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Abstract
We reviewed 13 studies that focused on analyzing student errors on achievement tests from the Kaufman Test of Educational Achievement–Third edition (KTEA-3). The intent was to determine what instructional implications could be derived from in-depth error analysis. As we reviewed these studies, several themes emerged. We explain how a careful analysis of errors is key to planning the most appropriate instructional interventions.
“Reading errors are of many types. Two children, reading the same paragraph, may make the same number of errors, receive the same reading grade, and yet their mistakes may be wholly different in nature. Their reading performances may be quantitatively the same but qualitatively unlike.”
—(Monroe, 1932, p. 34)Over eight decades ago, Monroe (1932) discussed the value of error analysis for understanding a reader’s particular difficulties. To facilitate an analysis of reading errors, she created a profile of errors to guide intervention. She found that when struggling readers were compared with a control group, they made more of the following error types: vowels, reversals, omission of sounds, repetitions, consonants, and addition of sounds. Thus, as Monroe observed, to provide targeted interventions to students, instruction must be directed to eliminating a reader’s particular types of errors. For example, to help a student who is confused by certain vowel sounds, the teacher would identify the specific sounds and then provide additional practice with these sounds in both word lists and stories. She would dictate words with these sounds for the student to spell. Similarly, within mathematics, a student who is confused by place value when subtracting or does not understand how to find a common denominator when adding fractions will need specific instruction that focuses upon increasing understanding of those basic mathematical concepts.
This special issue of the Journal of Psychoeducational Assessment is focused on analyzing student errors in reading, writing, and math on the Kaufman Test of Educational Achievement–Third edition (KTEA-3; Kaufman & Kaufman, 2014). A careful error analysis goes beyond the quantitative results, and focuses upon the qualitative information that may be derived from reviewing an individual’s performance on the specific items of the various subtests. The purposes of error analysis are to (a) identify the types of errors that a student makes within an academic domain, (b) determine if there is a pattern among the errors within and across domains, (c) attempt to determine the reasons why the student is making the errors, and (d) design specific instruction to address and resolve any confusions and eliminate the errors. As noted by O’Brien and colleagues (2017), the overarching goals of error analysis are both evaluation and intervention. As we reviewed these 13 studies, several themes emerged regarding the findings and the implications of KTEA-3 error analysis for developing targeted interventions.
Errors Across and Within Domains
In conducting error analysis, it is important to consider the similarities of the underlying constructs both across and within domains. For example, listening comprehension and reading comprehension tend to involve similar abilities, as do word reading and spelling. Koriakin and Kaufman (2017) found that the Reading Comprehension Difficulties group (RCD) also had specific weaknesses in listening comprehension. This finding is to be expected as language comprehension is the basis for reading comprehension. Spencer, Quinn, and Wagner (2014) explained, “Individuals with problems in reading comprehension that are not attributable to poor word recognition have comprehension problems that are general to language comprehension rather than specific to reading” (p. 3). In other words, students with poor reading comprehension have a language-based problem (Oakhill & Cain, 2016). Because these students have language-related weaknesses, Koriakin and Kaufman remind evaluators of the importance of including a measure of language comprehension as a part of a reading evaluation.
When the difficulty stems from general language comprehension, intervention would be directed to improving oral language comprehension. For example, to improve listening comprehension, understanding the meaning of what is being said, students would be taught how to paraphrase and summarize the main ideas in a passage (Podhajski, 2016). In addition, students would be taught specific strategies to enhance reading comprehension. For example, through explicit instruction, students would learn how to ask questions that would help them monitor their own comprehension while reading. This might begin with simply asking themselves if what they read made sense. If not, they would employ repair strategies such as rereading the passage, or discussing the passage with a peer. They may learn and practice how to use a set of specific strategies, such as those found in Collaborative Strategic Reading (Klingner, Vaughn, Boardman, & Swanson, 2012). Students may also be taught specific vocabulary words, learn about various types of text structures (e.g., expository vs. narrative), and practice using graphic organizers to summarize the information in text.
