Connecticut Mastery Test
Vertical Scales
Frequently Asked Questions - 2009
This document contains answers to frequently asked questions regarding vertical scale score
results for the mathematics and reading sections of the Connecticut Mastery Test (CMT). This
information should be used to ensure appropriate understanding and interpretation of the CMT
vertical scale scores. Questions and/or comments about the CMT vertical scales should be
directed to the CMT Student Assessment Office at 860-713-6860.
1. Why were the vertical scales developed?
The CMT vertical scales were developed to measure growth (or change) across grades (i.e.,
from Grade 3 to Grade 4, from Grade 4 to Grade 5, etc.) on tests that have different
characteristics and items, but have similar content. The vertical scales were constructed so
that each vertical scale score represents the same theoretical achievement level whether
derived from a Grade 3, Grade 4, Grade 5, Grade 6, Grade 7, or Grade 8 CMT scale score. A
vertical scale can be used to interpret growth for individual students, schools or school
districts and for various subgroups (e.g., ethnicity, lunch status, special education).
2. How were the vertical scales developed?
During the 2007 CMT administration, a linking study was conducted that involved both
common students and common test items in the content areas of mathematics and reading.
Groups of Connecticut students were administered the on-grade level CMT along with one
session of an off-grade level CMT. For example, groups of Grade 5 students took sections of
the Grade 4 CMT (one grade-level below) or sections of the Grade 6 CMT (one grade-level
above) as well as the complete Grade 5 CMT. The end result is that students in different
grades taking different tests, have the same vertical scale score which represents the same
level of achievement as defined by the new vertical scale.
3. In what content areas are vertical scales available?
Vertical scales are available for the CMT Mathematics and Reading tests.
4. What is the score range of the vertical scale scores in mathematics and reading?
The vertical scales for both mathematics and reading range from 200 to 700.
Connecticut State Department of Education
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5. Where can the vertical scale score reports be accessed?
Vertical scale reports are available through the Connecticut CMT and CAPT Online Reports
Web site (www.ctreports.com).
6. How is growth calculated using a vertical scale?
Growth for individual students from one year to another year is defined as:
(Vertical Scale Score Year 2) minus (Vertical Scale Score Year 1)
Growth for groups of students from one year to another year is defined as:
(Mean Vertical Scale Score Year 2) minus (Mean Vertical Scale Score Year 1)
Growth at the individual or group levels can be assessed over one-year (e.g., 2006 Grade 3
students vs. 2007 Grade 4 students) or two-years (e.g., 2006 Grade 6 students vs. 2008 Grade
8 students).
Growth over time at the individual or group level can be positive or negative. Growth is
positive when the vertical scale score is larger in Year 2 than in Year 1. Negative growth
occurs when the vertical scale score is smaller in Year 2 than in Year 1.
Note: Negative growth is less likely at the group level than at the individual student level
because group mean scores are more stable than individual student scores.
7. Which students have vertical scale scores?
Students in Grades 3 through 8 who have a valid Generation 4 CMT score in mathematics
and/or reading also have a corresponding valid vertical scale score in mathematics and/or
reading. When assessing growth at the individual student level between years, a valid score is
needed for both years.
8. When generating growth reports, what happens if a student’s demographic information
changes across years?
When generating growth reports based on matched groups, each student’s demographic
information is determined by the student’s status in the most recent year. For example, when
generating a report for special education students, a student who was identified as a regular
education student in the first year but is identified as a special education student in the last
year would be considered a member of the special education subgroup in this report.
Connecticut State Department of Education
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9. Is it appropriate to compare vertical scale scores across content areas?
No, vertical scale scores are not equivalent or comparable across content areas. For example,
a mathematics vertical scale score of 550 does not necessarily represent the same relative
level of achievement as a vertical scale score of 550 in reading.
10. How are scores calculated on the Vertical Scale Score Analysis Report on the
ctreports.com Web site?
Sample report from ctreports.com:
Average Vertical Scale Score: Mathematics
The “Average” column represents the average vertical scale score of all students who had a
valid score in the defined year. The “Matched N Average” column represents the average
vertical scale score of only those students who had a score in the first and last years. Finally,
the “Matched N Growth” column represents the difference between the “Matched N
Average” in the first and last years.
11. Is the growth in one content area on the vertical scales comparable to the growth in
another content area?
Growth, in terms of vertical scale scores, is not comparable across content areas. For
example, if a particular group of students grew 20 vertical scale score points in mathematics
and 25 vertical scale score points in reading over a one-year period, it would be not be
appropriate to conclude that the group grew more in reading than in mathematics.
12. Has the Connecticut State Department of Education identified expected growth on the
vertical scale as students advance in grades?
The Connecticut State Department of Education has not identified expected growth on the
vertical scale.
Connecticut State Department of Education
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13. How can the Levels of Understanding descriptors help interpret vertical scale scores?
The reading and mathematics vertical scales are divided into five Levels of Understanding
(Stages 1 - 5), with a description of typical performance for each level. Each of the five
Levels of Understanding corresponds to content-referenced descriptions of student
performance. The vertical scale descriptors do not describe grade-level performance. The
descriptors span the six grades and are meant to provide a general (not grade-level specific)
description of what typical students know and can do within certain score ranges or levels of
understanding across the vertical scales.
See Appendix A for the Levels of Understanding descriptors in mathematics and reading.
14. Are the vertical scale Levels of Understanding related to the Performance Level
Descriptors at each grade (i.e., Below Basic, Basic, Proficient, Goal, and Advanced)?
