Iowa Tests of Basic Skills® (ITBS®)
Form C –Mathematics Subtests

Descriptive Information

Please provide a description of your tool:

The Iowa Tests of Basic Skills measure the skills, academic growth, and achievement of students from Kindergarten through Grade 8. Developed at The University of Iowa, and backed by a tradition of more than 70 years of educational research and test development experience, the ITBS provides an in-depth assessment of students’ achievement of important educational objectives. Tests in reading, language arts, mathematics, social studies, science, and information sources yield reliable and comprehensive information both about the development of students’ skills and about their ability to think critically. Form C reflects the most up-to-date thinking about curriculum as represented in current content standards, curriculum frameworks, and instructional materials. All test materials have been extensively field tested for psychometric soundness and evaluated for fairness to gender, racial, ethnic, and cultural groups. Test content was chosen for its appeal and interest to children in order to provide test takers with an engaging and motivating testing experience. The ITBS provides educators with accurate and detailed information, allowing them to tailor curricula to the individual educational needs of their students and address any achievement deficiencies early in the school year. By using this diagnostic data to drive instruction, students and educators benefit by higher performance on other assessments such as state tests. While both Complete and Survey batteries are available, we are presenting only the Complete Battery, as it was the battery used when the classification data were computed.

The tool is intended for use with the following grade(s).

Preschool / Pre - kindergarten
Kindergarten
First grade
Second grade
Third grade
Fourth grade
Fifth grade
Sixth grade
Seventh grade
Eighth grade
Ninth grade
Tenth grade
Eleventh grade
Twelfth grade

The tool is intended for use with the following age(s).

0-4 years old
5 years old
6 years old
7 years old
8 years old
9 years old
10 years old
11 years old
12 years old
13 years old
14 years old
15 years old
16 years old
17 years old
18 years old

The tool is intended for use with the following student populations.

Students in general education
Students with disabilities
English language learners

ACADEMIC ONLY: What skills does the tool screen?

Reading

Phonological processing:

RAN
Memory
Awareness
Letter sound correspondence
Phonics
Structural analysis

Word ID

Accuracy
Speed

Nonword

Accuracy
Speed

Spelling

Accuracy
Speed

Passage

Accuracy
Speed

Reading comprehension:

Multiple choice questions
Cloze
Constructed Response
Retell
Maze
Sentence verification
Other (please describe):

Listening comprehension:

Multiple choice questions
Cloze
Constructed Response
Retell
Maze
Sentence verification
Vocabulary
Expressive
Receptive

Mathematics

Global Indicator of Math Competence

Accuracy
Speed
Multiple Choice
Constructed Response

Early Numeracy

Accuracy
Speed
Multiple Choice
Constructed Response

Mathematics Concepts

Accuracy
Speed
Multiple Choice
Constructed Response

Mathematics Computation

Accuracy
Speed
Multiple Choice
Constructed Response

Mathematic Application

Accuracy
Speed
Multiple Choice
Constructed Response

Fractions/Decimals

Accuracy
Speed
Multiple Choice
Constructed Response

Algebra

Accuracy
Speed
Multiple Choice
Constructed Response

Geometry

Accuracy
Speed
Multiple Choice
Constructed Response

Other (please describe):

Please describe specific domain, skills or subtests:

BEHAVIOR ONLY: Which category of behaviors does your tool target?

Internalizing
Externalizing
Internalizing and Externalizing

BEHAVIOR ONLY: Please identify which broad domain(s)/construct(s) are measured by your tool and define each sub-domain or sub-construct.

Acquisition and Cost Information

Administration

BEHAVIOR ONLY: What type of administrator is your tool designed for?

General education teacher
Special education teacher
Parent
Child
External observer
Other

If other, please specify:

What is the administration setting?

Direct observation
Rating scale
Checklist
Performance measure
Questionnaire
Direct: Computerized
One-to-one
Other

If other, please specify:

Group administered

Does the tool require technology?