An interesting finding of this study was that the Reading Fluency Difficulties (RFD) group was weaker in spelling and oral expression than the RCD group. The authors suggest that these findings demonstrate difficulty with the efficiency of output for the RFD group. In typical developing readers, fluency is a bridge between word analysis and comprehension (Pikulski & Chard, 2005). However, Koriakin and Kaufman state that struggling readers may not follow the typical developmental course which begins with acquiring phonological skills, followed by phonics, fluency, and ends with comprehension (Ehri, 2005). The RFD group is likely still experiencing some difficulty with automatic phonic skills and mastery of phoneme–grapheme connections that is reflected in their slow reading speed, as well as their spelling difficulties. When a reader has weaknesses in reading rate and fluency, evaluators should use error analysis to reveal specific difficulties within word reading and spelling. Interventions for these individuals would focus on solidifying phonics knowledge, increasing knowledge of spelling patterns, and then increasing automaticity to facilitate the rapid recognition of words.
In addition, within specific domains, relationships exist among the subdomains (e.g., phonic concepts, mathematical calculations). O’Brien and colleagues (2017) found that phonics concepts (e.g., consonant digraph, short and long vowels, single and double consonants) loaded on the same factor for both the Nonsense Word Decoding (NWD) and Spelling (SP) subtests. From these findings, they infer that a high number of errors on the NWD subtest would be predictive of a high number of errors on the SP subtest. Although the number of errors and error categories were similar across NWD and SP, the composition of error factors differed due to differences in task demands and stimuli. A weakness in a particular skill area may result in different error patterns across domains. Thus, when considering errors, an evaluator should attempt to determine whether the pattern extends into other related errors. For example, on an item similar to the ones on the NWD subtest, a student may have trouble pronouncing medial vowel sounds, such as pronouncing the nonsense word “bip” as “bep.” This same difficulty may also be noted when he attempts to spell real words, such as spelling “pet” as “pit.” In addition, the evaluator may observe that the student also confuses the consonant digraphs, /ch/ and /sh/, both when reading and spelling. His difficulties with sound (phoneme)–letter (grapheme) mapping are consistent across both word reading and spelling.
Decoding and encoding share several linguistic skills including phonological awareness, orthographic awareness, and morphological awareness. Evaluating the individual’s performance in these three areas by analyzing the types of errors helps inform instruction. Decoding requires converting graphemes into phonemes and then blending them into a word. Encoding requires segmenting a word into phonemes and then converting them into graphemes to spell a word. Because of the connection between decoding and encoding, intervention is most effective when both areas are addressed in the instructional plan. Instruction would then weave back and forth between practice reading and spelling words so that the student has the opportunity to master specific phoneme–grapheme patterns.
Similarly, O’Brien and colleagues (2017) noted the shared communality among mathematical computations. A student who lacks an understanding of regrouping will likely make similar errors on both addition and subtraction problems. Interventions must then address difficulties across and within domains. A student would practice regrouping in a variety of addition and subtraction problems. Direct, explicit instruction in math is an effective, evidence-based approach for improving math skills (Kroesbergen & Van Luit, 2003). Conceptual understanding is developed when the teacher models the required task using a think aloud approach and then the student verbally rehearses the modeling.
Hatcher and colleagues (2017), however, remind us of the independence of the four language systems (listening, speaking, reading, and writing). They note listening comprehension differs from reading comprehension in that more demands are placed on attention and memory. They explain that errors in one language system will not necessarily correspond to errors in another system but caution that these findings may differ in clinical populations. Because each of these systems has distinct characteristics, instruction needs to address the areas of weakness to enhance overall language abilities. For example, for a student with dyslexia, the primary problem is with written language, not spoken language (Pennington, Peterson, & McGrath, 2009). Instruction would focus upon improving the student’s basic skills in reading and spelling as two language systems, reading and writing, are involved. Coupling phonemic awareness instruction with letters (graphemes) is most effective for developing phonics skills (National Reading Panel, 2000). Conversely, if a student was struggling with one of the oral language systems, listening or speaking, intervention would include vocabulary building activities and specific instruction in grammar, or if listening skills were the primary problem, instruction may focus on paraphrasing and verbal rehearsal.
