February 27, 2012
Assessment Creation Assignment
Part 1: Overview and Description
This assessment was created for Kindergarten mathematics and is focused on counting and number sense. These two ideas are perhaps the most pervasive and important ideas in Kindergarten mathematics, as they form the foundation for all other areas in mathematics covered both in kindergarten and the later grades. The kindergarten math curriculum builds on the student’s natural curiosity about the world—it encompasses several areas including counting,
patterns, shapes, time, and money. The major goal of this unit is for students to develop number sense. This includes developing an understanding of the ways to think about, represent and compare numbers. In order to achieve this, students will learn how to count forwards and backwards, compare numbers, group sets of objects, and represent numbers precisely using written and oral language. They will learn the vocabulary necessary for understanding said tasks and how to count objects with a one-to-one correspondence. By actively exploring their environment, students will model and manipulate numbers using objects. Because developing this number sense is the foundation for the Kindergarten curriculum, it is incorporated into a variety of daily activities throughout the entire year. This particular unit is designed for the third quarter, in which students will build on their basic knowledge about numbers. They will skip count by 5s and 10s, group numbers by 5s and 10s, and identify one more than and one less than a number. Additionally, they will extend their counting skills and count forward and backwards to and from 100.
This assessment stems from the Virginia Mathematics SOL K.4, which states: The student will a) count forward to 100 and backward from 10; b) identify one more than a number and one less than a number; and c) count by fives and tens to 100. The Intended Learning Outcomes (Table 1) for this SOL indicate that the student will understand the oral counting sequence and that skip counting can be used to count a collection of objects. They will investigate and describe patterns in skip counting and the benchmark numbers of 5s and 10s. Further, they will understand that numeric relationships include ―more than‖ and ―less than.‖ In
order to assess student learning of these components, this assessment will include two sections. The first section is a whole group assessment involving both fixed and supply-response items intended to measure concepts of more than/less than, one-to-one correspondence in counting objects, and patterns of skip counting. The second section is an individual assessment in which the student will use manipulatives to model counting and grouping objects. In this second individual section, the student will also be asked to orally count backwards by 5s and by 10s. Together these two sections will provide a more holistic picture of student learning in a manner that is developmentally appropriate.
The classroom in which this assessment will take place is made up of twenty students, eleven female and nine male, of diverse cultural and economic backgrounds at Magruder Elementary. Thirteen students are Caucasian, five are African-American, and two are of mixed race. One student in the class has a speech IEP plan and one student receives ELL services. Five students receive pull-out targeted reading instruction daily with a reading specialist. Two students have been identified for participation in the York County gifted program. These student characteristics have greatly informed the creation of the assessment. Instructions and questions will be read-
aloud by the teacher to accommodate for students who are still experiencing great difficulty with reading as well as to increase validity of the assessment. The use of pictures, verbal responses, and manipulatives in the assessment are also intended to increase the validity by allowing students to display their knowledge through multiple avenues.
Use and Purpose of Assessment
This assessment has two distinct purposes. Primarily, the assessment will act as a pre-
rdcursor to the 3 quarter York County DBA assessment as it will include the intended learning outcomes that will be reflected in the upcoming DBA assessment. Delivering formal assessments in kindergarten can be difficult and often yield unreliable results due to the fact that students are not as familiar or experienced with testing as older students are. The DBA assessments are mandatory each quarter and any additional explicit preparation will be beneficial. This assessment will help prepare students for the format, experience, and content of the upcoming DBA assessment.
Further, the results of this assessment will be used to guide instruction and target intervention as necessary. The goal is that students will possess a strong idea of number sense
stand counting abilities before moving on to 1 grade. Results from this assessment will be
valuable in targeting any necessary interventions and specific instruction so that this goal will be reached.
Part 2: Design Elements of Assessment
The intended learning outcomes are attached as Table 1. These outline the essential knowledge and skills that this assessment was created to measure. The table of specifications
(ToS) acts as a guide for distributing items throughout the assessment with appropriate weight. The ToS is attached as Table 2 and includes the intersection of test items with content alignment. Validity
This assessment is a valid and reliable measure of student’s number sense. The ToS
indicates that the assessment has construct validity because it appears to measure what it is intended to measure. It is a mathematics assessment that is designed to provide an accurate representation of the intended learning outcomes. Further, it has strong content validity because it is aligned with the Virginia SOL standards in both range of knowledge and skills as well as the different cognitive demands required of the student. The individual questions in this assessment were specifically created to assess the particular knowledge and skills required of kindergarten
rdstudents by the 3 quarter. The questions were designed to assess true counting ability and number sense, as opposed to numeral recognition. Whenever possible, all questions and answer choices include pictures to assess one-to-one correspondence in counting. Further, all questions are read orally by the teacher, so that the student will not be unfairly punished if they are not able to read the numeral in the question. The content validity of this assessment is outlined in the ToS, where it is evident that the test items address multiple cognitive levels.
