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Clinical and Special Education Woodcock-Johnson

Assessment Plan: A Guide to Evaluating for Dyscalculia

Dr. Geremy Grant
Written By Dr. Geremy Grant
On Nov 8, 2021
8 minute read

Assessment Considerations for Dyscalculia:

Using the WJ IV COG & ACH


According to the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5; APA, 2013), Dyscalculia is characterized by academic achievement that is substantially below age expectations in the areas of understanding number concepts, number facts or calculation; and/or mathematical reasoning (e.g., applying math concepts or solving math problems). Complications may be present during formative school years, although some deficits may not present until later in life when demands increase. These mathematical deficits must cause problems in the individual’s day-to-day functioning (e.g., school), and must not be due to any other condition (e.g., intellectual disability, lack of access to adequate instruction).

The WJ IV COG and ACH are powerful tools in the assessment of Dyscalculia¹, allowing the examiner to investigate various latent and applied abilities related to these aspects of mathematical achievement. Clusters and tests of interest from the respective instruments are listed below for your review.


Using the WJ IV COG for Dyscalculia

Administering the WJ IV COG allows an examiner to investigate underlying abilities which lend themselves to academic achievement.


Fluid and Quantitative Reasoning

Tests in the Fluid Reasoning cluster assess a host of cognitive functions (e.g., drawing inferences, identifying and forming concepts, and identifying relationships). Fluid Reasoning supports an individual’s ability to think flexibly (“cognitive flexibility”) and apply their knowledge across various domains. Quantitative Reasoning ² is assessed as an extension of Fluid Reasoning and is defined as the extent to which an individual can understand and reason using mathematical concepts. An examiner can obtain scores for these clusters by administering Number Series, Concept Formation, and Analysis-Synthesis.

      • Number Series assesses quantitative reasoning and inductive reasoning (i.e., drawing general conclusions from specific details). This test requires the examinee to determine the missing number in a sequence.
      • Concept Formation measures categorical and inductive reasoning, while incorporating an element of mental flexibility, as the examinee must remember what is learned while completing the task.
      • Analysis-Synthesis is a controlled-learning task, which tests deductive reasoning (i.e., the ability to form conclusions based on general principles)

¹ Please refer to Schrank et al. (2017) for more comprehensive details on how to use the WJ IV Core-Selective Evaluation Process to identify a SLD. For more detailed information regarding cluster and test descriptions, please consult the WJ IV COG and ACH examiner’s manuals (Mather & Wendling, 2014) and the WJ IV Interpretation and Instructional Interventions Program Manual (WIIIP; Schrank & Wendling, 2015). For more information regarding the intra-achievement variations, please refer to the WJ IV Technical Manual (McGrew et al., 2014).
² Analysis-Synthesis is needed to derive the extended Fluid Reasoning Cluster and the Quantitative Reasoning Cluster.


Number Facility

Number Facility can be defined as an individual’s speed and accuracy when working with numbers. It includes Numbers Reversed and Number-Pattern Matching.

      • Numbers Reversed measures an individual’s short-term working memory and attentional capacity. Examinees are asked to hold strings of digits in their immediate awareness and then manipulate those digits by reversing the sequence.
      • Number-Pattern Matching is a measure of processing speed, which assesses how quickly and accurately an examinee can visually discriminate to locate identical numbers amongst distractors.

Scholastic Aptitude Cluster for Mathematics

Examiners can also elect to administer tests that are evidence-based to predict mathematical achievement with respect to calculation and problem-solving. Examiners can then use Riverside Score to analyze Scholastic Aptitude/Achievement Comparisons. These comparisons can be useful in discerning whether an examinee’s tested academic performance level aligns or is inconsistent with, their performance on tasks of related cognitive abilities. The WJ IV COG tests for the Mathematics Aptitude Cluster are listed below:

      • Oral Vocabulary tests vocabulary knowledge via two subtasks. One subtask requires the examinee to provide a synonym for a target word, and the other requires antonyms.
      • Visualization is another two-part task assessing distinct aspects of visual processing including the ability to mentally manipulate stimuli.
      • Pair Cancellation is a measure of cognitive processing speed which provides information related to an examinee’s ability to sustain attention and maintain vigilance.
      • Number Series (discussed above under Fluid and Quantitative Reasoning)