Developmental Levels
Another important theme that emerged is the importance of considering developmental levels. When analyzing errors, an evaluator needs to determine the difficulty level of the task, and where the errors fit into a developmental sequence. Choi and colleagues (2017) pinpoint the importance of assessing both easy and difficult phonological processing skills. They identify two error factors: basic phonological processing (rhyming, blending, and phoneme matching) and advanced phonological processing (deleting and segmenting). Although it seems logical that individuals would perform better on the easier tasks, this was not true in all cases. Some individuals performed better on the easier tasks, whereas others did better on the more difficult tasks.
Deletion and segmentation, the more difficult tasks, were better predictors of reading, writing, and oral language skills across all ages than the basic tasks. These findings suggest that when a student has difficulty with phonological tasks, an evaluator should administer different types of tasks and then attempt to determine exactly what a student can and cannot do. The student may be able to rhyme words and blend phonemes, but have trouble segmenting phonemes.
Developmental differences may also exist within each type of phonological task. For example, a student may be able to segment compound words and syllables, but not be able to segment phonemes. Or, a student may be able to recognize rhymes, but not produce rhymes. Intervention would then begin where the student first has difficulty within the developmental sequence. As a general principle when teaching phonological awareness, students need to move from easier tasks, such as rhyming, to more complex tasks, such as blending, segmenting, and manipulating phonemes (Anthony & Francis, 2005; Chard & Dickson, 1999).
The two most important phonological processing skills are blending and segmenting (Ehri, 2006). Instruction in blending and segmenting results in more improvement in reading than programs that focus on mastery of multiple skills (National Reading Panel, 2000). Although phonological processing is generally thought to be a good predictor of reading at younger ages, Choi et al. found that it was predictive of reading for older students as well. Therefore, evaluators should consider the need for evaluation of phonological processing skills and appropriate interventions when older students are struggling with reading.
Similarly, through error analysis, an evaluator may determine that a student is able to read one-syllable words, but has difficulty pronouncing multisyllabic words. The instruction would then be geared to helping the student with structural analysis, or how to break words into meaningful parts. The student would learn about roots and base words and how to add affixes (prefixes and suffixes). In addition, instruction in morphology, the meaning units of language, as well as teaching the six syllable types could help improve a student’s ability to read and spell multisyllabic words.
Within reading comprehension, a student may be able to respond to literal questions, but have difficulty with ones involving inferential comprehension. Intervention efforts would then be directed to instruction in strategies that improve ability to make inferences and draw conclusions. This may include teaching students how to visualize while reading, a proven way to improve comprehension. Students often require explicit instruction in how to make a movie in their minds or use mental imagery while reading. It may begin with the teacher asking specific questions about how something looks, tastes, smells, feels, or sounds. The teacher may need to model visualization of a passage using a think aloud method, followed by guided practice. Through error analysis of various types of comprehension questions, an evaluator can determine a student’s development and design the most effective instructional program.
Lower-Level Versus Higher-Level Academic Skills
A further consideration when performing error analysis is comparing how a student does on lower-level academic skills (word reading, spelling, and math calculation) versus how a student performs on higher-level abilities (reading comprehension, written expression, and math problem solving). Lower-level academic skills are more related to attention, perception, and memorization, whereas the higher-level academic abilities are more related to reasoning and language. Individuals with specific learning disabilities often have difficulty with lower-level skills because they have weaknesses in one or more of the less complex, or lower g, cognitive abilities, such as phonological processing or perceptual speed. Conversely, individuals with limited language or intelligence may do well on lower-level tasks but struggle on higher-level skills that require more language and reasoning.
Root and colleagues (2017) found that students in the mild intellectual disability (ID) group scored lower than the low achievement with average intelligence control group on most error factors except the Letter-Word Recognition–Consonant Pattern Knowledge factor and the Math Computation–Basic Math Concepts factor. They explain that these skills rely more on rote memorization, rather than on more complex reasoning. However, the Mild ID group performed similarly to the two control groups on some error categories in the higher-level abilities, such as Math Concepts and Applications–Geometric Concepts. It is suggested this may be due to the importance of visual–spatial skills on the geometry tasks, a relative strength area for the Mild ID group. In regard to intervention, they note that students with mild intellectual disabilities can benefit from the same intensive evidence-based interventions in reading and math that other students receive and should not be limited to sight- or survival-word instruction or basic math computation skills.