If yes, what technology is required to implement your tool? (Select all that apply)

Computer or tablet
Internet connection
Other technology (please specify)

If your program requires additional technology not listed above, please describe the required technology and the extent to which it is combined with teacher small-group instruction/intervention:

What is the administration context?

Individual
Small group   If small group, n=
Large group   If large group, n=
Computer-administered
Other

If other, please specify:

ACADEMIC ONLY: What are the discontinue rules?

No discontinue rules provided
Basals
Ceilings
Other

If other, please specify:

Are norms available?

Yes

Are benchmarks available?

No

If yes, how many benchmarks per year?

If yes, for which months are benchmarks available?

BEHAVIOR ONLY: Can students be rated concurrently by one administrator?

If yes, how many students can be rated concurrently?

Training & Scoring

Training

Is training for the administrator required?

Yes

Describe the time required for administrator training, if applicable:

Less than 1 hour of training

Please describe the minimum qualifications an administrator must possess.

Professional

No minimum qualifications

Are training manuals and materials available?

Yes

Are training manuals/materials field-tested?

No

Are training manuals/materials included in cost of tools?

No

If No, please describe training costs:

Can users obtain ongoing professional and technical support?

Yes

If Yes, please describe how users can obtain support:

toll-free telephone support & Riverside Field Staff

Scoring

How are scores calculated?

Manually (by hand)
Automatically (computer-scored)
Other

If other, please specify:

Do you provide basis for calculating performance level scores?

Yes

What is the basis for calculating performance level and percentile scores?

Age norms
Grade norms
Classwide norms
Schoolwide norms
Stanines
Normal curve equivalents

What types of performance level scores are available?

Raw score
Standard score
Percentile score
Grade equivalents
IRT-based score
Age equivalents
Stanines
Normal curve equivalents
Developmental benchmarks
Developmental cut points
Equated
Probability
Lexile score
Error analysis
Composite scores
Subscale/subtest scores
Other

If other, please specify:

predicted scores are available

Does your tool include decision rules?

If yes, please describe.

Can you provide evidence in support of multiple decision rules?

No

If yes, please describe.

Please describe the scoring structure. Provide relevant details such as the scoring format, the number of items overall, the number of items per subscale, what the cluster/composite score comprises, and how raw scores are calculated.

The number of questions a student gets right on a test is the student’s raw score. By itself, a raw score has little or no meaning, and so raw scores are usually converted to other types of scores for interpretational purposes, including standard scores. Composite scores are obtained by averaging the developmental standard scores from certain component tests. The average standard score can be converted to a percentile rank, grade equivalent, or other type of score for interpretational purposes.

Describe the tool’s approach to screening, samples (if applicable), and/or test format, including steps taken to ensure that it is appropriate for use with culturally and linguistically diverse populations and students with disabilities.