Error has been guarded against in this assessment through multiple means. The language and scenarios used in each of the questions are those that are familiar to students, so as to reduce error due to cultural-biases or developmentally inappropriate language. Questions involving pictorial representations of numbers reduce the possibility that the results will be due to student
knowledge of numerals, instead of ability to count accurately. Multiple direct questions for each ILO reduce the threat of systematic error and allow for explicit evidence of learning.
This assessment was further proofread by the veteran classroom teacher. This teacher commented that the pictorial representations and individual assessment portion should contribute to reducing error in the results. It is possible that random error could be introduced in the administration of the test via fire alarms, student illness, or student distractions. Kindergarten students are still unfamiliar with the rules of formal testing procedures and may cause disruptions when they likely will ask for help with questions from the teacher or their peers. The teacher administering this assessment should pay careful attention to minimize distraction and provide specific, direct instructions for each question.
The rubrics provided for each individual supply-response item ensure both inter-rater and intra-rater reliability. The direct nature of the language in the rubric and the subject matter being assessed leave little room for interpretation, thus greatly reducing subjectivity in scoring. Rationale
This assessment consists of nine select-response items and five supply-response items. The test is divided into two parts, whole group and individual, with three of the supply-response items on the individual section. The rationale for creating these questions was to provide an adequate sample of items across the intended learning outcomes. The individual part of the assessment was created in order to bolster validity and reliability. Where select-response items exist on the whole group assessment that include strictly numerals in the question or answers, items assessing the same ILO exist on the individual assessment. Further, the supply response items were created in order to provide a developmentally appropriate avenue of testing for
kindergarten students. All items were personally created, with the exception of items #6, 8, 9, and 10 which are adapted from the Scott Foresman-Addison Wesley enVisionMATH Virginia Grade K series.
This assessment has the potential for high predictive validity for the aspects of the upcoming DBA assessment that cover number sense. The format and types of questions are
similar to those presented in the DBA. Further, the testing environment for the whole group assessment will be similar, so predictive validity is strong. However, this assessment only covers
rdnumber sense and the 3 quarter DBA will also cover topics such as money and time. While a strong number sense will contribute to greater understanding of topics like time and money, it is not directly related. Therefore, it cannot be wholly predictive of student performance on the DBA because it does not include all content areas.
Scoring and Grading
Students will receive an overall grade for this assessment, following the grading procedures for kindergarten in York County, which are as follows: S=Satisfactory, P=Progressing, and N=Needs Improvement. The rubrics for each supply response item mirror this scale with ―Excellent,‖ ―Developing,‖ and ―Needs Improvement.‖ Each item is worth 1 point,
except items with rubrics. Each rubric will be worth 3 points, because there are multiple questions involved in each one. Points are distributed in those items with 3 points for Excellent, 2 for Developing and 1 for Needs Improvement. Overall grade for the assessment will be determined by total number of points, with 22 total points available. The grading scale is as
follows: S= at or above 80% (18 of 22 points), P= at or above 60-79% (14 of 22 points), N= below 60% (13 or fewer of 22 points).
rdPerformance on this assessment will be roughly 15-20% of the students’ 3 quarter grade
in mathematics. As mentioned previously, such summative assessments are still new to kindergarten students and it is not the intent of this assessment to provide a grade for students.
rdDaily formative assessments will provide the bulk of the students 3 quarter mathematics grade.
The assessment is important because it acts as a preparation for future assessments for the student and as an instructional guide for the teacher.
Table 1. Intended Learning Outcomes
The intended learning outcomes for the Virginia Mathematics SOL K.4 are as follows:
Intended Learning Outcome Content Cognitive Level on Blooms’ Taxonomy
The student will count forward from 0 to Explicit – counting from 0-100 Knowledge 100.
Implied – know how to count, numbers
Conditional – from 0-100
The student will group 100 or fewer Explicit – counting Application objects together into sets of fives or tens
and then count them by fives or by tens Implied – what a set is, how to
Conditional – into sets of 5s or 10s,
count by 5s and 10s
The student will recognize the relationship Explicit – one more than/one less than Comprehension of one more than and one less than a
number using objects (i.e., five and one Implied – number order
more is six; and one less than ten is nine)
Conditional – using objects
The student will investigate and recognize Explicit – counting by 5s to 100 Analysis the pattern of counting by fives to 100, Comprehension using a variety of tools Implied – what a pattern is
Conditional – using variety of tools
Table 2. Table of Specifications
Bloom’s Taxonomy Content
Knowledge Comprehension Application Analysis Synthesis Evaluation
; The student will count forward
#A4, A6, A9 from 0 to 100.
; #A7, B4 The student will count backwards
from 0 to 100.
The student will group 100 or
; fewer objects together into sets of
#A11, B1* fives or tens and then count them
by fives or by tens
The student will recognize the
; relationship of one more than and
#A1, A2, A8, one less than a number using
A10 objects (i.e., five and one more is
six; and one less than ten is nine)
The student will investigate and
; ; recognize the pattern of counting
#A3 #B2* by fives to 100, using a variety of
; ; The student will investigate and
#A5 #B3** recognize the pattern of counting
by tens to 100, using a variety of
*To be assessed individually, using manipulatives
**To be assessed individual, through verbal response