Ottone-Cross and colleagues (2017) compared the error patterns of three groups: academically gifted students, gifted students with learning disabilities, and students with learning disabilities. As one would expect, the sample of gifted students with learning disabilities’ scores across subtests fell between the two control groups. The gifted students with learning disabilities scored similarly to the gifted group on many of the higher-level thinking tasks. They scored similarly to the students with learning disabilities on the lower-level skills of decoding, reading nonsense words with silent letters, and computing addition facts.
The authors refer to the term “masking” which they describe as “when a gift compensates for a disability, or a disability lessens the impact of a gift.” Some people claim that these academically successful students with learning disabilities should not receive accommodations as they may fall within the average range on a battery of tests; however, a thorough clinical history is needed to explore the manner, condition, and duration of the learning experiences, including how the person learns and studies (Russell, 2004). These twice exceptional students often have adequate achievement until the demands become too great. Ottone-Cross et al. cite the following relevant quote from the Diagnostic and Statistical Manual of Mental Disorders (5th ed.; DSM-5; American Psychiatric Association, 2013):
These individuals may be able to sustain apparently adequate academic functioning by using compensatory strategies, extraordinarily high effort, or support, until the learning demands or assessment procedures (e.g., timed tests) pose barriers to their demonstrating their learning or accomplishing required task. (p. 69)
When evaluating gifted students with learning disabilities, although their achievement levels may fall within the average range, they often have strengths in higher-order abilities, including oral language and reasoning that mask their weaknesses in lower-order abilities. Thus, these students often require specific accommodations, such as extended time, to allow them to demonstrate the breadth and depth of their knowledge.
Diagnostic Category Does Not Determine Educational Needs
Avitia, DeBiase, and colleagues (2017) explored the differences in error patterns between students with reading versus math disorders. An interesting finding was that there were more similarities between the two groups than there were differences. In fact, out of the 22 error factor scores, only four were found to differ significantly between the samples. As expected, phonological processing was significantly lower for the reading group (SLD-R/W) and basic math concepts was significantly lower for the math group (SLD-M). Letter-sound knowledge and sound-to-letter mapping were significantly different for both clinical groups and the control group. The SLD-R/W group scored the lowest but the SLD-M group was also significantly below the control group. Both clinical groups were significantly below the control group in complex math problems. These findings suggest that students who have been identified with reading disorders may also require support in certain areas of math, whereas students with math disorders may also require specific reading interventions. For example, explicit instruction in phonics and use of the concrete-representational-abstract teaching sequence in math may benefit both clinical groups. Math and reading problems frequently coexist and, in fact, 15% of the SLD-R group also had SLD-M. This may explain some of the similarities found in this study. Although mathematics has received less attention than reading, some researchers have indicated that individuals with coexisting reading and math difficulties have a phonological deficit (e.g., Geary, 2007). Support for this is indicated by the limited performance of both clinical groups on letter-sound knowledge and sound-to-letter mapping noted previously.
Avitia, Pagirsky, and colleagues (2017) examined the errors of two clinical groups: those with specific learning disabilities in reading and writing (LDRW) and those with a language impairment (LI). As would be expected, both clinical groups made more errors than the matched controls across several error categories. The LDRW group had more errors in reading than the LI group, but the LI group also had more errors on consonant digraphs and blends than controls. Although one would expect that the LDRW group would have higher scores in listening comprehension and oral expression than the LI group, this was not the case. In addition, the LDRW group had more errors than the control group on the error factors of Math Calculations and Miscellaneous Math Concepts.
The results from these studies illustrate the importance of planning instruction to address the specific instructional needs of a student and the types of errors a student makes rather than focusing instruction solely on a diagnostic category. Students identified with learning disabilities in reading and writing may also need assistance with oral language development and mathematics. Students identified with LI may require specific instruction in sound–letter (phoneme–grapheme) relationships.
