PENS: Preschool Early Numeracy Screener

David J. Purpura
SKU: 14630
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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


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 researchers to quickly identify children who need further evaluation and instruction and to reliably measure their progress during the year.


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 attainment of specific numeracy skills.

Technical and Statistical Characteristics of the PENS

The PENS was normed on a weighted sample of 1,122 children from 27 states and 243 different 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 impact 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)