Introduction
In May 1996, the New Jersey State Board of Education adopted
Core Curriculum Content Standards that define New Jersey's
expectations for student learning. The standards were
developed by a statewide panel of representatives from
education, business, industry and the interested public.
These representatives participated in a two-year process
to develop the core standards in seven content areas.
. Visual and Performing Arts
. Comprehensive Health and Physical Education
. Language Arts Literacy
. Mathematics
. Science
. Social Studies
. World Languages
In addition, all areas of instruction include the following
cross-content workplace readiness standards:
1. All students will develop career planning
and workplace readiness skills.
2. All students will use technology, information, and
other tools.
3. All students will use critical-thinking, decision-making,
and problem-solving skills.
4. All students will demonstrate self-management skills.
5. All students will apply safety principles.
Since public education must prepare all students for
the world of work, all content areas need to address
these cross-content workplace readiness standards.
To gauge student progress toward meeting the Core Curriculum
Content Standards, the New Jersey Department of Education
is developing a comprehensive set of assessments that
measure knowledge and skills at grades four, eight,
and eleven. The grade four Elementary School Proficiency
Assessment (ESPA) is the third component of the state's
assessment program which also includes the Grade Eight
Proficiency Assessment (GEPA) and the eleventh-grade
High School Proficiency Assessment (HSPA). Since not
every indicator can be assessed through a statewide,
standardized, written examination, individual districts
will be involved in measuring the attainment of some
performance expectations outlined in the standards.
This Directory of Test Specifications and Sample Items
for the Elementary School Proficiency Assessment (ESPA)
in Mathematics is a companion document to the New Jersey
State Department of Education's Core Curriculum Content
Standards, May 1996 and the Elementary School Proficiency
Assessment Content Domain Outline, February 1997. The
Directory of Test Specifications consists of Content/Skill
Outlines, ESPA test scores and subscores, and sample
items. All of these components and the Mathematics portion
of the Elementary School Proficiency Assessment Content
Domain Outline, February 1997, were developed by the
Mathematics Content Committee. This committee is composed
of fifteen New Jersey educators (nine elementary school
teachers, five mathematics supervisors, and a testing
specialist) who met for five weeks during the summer
of 1996 and who have continued to meet regularly.
The committee members relied upon their expertise to
design a test that is universally accessible to all
fourth graders and is composed of test questions that
are age- and grade-appropriate.
Curriculum specialists and teachers may use these specifications,
along with the New Jersey Mathematics Curriculum Frameworks
and the standards themselves, to improve instruction
at the district, school, and classroom levels.
Overview of the Grade 4 Mathematics
Test
The mathematics section of the Grade 4 ESPA assesses student's
knowledge and skills in five content clusters of mathematics:
. Number Sense, Operations, and Properties
. Data Analysis, Probability, and Discrete Mathematics
. Measurement
. Spatial Sense and Geometry
. Patterns and Algebra
The test items are distributed so that approximately 36%
of the items assess skills from the first cluster, Number
Sense, Operations, and Properties. Each of the other four
clusters contains approximately 16% of the items. There
are a total of 42 multiple-choice and 6 open-ended items
in the test. Of these, 32 multiple-choice and 5 open-ended
items are considered as operational and are distributed
as shown in the chart below.
Test Format
|
Cluster
|
Number of Multiple
Choice Items
|
Number of
Open-Ended Items
|
I: Number Sense,
Operations, and Properties |
12
|
1
|
| II: Measurement |
4
|
1
|
| III: Spatial Sense and Geometry |
5-6
|
1
|
IV: Data Analysis,
Probability, and Discrete Mathematics |
5-6
|
1
|
| V: Patterns and Algebra |
5
|
1
|
The remaining 10 multiple-choice and 1 open-ended items
are field test items and will not contribute to the
student's score.
The majority of the test allows students to use a calculator.
The basic four-function calculator will be sufficient.
Students taking any of the New Jersey tests in mathematics
should be prepared to use calculators by regularly using
those calculators in their instructional programs. Calculators
that have been given to students only on the day of
the assessment may actually cause them to perform less
well than they would have performed without such calculators.
Students must be comfortable with, and have practice
with calculators, or they will be of little benefit
during the assessment. Students should be permitted
to use their calculators, rather then the school's,
if they choose to do so.
The calculator section of the test contains two types
of questions, multiple-choice and open-ended. The multiple-choice
items have four choices. Each item is stated as a question
or as a completion statement.
The calculator section also includes five open-ended
items. These are designed to give students the opportunity
to explain their responses and show how they arrived
at their answers. Students can use diagrams, charts,
pictures, and/or words to explain their thinking. These
open-ended items are scored holistically, rather than
analytically, with a 0-to-3-point rubric specific to
each question, but derived from the general rubric that
follows. Scoring decisions are based on student demonstration
of conceptual understanding of the fundamental concept
being tested in the question. For example, a student
response that showed minor computational errors would
not severely penalize the student if the fundamental
concept being tested was not basic computation with
real numbers.
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