, 8 or 10 minutes of elapsed time would have passed.)
3. Score the two practice exercises provided to you in your packet, according to the proper administration and scoring rules.
4. Discuss your results with your Trainer when the group has completed the task.
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FAQsQUESTION: How may accommodations be used for certain students taking M-CAP?
Excerpt from M-CAP Manual
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The general principles governing the use of accommodations in aimsweb administration for students with disabilities are described in the Introduction to aimsweb. Whenever normative data will be used to interpret performance, it is very important to adhere to the specific guidelines provided for each aimsweb measure so that interpretations are accurate. A wider range of accommodations may be used during progress monitoring, as long as the accommodations are used consistently in the instructional program and across the monitoring period.
Like any other test, M–CAP may be inappropriate for some students. For example, M–CAP requires paper-pencil test-taking skills, so using it with students who have severe motor problems may not be appropriate. Because the problems include written text, M–CAP is not appropriate for students who are not proficient in English. M–CAP scores of students with severe reading disabilities should be interpreted with care. Whenever language or reading ability is a concern, it can be informative to compare M–CAP results with M–COMP scores, because the M–COMP tasks require little or no reading.
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FAQsQUESTION:May the examiner read the M-CAP or M-COMP item directions for students with reading difficulties?
ANSWER: It is not appropriate to read the questions to students. However, reading the problems to the student MAY be permitted in cases where the student has been formally identified as having a moderate or severe reading disability, and this accommodation is part of the student’s instructional program. Any accommodations made during screening must be documented in the student’s record.
QUESTION:Does the answer have to be written on the blank line?
ANSWER: The answer does NOT have to be written on the blank line. As long as the response is clear and correct, give credit. For problems that have multiple blanks, give credit if the student meant to put the answers near the correct blanks.
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FAQsQUESTION:May students use calculators/manipulatives for M-CAP or M-COMP?
ANSWER: No.In addition to the use of calculator thus altering how the test was normed and standardized, we are also looking for authentic skill assessment of how well students can complete math applications. Fluent math computation skills are an underlying—and often prerequisite—component of Math Applications skill.
QUESTION:
What about using the calculator for progress monitoring but not screening?
ANSWER: The use of a calculator is not recommended for progress monitoring because it changes the nature of the task.
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QUESTION:On the Practice Exercise from the Training Module for M-CAP, the 7th grade probe, question 11 results in an answer of:
What if the student writes the answer as:
AB
(without the line above AB)
FAQs
ANSWER: We allow for some teacher discretion as clarified in the M-CAP Administration and Scoring manual. Either answer would seem acceptable.
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FAQs
QUESTION:May students use the probes as practice after testing? May teachers review the content with the students after testing?
ANSWER:Standardized tests should never be used for practice.
Example: What if the student, if being progress monitored, is to take a very similar test in the near future? This would be problematic and potentially influence outcomes due to practice effect. The teacher should work with the student on the item types outside of the actual test.
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FAQsQUESTION:Why are there no probes for M-CAP for Grade 1?
ANSWER: Grade 2 is generally when students are able to complete applied mathematics and the related reading involved in the M-CAP problems.
QUESTION:
Can students use scratch paper?
ANSWER: Students may use scratch paper, but they should not need it because they are allowed to write in the test booklets.
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FAQs
QUESTION:
Is there a typo on the answer key for time-telling problems?
Example:Problem: Answer Key:
ANSWER: No, there is no “typo.” The answer key provides the two digits needed to the left and right of the “:” (colon) in the answer blank.
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FAQs
QUESTION:Can we give the math probe one page at a time if we suspect the kids will shut down before they even start if they see a 3-page probe?
ANSWER: This measure is designed to not have a “ceiling,” meaning that there are more problems on the test than we anticipate even the most expedient of students to complete. Letting your students know that the test is designed to have more on it than what you expect them to complete in 8 (or 10) minutes may be helpful. That said, the standardized directions are not alterable.
It may be helpful to know that this measure was field tested and piloted extensively. Additionally, it was vetted through a variety of working school professionals in the field (e.g., teachers, administrators, math specialists, etc.). Items found to be significantly problematic during our field testing and piloting was addressed so that the final measures released were sound. It appears, via that process, that the ~3 pages presented at once did not pose a significant problem for students to the point where it impacted the results of the test or their performance.
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