3-point response
The response shows complete understanding of the problem's
essential mathematical concepts. The student executes
procedures completely and gives relevant responses to
all parts of the task. The response contains few minor
errors, if any. The response contains a clear, effective
explanation detailing how the problem was solved so that
the reader does not need to infer how or why decisions
were made.
2-point response
The response shows nearly complete understanding of
the problem's essential mathematical concepts. The student
executes nearly all procedures and gives relevant responses
to most parts of the task. The response may have minor
errors. The explanation detailing how the problem was
solved may not be clear, causing the reader to make
some inferences.
1-point response
The response shows limited understanding of the problem's
essential mathematical concepts. The response and procedures
may be incomplete and/or may contain major errors. An
incomplete explanation of how the problem was solved
may contribute to questions as to how and why decisions
were made.
0-point response
The response shows insufficient understanding of the
problem's essential mathematical concepts. The procedures,
if any, contain major errors. There may be no explanation
of the solution or the reader may not be able to understand
the explanation. The reader may not be able to understand
how and why decisions were made.
The above generic rubric is used as a guide to develop
specific scoring guides for each of the open-ended (OE)
items which appear on the New Jersey fourth-grade, eighth-grade,
and eleventh-grade proficiency assessments in mathematics.
More information on open-ended questions and related
scoring is also provided in the Mathematics Instructional
Guide.
The Grade 4 ESPA also includes a non-calculator section
that consists of multiple-choice questions using mental
mathematics and estimation to solve problems.
The test also assesses the way students think. Items
are classified as requiring conceptual understanding,
procedural knowledge, problem-solving skills, or some
combination of these.
Because of the relationship among the content clusters,
the mathematical assessment identified certain abilities
and experiences that are relevant in all of the clusters
outlined above. These skills comprise the power base
and have been identified as: logical reasoning, connecting
mathematical ideas to one another and to other disciplines,
communicating mathematical understanding, problem solving,
using tools and technology, and estimating effectively.
Every item in the test has been
classified according to the power base skill it assesses.
The framework on the following page shows the content
clusters and cognitive skills assessed in the Grade
4 ESPA mathematics test. Although the framework provides
a two-dimensional classification system that can be
used to categorize test items, some items belong in
more than one cell. Several items assess both knowledge
and problem-solving skills, and a few items contain
overlapping content. The underlying power base skills
are shown as the base of the framework. Because the
power base is integrated throughout the assessment,
every item has been analyzed to indicate which skills
are being assessed. Many items require more than one
skill and therefore reflect the use of more than one
power base ability.
Power Base by Cluster
The items in Cluster I: Number Sense, Operations,
and Properties reflect Core Curriculum Content Standards
4.1 through 4.5, and 4.10 and their respective indicators
with the following exceptions: 4.10.2 and 4.10.3.
In addition to the exceptions already stated, items in
this cluster only reflect indicator 4.16.2 of Standard
4.16.
The items in Cluster II: Measurement reflect
Core Curriculum Content Standards 4.1 through 4.5, and
4.10, inclusive. Items in this cluster only reflect
indicators 4.16.1, 4.16.2, 4.16.4. and 4.16.10 of Standard
4.16.
The items in Cluster III: Spatial Sense and Geometry
reflect Core Curriculum Content Standards 4.1 through
4.5, and 4.10 and their respective indicators with the
following exceptions: 4.2.4, 4.5.5, and 4.10.1.
In addition to the exceptions already stated, items
in this cluster only reflect indicators 4.16.1
and 4.16.2 of Standard 4.16.
The items in Cluster IV: Data Analysis, Probability,
and Discrete Mathematics reflect Standards 4.1 through
4.5, and 4.10 and their respective indicators with the
following exceptions: 4.2.1, 4.2.4, 4.5.3, 4.5.5,
4.10.1, 4.10.2, 4.10.3, and 4.10.7. In addition to the
exceptions already stated, items in this cluster only
reflect indicators 4.16.1, 4.16.2, 4.16.3, 4.16.4,
4.16.9, 4.16.10, and 4.16.11 of Standard 4.16. .
The items in Cluster V: Patterns and Algebra
reflect Core Curriculum Content Standards 4.1 through
4.5, and 4.10 and their respective indicators with the
following exceptions: 4.2.4, 4.5.4, 4.10.1, 4.10.2,
4.10.3, 4.10.4, 4.10.5, and 4.10.7. In addition to the
exceptions already stated, items in this cluster
indicators 4.16.1, 4.16.2, 4.16.9, 4.16.10, and 4.16.11
of Standard 4.16.
|