Overview of The Iowa Tests The Iowa Tests of Basic Skills are a series of norm-referenced measures that assess student achievement in Kindergarten through Grade 8. The tests are designed to provide a thorough assessment of progress in skills and standards that are essential to successful learning. The overall approach of The ITBS is one of width, not depth, making them an ideal screening tool as part of an RtI program, especially when considering the breadth of skills information obtained within very efficient testing time requirements. Riverside recommends using the tests early in the school year so that students requiring further diagnostic assessment and interventions get needed attention as soon as possible. The ITBS align closely with the recommendations from the National Research Center for Learning Disabilities on Implementing RTI. The Center calls for screening that is school-wide, meets accepted psychometric standards, and has evidence of documented reliability and concurrent and predictive validity within school settings. Because the ITBS can be administered quickly and efficiently to groups of students, they can conveniently be administered to entire school populations. The strong psychometric rigor documented in the accompanying technical information further underscore the ITBS’ appropriateness for use in an RtI program. Test Descriptions Descriptive information on the scope and sequence of the content areas in the ITBS can be found in the Guide to Research and Development. Additional information can be provided upon request. What follows here are some important summary points to note. In the area of mathematics, two separate tests comprehensively screen the broad foundation skills related to math literacy: Math Concepts and Estimation and Math Problem Solving and Data Interpretation. In the Concepts and Estimation test, the Concepts items measure students’ understanding of the logic of mathematical processes and relationships, including: number systems and numeration theory; arithmetic operations and procedures for integers; geometric operations and procedures; measurement; fractions, decimals, and percents; probability and statistics; equations, inequalities, and number sentences. The Estimation items measure students’ number sense, mental arithmetic, and computational estimation skills. Multiple strategies are represented, including standard rounding, front ending, use of compatible numbers, and compensation for rounding error. In addition, some items place estimation tasks in context, while others use a simple symbolic form because the application of estimation strategies in situations where students are using calculators or computers seldom involves context. In the Problem Solving and Data Interpretation test, the items connect knowledge of mathematics to other subject areas and to real-world applications. Items measure students’ mathematical reasoning abilities and the problem solving process, as well as students’ ability to analyze and interpret data presented in charts, graphs, tables, and other displays. Items in problem solving vary in terms of the number of required operational steps, the types of required operations, and the kinds of numbers on which operations must be performed. This test structure ensures that a wide variety of math items are used to assess students’ problem solving skills and to help in the diagnosis of the difficulties some students have with problem solving. Test Fairness In addition to statistical analyses undertaken to ensure that the ITBS is appropriate for use with culturally and linguistically diverse student populations, an expert panel reviewed content materials in a research pilot stage of test development. One important role of this independent review by educators with diverse social, cultural, and geographic perspectives was to ensure that items on the tests are readily accessible to all students and that sources of construct-irrelevant variance are minimized. Test Accommodations In collecting normative data during the national standardization of the ITBS, schools were given detailed instructions on the testing of students with disabilities and English Language Learners (ELL) or Limited English Proficiency (LEP) students. Test accommodations included out-of-level testing, extended time, individual/small group administration, repeated directions, provision of English/Native Language word-to-word dictionary, and test administration by ESL teachers or individuals performing language services.

Classification Accuracy & Cross-Validation Summary

Grade	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Classification Accuracy Fall
Classification Accuracy Winter
Classification Accuracy Spring

Legend

Convincing evidence

Partially convincing evidence

Unconvincing evidence

Data unavailable

^dDisaggregated data available

State Accountability Test

Classification Accuracy

Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.

The participating students all took the state accountability test at the end of the school year. The lowest proficiency level (Below Basic) was used as the indicator of Risk; the upper three proficiency levels were used as the No-Risk category

Describe when screening and criterion measures were administered and provide a justification for why the method(s) you chose (concurrent and/or predictive) is/are appropriate for your tool.

Describe how the classification analyses were performed and cut-points determined. Describe how the cut points align with students at-risk. Please indicate which groups were contrasted in your analyses (e.g., low risk students versus high risk students, low risk students versus moderate risk students).

The cut-points on the instrument used as the screener were identified as the 19th percentile of the national standardization sample.

Were the children in the study/studies involved in an intervention in addition to typical classroom instruction between the screening measure and outcome assessment?

No

If yes, please describe the intervention, what children received the intervention, and how they were chosen.

Cross-Validation

Has a cross-validation study been conducted?

No

If yes,

Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.

Describe when screening and criterion measures were administered and provide a justification for why the method(s) you chose (concurrent and/or predictive) is/are appropriate for your tool.

Describe how the cross-validation analyses were performed and cut-points determined. Describe how the cut points align with students at-risk. Please indicate which groups were contrasted in your analyses (e.g., low risk students versus high risk students, low risk students versus moderate risk students).

Were the children in the study/studies involved in an intervention in addition to typical classroom instruction between the screening measure and outcome assessment?

