MATH
PENS: Preschool Early Numeracy Screener David J. Purpura AGES: 3-0 through 5-11 TESTING TIME: 5 minutes or less, depending on child’s age and ability ADMINISTRATION: Individual
TECHNICAL AND STATISTICAL CHARACTERISTICS OF THE PENS The PENS was normed on a weighted sample of 1,122 children from 27 states and 243 zip codes. Its raw scores can be converted to percentile ranks and index scores. The Examiner’s Manual includes a comprehensive discussion of the test’s theoretical and research-based foundation, item development, standardization, administration and scoring procedures, norms tables, and guidelines for using and interpreting the test’s results. The PENS internal consistency reliability coefficient is .89, and the test–retest reliability coefficient is .87. Extensive studies of the floors, ceilings, and item gradients for the PENS index scores are included. The results indicate that the test has very good floors, even for assessing the functioning of children of low numeracy ability across the entire age range of the test. Diagnostic accuracy studies demonstrate the test’s ability to differentiate children who have exceptionalities that might negatively affect numeracy skills from those who do not. Specifically, a PENS Early Numeracy Index cutoff score of 91 resulted in a sensitivity of .85, a specificity of .75, and a receiver operating characteristic/area under the curve (ROC/AUC) of .86 in differentiating children with a developmental delay or intellectual disability diagnosis from children with no diagnosis. COMPLETE PENS KIT INCLUDES: Examiner’s Manual, Picture Book, and 25 Examiner Record Forms, all in a sturdy storage box. (©2021) #14630 PENS Complete Kit $190.00 #14631 PENS Examiner’s Manual . . . . . . . . . . . . . . ............... 42.00 #14631E PENS Virtual Examiner’s Manual . . . . . . . . . . . ............. 39.00 #14632E PENS Virtual Picture Book . . . . . . . . . . . . . ............... 102.00 #14633 PENS Examiner Record Forms (25) . . . . . . . . . . ............ 40.00 addition and subtraction. Items become progressively more difficult in size and type of numerical representation from grade to grade (i.e., from Pre-K to Kindergarten to Grade 1). TECHNICAL AND STATISTICAL CHARACTERISTICS OF THE SENS The SENS was validated on a weighted sample of 1,150 children from diverse socio- economic and linguistic backgrounds. Scoring the SENS is straightforward: Each item is scored as correct/incorrect and then a Total Raw Score is computed based on the total number of correct items. This Total Raw Score can be used to determine a student’s risk status for mathematical learning difficulties by referring to the Risk Status table for each grade level in Appendix A of the SENS Manual. The cut scores on the Risk Status tables help to identify students who need targeted instructional support or further diagnostic evaluation. The SENS Manual also includes a comprehensive discussion of the test’s the- oretical and research-based foundation, item development, standardization, administra- tion and scoring procedures, and guidelines for using and interpreting the test’s results. The SENS internal consistency and test–retest reliability coefficients at each grade level are > 0.9. Predictive validity is high across grade levels (> 0.79). Diagnostic accuracy studies demonstrated the test’s ability to differentiate children who have exceptionalities that might negatively impact numeracy skills from those who do not. Specifically, receiver operating characteristic (ROC) curve analyses revealed that the SENS is highly accurate in discriminating between children at risk and not at risk for showing math learning difficulties one year later. EACH GRADE LEVEL SENS KIT CONTAINS: Examiner’s Manual, Picture Book, 25 Examiner Record Forms, and Manipulatives Card, all in a sturdy storage box. (©2024) #40032 SENS Pre-Kindergarten Complete Kit $139.00 #40042 SENS Kindergarten Complete Kit $139.00 #40052 SENS First Grade Complete Kit $139.00
The Preschool Early Numeracy Screener (PENS) is a 25-item, standardized, norm-referenced screening test that measures the numeracy skills of children ages 3 through 5. The screener format allows teachers and research- ers to quickly identify children who need fur- ther evaluation and instruction and to reliably measure their progress during the year. FEATURES
• The PENS items broadly assess many of the key domains identified by the National Council of Teachers of Mathematics and the National Mathematics Advisory Panel as being critical precursors of mathematics mastery. • Test items cover counting, numerical relations, arithmetic operations, and numeral knowledge and were designed to measure the breadth and depth of each numeracy component (e.g., one-to-one counting, cardinal-number knowledge, numeral and set comparison, story problems, formal addition). • The PENS items are arranged in a progression according to developmental attain- ment of specific numeracy skills.
SENS: Screener for Early Number Sense Nancy C. Jordan • Alice Klein • Chun-Wei Huang AGES: 4-0 through 6-11 TESTING TIME: 20 minutes or less, depending on the child’s age and ability ADMINISTRATION: Individual The Screener for Early Number Sense (SENS) is an individually administered, criterion-referenced early screening tool available in three grade-level kits that (a) identify young students at risk for mathematical difficul- ties/disabilities and (b) provide information about identi- fied students that can lead to effective early interven- tion. The SENS spans the early childhood period from pre-K to first grade (4 to 7 years of age) when crucial math foundations are built and consolidated. FEATURES The SENS is grounded in a conceptual framework that reflects state-of-the-art research on number sense
development, including work by two of the SENS authors, Nancy C. Jordan and Alice Klein. The SENS framework is based on three evidence-informed assumptions: 1. Number sense encompasses subdomains of number, number relations, and number operations; 2. Number sense difficulties predict later math achievement and can be identified early; and 3. Number sense is malleable and can be taught to most children. Test items cover knowledge of number (e.g., counting, cardinality, place value), relationships between numbers (e.g., number comparison, number line), and number operations involving
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32 | 2025–2026 ASSESSMENTS
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