Performance on Cognitive and Linguistic Processes Also Informs Intervention
Several of the studies in this special issue addressed how different patterns of cognitive strengths and weaknesses affected the kinds of errors students made on tests of achievement. Some cognitive abilities are stronger predictors of certain academic areas than others. For example, in examining the normative data from the Woodcock-Johnson IV (Schrank, McGrew, & Mather, 2014), Cormier, Bulut, McGrew, and Frison (2016) found that the broad Cattell-Horn-Carroll abilities of comprehension-knowledge, processing speed, and fluid reasoning were especially important predictors of basic writing skills and written expression during the school age years. Within the components of reading during the school years, fluid reasoning, comprehension-knowledge, short-term working memory, and auditory processing were the strongest predictors of basic reading skills; processing speed was the strongest predictor of reading rate and fluency; and fluid reasoning and comprehension-knowledge were the strongest predictors of reading comprehension (Cormier, McGrew, Bulut, & Funamoto, 2016). Thus, consideration of cognitive profiles is important not only for eligibility determinations, but also for instructional planning.
Within clinical groups, cognitive profiles, as well as the types of errors, can help inform the selection of interventions. Pagirsky and colleagues (2017) examined the difference on error factors for students diagnosed with attention deficit hyperactivity disorder (ADHD) and those with ADHD and reading difficulties. No differences existed on error factors between the ADHD and the control group, whereas the students with ADHD and reading difficulties demonstrated a greater amount of errors on factors that required phonemic awareness, language skills, and inhibition. A combination of phonemic awareness, language skill, and processing speed accounted for approximately 80% of the variance in accuracy and speed of single word reading. The type of intervention would differ for a student with poor phonemic awareness versus a student with slow processing speed. In the first case, the intervention would focus upon intervention in specific phonemic awareness skills, such as explicit instruction in phoneme–grapheme relationships. In the second case, instruction would likely focus on methods designed to build reading speed, for example, using a method like repeated readings with corrective feedback
Koriakin, White, and colleagues (2017) found that particular patterns of cognitive strengths and weaknesses differentially predicted performance on math tests. Students with high crystallized ability (Gc) but low cognitive processing speed (Gs) and long-term retrieval (Glr) were stronger in basic skills and complex math problem solving than students with low Gc, but high Gs and Glr. They suggest that one reason for the stronger performance by the high Gc group is that higher-level reasoning abilities are required for math problem solving which is affected by intelligence, represented by Gc in this study.
Koriakin et al. found that the low Gc-high Glr/Gs group did not differ significantly from the high Gc-low Glr/Gs group in the area of simple addition problems. This may be due to the nature of basic math facts, which requires associative memory, a Glr ability. In addition, Gs has been found to be more related to math computation than math problem solving (e.g., Floyd, Evans, & McGrew, 2003). A possible extension of this study would be to explore the mathematical performance of individuals with high fluid reasoning (Gf) abilities compared with a low Gf group.
For the low Gc-high Glr/Gs group, interventions would focus more on increasing language comprehension and vocabulary, and learning to employ strategies for math problem solving. Schema-based strategy instruction would be an effective approach for teaching procedural and conceptual understanding related to math word problem solving (Fuchs & Fuchs, 2007; Xin & Jitendra, 2006). Although the high Gc-low Glr/Gs group did not demonstrate specific problems in the areas of math assessed, there may be a need to address their relatively weaker performance in Glr and Gs, especially in the fluency area. Examples of interventions for building math fluency would be using computer-assisted instruction, speed drills, and graphing of student progress.
In addition to exploring a cognitive profile, Stewart et al. (2017) remind us to consider gender differences when evaluating an individual’s math abilities. They found that the stereotype of males being better in math than females was the prevailing reason for differences in performance rather than a lack of skill or ability. There were no significant differences in male/female performance on four of the five error groups evaluated. For females, math instruction should address and attempt to eliminate the impact of the existing stereotype which, as noted in this study, results in improved performance.
Liu and colleagues (2017) also found that Gc was an important broad ability for basic reading skills, reading comprehension, and written expression. In almost every case, the high Gc group outperformed all other groups in the study on the phonological processing, word reading, and decoding error factors. One exception was the Letter-Word Reading (LWR) Intermediate Letter-Sound Knowledge error factor where the high Gs/Glr group’s performance was not significantly different from the high Gc group. Mastery of phoneme–grapheme relationships requires associative memory which is a Glr ability so this result is not surprising. The high Gc group also outperformed all groups on the reading comprehension and written expression error factors, reinforcing the importance of crystallized intelligence for these achievement areas.