Vertical scale Levels of Understanding are not related to and cannot be compared to the
Performance Level Descriptors (PLD) that describe the five performance levels (i.e., Below
Basic, Basic, Proficient, Goal, and Advanced) for each content area PLDs relate to student
performance within a specific grade while the vertical scale Levels of Understanding relate to
student performance across multiple grades.
For analysis purposes, the performance bands at each grade have been mapped against the
vertical scale scores for mathematics and reading in Appendix B. These charts outline how a
performance level scale score in a grade would convert into the corresponding vertical scale
score.
15. Does the Connecticut Academic Performance Test (CAPT) have a vertical scale?
Vertical scales are not available for the CAPT because it is a single grade-level test.
Additionally, there is not a vertical scale that relates CMT performance to CAPT
performance.
Questions and/or comments about the CMT Vertical Scales should be directed to the CMT
Student Assessment office at 860-713-6860.
Connecticut State Department of Education
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Appendix A
Connecticut Mastery Test Vertical Scale Descriptors
Mathematics
Level of
Understanding
Description
Vertical
Scale Score
Stage V
Generally, students who perform at this level
demonstrate extensive knowledge of all assessed
content areas.
Stage IV
Generally, students who perform at this level
demonstrate extensive knowledge of most of the
assessed content areas. These students demonstrate
adequate knowledge of some of the assessed
content areas including, measurement, ratio,
proportion and percent.
540 - 577
Stage III
Generally, students who perform at this level
demonstrate adequate knowledge of most and
extensive knowledge of some of the assessed
content areas. These students demonstrate limited
knowledge of estimating solutions to problems,
measurement, ratio, proportion and percent.
502 - 539
Stage II
Generally, students who perform at this level
demonstrate adequate knowledge of some of the
assessed content areas. These students demonstrate
limited knowledge of rational number concepts and
computation, estimation, and measurement.
464 - 501
Stage I
Generally, students who perform at this level
demonstrate limited knowledge of most of the
assessed content areas. These students demonstrate
adequate knowledge of basic number concepts and
computation skills.
Less than
464
Connecticut State Department of Education
578+
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Appendix A
Connecticut Mastery Test Vertical Scale Descriptors
Reading
Level of
Understanding
Description
Vertical
Scale Score
Stage V
Students who perform at this level are likely to
demonstrate an exceptional ability to read and
respond to informational and literary texts without
assistance. Students at this level effectively use
sophisticated strategies before, during and after
reading to understand, interpret and evaluate text.
529+
Stage IV
Students who perform at this level are likely to
demonstrate a consistent ability to read and
respond to informational and literary texts with
minimal assistance. Students at this level use
strategies effectively before, during, and after
reading to understand, interpret and evaluate text.
495 - 528
Stage III
Students who perform at this level are likely to
demonstrate an adequate ability to read and
respond to informational and literary texts with
some assistance. Students at this level use some
strategies effectively before, during, and after
reading to understand, interpret and evaluate text.
460 - 494
Stage II
Students who perform at this level are likely to
demonstrate a limited ability to read and respond to
informational and literary texts, and require
assistance to complete many reading tasks.
Students at this level use some strategies
inconsistently before, during and after reading to
understand and interpret text.
425 - 459
Stage I
Students who perform at this level are likely to
demonstrate a very limited ability to read and
respond to informational and literary texts and
require significant assistance to complete most
reading tasks. Students at this level are not able to
use strategies to understand and interpret text.
Less than
425
Connecticut State Department of Education
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Appendix B
2009 Mathematics Performance Level Cut Points on the Vertical Scale
Advanced
Goal
Proficient
Basic
Below Basic
Grade 3
484 – 510
450 – 483
417 – 449
395 – 416
200 – 395
Grade 4
529 – 562
484 – 528
451 – 483
430 – 450
265 – 429
Connecticut State Department of Education
Grade 5
556 – 600
506 – 555
476 – 505
451 – 475
295 – 450
Grade 6
572 – 637
526 – 571
493 – 525
466 – 492
325 – 465
Grade 7
593 – 664
544 – 592
510 – 543
481 – 509
355 – 480
Grade 8
607 – 700
558 – 606
523 – 557
497 – 522
380 – 496
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Appendix B
2009
2008 CMT Reading Vertical Score Scale Scores
Matched with Performance Level Scale Scores
700
600
Advanced
Advanced
Advanced
Advanced
Vertical Score Scale
Advanced
Advanced
500
400
Goal
Goal
Goal
Proficient
Basic
Proficient
Basic
Proficient
Basic
Goal
Goal
Goal
Proficient
Basic
Below Basic Below Basic
Proficient
Basic
Proficient
Basic
Below Basic Below Basic
Below Basic
300
Below Basic
200
3
4
5
6
7
8
Grade Level
2009 Reading Performance Level Cut Points on the Vertical Scale
Advanced
Goal
Proficient
Basic
Below Basic
Grade 3
478 – 547
425 – 477
401 – 424
381 – 400
200 – 380
Grade 4
506 – 555
449 – 505
428 – 448
412 – 427
250 – 411
Connecticut State Department of Education
Grade 5
524 – 582
466 – 523
448 – 465
434 – 447
279 – 433
Grade 6
539 – 603
475 – 538
456 – 474
440 – 455
290 – 439
Grade 7
549 – 617
487 – 548
470 – 486
454 – 469
300 – 453
Grade 8
561 – 700
500 – 560
481 – 499
466 – 480
305 – 465
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