If yes, please describe the intervention, what children received the intervention, and how they were chosen.

Classification Accuracy - Fall

Reliability

Grade	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Rating

Legend

Convincing evidence

Partially convincing evidence

Unconvincing evidence

Data unavailable

^dDisaggregated data available

*Offer a justification for each type of reliability reported, given the type and purpose of the tool.

*Describe the sample(s), including size and characteristics, for each reliability analysis conducted.

Reliability estimates were derived from the 2000 and 2005 ITBS national standardization samples of approximately 4,000 to 15,000 nationally representative students, and include both Fall and Spring estimates.

*Describe the analysis procedures for each reported type of reliability.

*In the table(s) below, report the results of the reliability analyses described above (e.g., internal consistency or inter-rater reliability coefficients).

Results from other forms of reliability analysis not compatible with above table format:

Manual cites other published reliability studies:

Yes

Provide citations for additional published studies.

See Guide to Research and Development and Norms and Score Conversions Booklet.

Do you have reliability data that are disaggregated by gender, race/ethnicity, or other subgroups (e.g., English language learners, students with disabilities)?

If yes, fill in data for each subgroup with disaggregated reliability data.

Results from other forms of reliability analysis not compatible with above table format:

Manual cites other published reliability studies:

Provide citations for additional published studies.

Validity

Grade	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Rating

Legend

Convincing evidence

Partially convincing evidence

Unconvincing evidence

Data unavailable

^dDisaggregated data available

*Describe each criterion measure used and explain why each measure is appropriate, given the type and purpose of the tool.

*Describe the sample(s), including size and characteristics, for each validity analysis conducted.

*Describe the analysis procedures for each reported type of validity.

*In the table below, report the results of the validity analyses described above (e.g., concurrent or predictive validity, evidence based on response processes, evidence based on internal structure, evidence based on relations to other variables, and/or evidence based on consequences of testing), and the criterion measures.

Results from other forms of validity analysis not compatible with above table format:

NOTE: Results from each construct/convergent analysis, by grade level, involved a range of students from two states. Across grades, the minimum range value was 1,000 and the maximum range value was 11,500. Alignment of test with National Council of Teachers of Mathematics (NCTM) Assessment Standards for School Mathematics; Curriculum and Evaluation Standards for Mathematics. Fairness review by independent and representative panel, of all Mathematics Test items identified as functioning differently based on gender or ethnicity (African American/Caucasian, Hispanic/Caucasian). A conditional group difference of .15 or greater on the proportion correct scale was used as the criterion for review. Of the 589 Mathematics items analyzed, 40 were flagged for review. Items identified by reviewers as problematic were either revised to eliminate objectionable features of eliminated from the final test form. Correlation of ITBS Math scores with Math scores of two state (one Southeastern; one Midwestern) end-of- grade assessments.

Manual cites other published reliability studies:

Yes

Provide citations for additional published studies.

See Guide to Research and Development and Norms and Score Conversions Booklet.

Describe the degree to which the provided data support the validity of the tool.

Do you have validity data that are disaggregated by gender, race/ethnicity, or other subgroups (e.g., English language learners, students with disabilities)?

If yes, fill in data for each subgroup with disaggregated validity data.

Results from other forms of validity analysis not compatible with above table format:

Manual cites other published reliability studies:

Provide citations for additional published studies.

Bias Analysis

Have you conducted additional analyses related to the extent to which your tool is or is not biased against subgroups (e.g., race/ethnicity, gender, socioeconomic status, students with disabilities, English language learners)? Examples might include Differential Item Functioning (DIF) or invariance testing in multiple-group confirmatory factor models.

No

If yes,

a. Describe the method used to determine the presence or absence of bias:

b. Describe the subgroups for which bias analyses were conducted:

c. Describe the results of the bias analyses conducted, including data and interpretative statements. Include magnitude of effect (if available) if bias has been identified.