Using the WJ IV ACH for Dyscalculia

Examiners using the WJ IV ACH can derive several mathematics clusters of interest in the evaluation of Dyscalculia. These include Mathematics, Broad Mathematics, Math Calculation Skills, and Math Problem Solving. The breakdown of these clusters is listed within the WJ-IV Selective Testing Table (Mather & Wendling, 2014, p. 14). There are also several tests of mathematical achievement on the WJ IV ACH, including Applied Problems, Calculation, Math Facts Fluency, and Number Matrices. These tests are listed below in relation to the DSM-5 criteria:


Understanding Number Concepts

      • Applied Problems assesses logical and quantitative reasoning. The examinee is required to determine appropriate mathematical operations and the values needed for those operations. The calculations increase in difficulty from relatively simple to complex.
      • Calculation assesses an examinee’s ability to execute mathematical computations. Items progress in difficulty from being asked to write individual numbers, to completing various mathematical operations (e.g., addition, subtraction, multiplication, division, geometry, trigonometry, etc.). Other math concepts are included in this task, as well (e.g., whole numbers, negative numbers, percentages, decimals, and fractions).

Number Facts

      • Math Facts Fluency measures an examinee’s accuracy and speed with addition, subtraction, and multiplication. Qualitative item analysis can help the examiner determine whether the examinee has more difficulty with one operation over another and can provide insight into an examinee’s approach to the task (e.g., working quickly and inaccurately, working slowly, yet accurately).
      • Calculation (described above)

Calculation and Mathematical Operations

      • Calculation (described above)

Math Reasoning and Problem Solving

      • Number Matrices tests quantitative reasoning, while also tapping an examinee’s fluid reasoning capacity. Examinees are shown number matrices and asked to identify the missing number.
      • Applied Problems (described above)


WJ IV ACH Tests by Dyscalculia DSM-5 Criteria


Intra-Achievement Variation Procedure

When reviewing an examinee’s performance, examiners can run an intra-achievement variation procedure using Riverside Score. This procedure compares an examinee’s performance in one achievement area to their expected performance³. Examiners with access to the WJ IV Interpretation and Instructional Interventions Program Manual (WIIIP; Schrank & Wendling, 2015) can also run comprehensive reports for an in-depth analysis of an examinee’s profile and generate personalized interventions and accommodations to support educational planning. There is a sample comprehensive report available with a WIIIP subscription.


With the selective testing model of the WJ IV and the robust scoring methods offered via Riverside Score and WIIIP, examiners can efficiently and effectively evaluate for Dyscalculia.


³ An examinee’s “expected” or predicted performance is based on their average performance on other achievement areas. Table 5-15 in the WJ-ACH Examiner’s Manual offers an outline of tests required for the intra-achievement procedure (Mather & Wendling, 2014, p. 102)

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American Psychiatric Association (2013). Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5). Washington, D.C.: American Psychiatric Association Publishing.

Mather, N., & Wendling, B.J. (2014). Examiner’s Manual. Woodcock-Johnson IV Tests of Achievement. Rolling Meadows, IL: Riverside Publishing.

Mather, N., & Wendling, B.J. (2014). Examiner’s Manual. Woodcock-Johnson IV Tests of Cognitive Abilities. Rolling Meadows, IL: Riverside Publishing.

McGrew, K. S., LaForte, E. M., & Schrank, F. A. (2014). Technical Manual. Woodcock-Johnson IV. Rolling Meadows, IL: Riverside Publishing

Schrank, F. A., Stephens-Pisecco, T. L., & Schultz, E. K. (2017). The WJ IV Core-Selective Evaluation Process Applied to Identification of a Specific Learning Disability (Woodcock-Johnson IV Assessment Service Bulletin No. 8). Itasca, IL: Riverside Assessments, LLC

Schrank, F. A., & Wendling, B. J. (2015). Manual and Checklists. WJ IV Interpretation and

Instructional Interventions Program. Rolling Meadows, IL: Riverside Publishing

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