Liu et al. also found that students who had weaknesses in both phonological and orthographic processing had poor error scores on writing mechanics and written expression skills, but these weaknesses had less of an impact on errors in reading comprehension. Writing tasks require complete recall of the connection between sounds and letters and correct sequencing whereas reading is a recognition task. This may explain why the group with weaknesses in both phonological and orthographic processing had more difficulty with writing tasks than with reading tasks. Intervention would include explicit phonics instruction to increase proficiency with phoneme–grapheme relationships. In addition, intervention may be enhanced by teaching high frequency words, using multisensory spelling methods, and making use of technology.
When integrating the results from the KTEA-3 with other instruments, Breaux and colleagues found that the high Gc group outperformed the low Gc group in Oral Expression and Written Expression. In contrast to the results of the Koriakin et al. study, the high Gc group did not, however, differ from the other groups on math error factors. The authors suggest that this difference may have resulted from the use of different measures of broad abilities to identify the cognitive profiles (Wechsler Intelligence Scale for Children-Fifth Edition, Differential Abilities Scale-Second Edition, or Kaufman Assessment Battery for Children-Second Edition), whereas in the Koriakin study, all measures were selected from the KTEA-3.
As noted by several studies in this issue, crystallized intelligence (Gc) is an important cognitive ability for academic achievement. It is sometimes referred to as a domain general ability because it impacts performance across the domains of reading, writing, and math. Additionally, oral language abilities, such as vocabulary, listening comprehension, language development, are all Gc abilities. Crystallized intelligence develops through multiple sources including the four language systems (listening, speaking, reading, and writing) and continues to develop across the life span (Perfetti, Landi, & Oakhill, 2007). Thus, strong crystallized ability facilitates performance in most academic areas, and conceivably students with this protective factor will respond more quickly to interventions.
When an individual has limits in vocabulary and knowledge, an instructional program must address these areas. Interventions would focus on building the individual’s store of acquired knowledge by increasing lexical knowledge, developing oral language skills, and building procedural and declarative knowledge. Examples of interventions would include engaging the individual with language through read aloud methods, providing explicit vocabulary instruction, and employing strategies to increase and organize knowledge prior to reading and writing tasks.
Assessment Needs to Lead to Differentiated Instruction
The overarching theme of these articles is that assessment needs to lead to the selection and implementation of targeted interventions, and that in-depth error analysis provides valuable information for planning instruction. Too often an assessment focuses only on standard scores and eligibility determinations. A standard score only indicates an individual’s relative standing within a normative distribution of age or grade mates. It does not indicate the specific skills that are mastered or those that require intervention.
We are reminded by several studies in this issue that when two individuals have the identical number of errors in a category, how the total was obtained can be very different. One person may have gotten all the easier items correct followed by errors on the more difficult items. Another person may have errors across all levels of item difficulty. Although the same number of errors may result in the same standard score, the instructional implications are quite different for these two individuals. Assessment must lead to planning a program that meets each individual’s needs and analyzing the errors is the only way to accomplish this important goal of responsive teaching.
Responsive teaching simply refers to differentiated, prescriptive instruction. Because all students are not alike, a teacher plans varied approaches to address what individual students need to learn, how they will learn it, and how they will demonstrate what they have learned; this type of teaching increases the likelihood that each student will learn as much as possible (Tomlinson, 2006). With the growing diversity within populations and the increased demand for accountability in education, the need to accommodate individual learners in general education has intensified.
Over three decades ago, Cruickshank (1977) reminded us that “diagnosis must take second place to instruction, and must be made a tool of instruction, not an end in itself.” Assessments must lead to instruction. Cruickshank further explained that “a variety of programs must be available for children who have a variety of needs” (p. 194). The results of an assessment can help us design specific, differentiated instruction to address the referral concerns. As noted in the introduction of this special issue, the articles in this special issue “stem from a core belief that the kinds of academic errors a student makes are directly relevant to determining the most effective intervention approach for that student” (Breaux, Bray, Root, & Kaufman, 2017, pp. 4-6). We wholeheartedly agree. It is our belief that error analysis is key to understanding the achievement skills of the individual being evaluated and is at the heart of planning the most appropriate instructional program.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.
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