The assessment of intelligence is usually only one component of the assessment process. Psychologists often administer a battery of tests to pinpoint the nature and extent of a child's learning problems.
Achievement Testing
Academic assessment is often an integral part of the comprehensive assessment. Children are often referred for assessment because they are experiencing academic problems. Recall that although IDEA 2004 does recognize thirteen categories of disabilities, special education assistance would only be warranted if the disability was found to interfere significantly with the child's learning. Therefore, assessment of achievement is vital to determining whether a child qualifies for special education assistance based on his or her current level of academic performance. Furthermore, the psychologist has access to a wide variety of norm-referenced instruments that measure achievement and provide a profile of the child's achievement in core areas (reading, math, and written expression) relative to peers of a similar age and grade level. These norms are based on administrations of the test to large samples of children from different geographical locations and social-economic backgrounds across the United States.
How Do Psychologists Measure Achievement?

Standardized Achievement Tests When the psychologist administered an intelligence test, he was able to determine that relative to similarly aged peers, Jason's ability level was roughly within the average range (upper Low Average). Jason's profile revealed weaknesses in abstract verbal reasoning, and his slow speed of copying could contribute to academic concerns; however, all things being equal, his learning ability does not explain why Jason is experiencing academic difficulties. The next likely step in the process would be to compare Jason's achievement scores with academic scores of other children of similar ages or grade level to determine where Jason's academic functioning levels are in three core areas of academic performance: reading, written expression, and mathematics. The psychologist would be interested in obtaining answers to the following questions:
- Given Jason's age, where should he be functioning academically?
- Given Jason's IQ, is he functioning at the predicted academic levels?
- Is Jason's academic performance consistent across the three major academic areas of reading, written expression, and mathematics?
In order to answer these questions, the psychologist administers a normreferenced achievement test, which allows him to compare Jason's academic performance with the academic skills expected of other children Jason's age, and additionally, to compare academic levels to levels expected, given his IQ level.
How Can the Psychologist Determine What Is "Normal'' Academic Functioning for Jason?
Remember that IQ scores were reported as standard scores with a mean (average) of 100 and a standard deviation of 15. There are a number of individual achievement tests available, such as the Wechsler Individual Achievement Test, Third Edition (WIAT-III), the Kaufman Test of Educational Achievement, Second Edition (KTEA-II), Diagnostic Achievement Battery, Third Edition (DAB-3), and the Woodcock-Johnson III Tests of Achievement, that report results of achievement as standard scores, allowing for a direct comparison between expectations (IQ scores) and academic performance.
Jason's scores on the WJ III Achievement Test are presented in Table 8.1; they indicate that both reading and written expression are in the extremely low range based on age expectations.
Comparison of Academic Scores Based on Age Expectations (Age Norms) When Jason's academic responses on the WJ III Achievement Test are compared with the expected responses based on norms available for eight-year-old boys, Jason performs well below the expected levels for reading and written expression. In fact, Jason's responses are more typical of an average child between 6 years, 1 month of age (written expression) and 6 years, 4 months of age (reading).
In considering grade equivalents, although the majority of the class has passed the midway point of the first-grade program, Jason is at a late-kindergarten (written expression) to beginning first-grade (reading) level in language arts. However, because Jason is already one year behind his classmates (remember, he repeated kindergarten), these lags are even more pronounced than they appear on the surface. In reporting test scores, it is more important to base comparisons on age rather than grade-based comparisons for this and other reasons that are beyond the scope of this book.

Comparison of Achievement Scores Based on Intellectual Expectations Remember that IQ scores are presented as standard scores with a mean of 100 and standard deviation of 15. A child's standard score for achievement should be within one standard deviation (15 points) of his IQ score.

A comparison of Jason's achievement scores and IQ scores is presented in Table 8.2. When we compare Jason's standard scores for reading (65) and written expression (63) to his expected level of performance suggested by his IQ (87), we find that Jason is well in excess (22- to 24-point differences) of this 15-point discrepancy in both areas. However, when we compare his mathematics score (89) to his predicted level (87), we find that the difference between these two scores is very small. Jason is just about where we would predict he would be in math. The relationship between standard scores obtained for academic performance relative to Jason's Full Scale IQ score is shown in Figure 8.1.


Is the Discrepancy Formula Used by All Districts, and Is It Universal?
Comparing standard score differences between ability and achievement scores is referred to as a discrepancy model or using a discrepancy criterion. This model has met with great controversy. Some people feel that this method penalizes children at the lower extreme. For example, if a child has an IQ of 85, he would need to score below 70 to demonstrate a significant discrepancy between ability and achievement. However, if a child has an IQ of 115, he could obtain a standard score of 100 academically, which is in the average range, and still be considered to have a significant discrepancy between ability and achievement.
Some districts consider a 15-point discrepancy between ability and achievement significant for younger children (under eleven years of age), but then require a 22-point difference (one and a half standard deviations) for children above eleven years of age. Other school districts may require as much as a two standard deviation difference, which would mean a 30-point difference between achievement and IQ. The rationale is that it is more difficult to have a large gap between achievement and ability at younger age levels. Despite the inherent flaws in the discrepancy model noted previously, many districts will continue to use this model, while others may follow a response-to-intervention (RTI) approach, as allowed by IDEA 2004. The RTI model was discussed at length in Chapter Four but, to review, the three-tiered model includes the following phases:
- Determining whether effective instruction is in place for groups of students
- Providing effective instruction to target students and measuring its effect on their performance
- Referring students for an assessment whose response-to-intervention warrants additional interventions

What Are the Academic Skills That Achievement Tests Measure?
As outlined in the previous example, most standardized achievement tests provide a composite score for reading based on a number of subtests, which may include tasks of single-word decoding, reading fluency, and comprehension. A composite mathematics score would likely involve tasks of calculation, fluency, and problem solving. Written expression is often measured through spelling tests and tasks designed to measure sentence and paragraph construction. It is important that whatever instrument is used to measure these core academic areas, that measures include more than just decoding, spelling, and math calculation skills, but also include assessment of a child's reading comprehension, math problem solving, and written expression (beyond spelling).
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