![[PDF]](/pb-assets/Icons/adobe-pdf-icon-1498649896243.png){kind=icon}
Abstract
The purpose of this study was to understand and compare the types of errors students with a specific learning disability in reading and/or writing (SLD-R/W) and those with a specific learning disability in math (SLD-M) made in the areas of reading, writing, language, and mathematics. Clinical samples were selected from the norming population of the Kaufman Test of Educational Achievement–Third Edition (KTEA-3) as well as matched controls. Although the authors expected to find overall differences between the groups in their area of difficulties, the study revealed that the two clinical samples were more similar than different. In particular, the SLD-M clinical group performed lower on some errors that were not related to their area of disability compared with the SLD-R/W group. Implications of the study show the importance of error analysis especially when creating goals for individual education plans. Although a student may have an SLD-R/W, he or she may still need support in certain mathematic areas, and vice versa.
According to the Individuals With Disabilities Education Improvement Act (IDEIA, 2004), a specific learning disability (SLD) is a difficulty in one or more areas of academic achievement due to a disorder in one or more of the basic psychological processes. Furthermore, the student’s observed area of difficulty must not be due to the presence of a visual, hearing, or motor disability; an intellectual impairment; an emotional disturbance; cultural factors; environmental or economic disadvantage; or limited English proficiency.
Students with learning disabilities represent 35% of all children receiving special education services under IDEIA (National Center for Education Statistics, 2015). Therefore, it is of critical importance to continue to gather and innovatively analyze data to identify effective interventions on student learning by better understanding the academic needs of students with SLDs. For the purposes of this study, we used a factor analysis–based method of error analysis to identify differences between the errors made by students identified with SLDs in reading (SLD-R) and SLDs in math (SLD-M). We also discuss implications for how this information may better support these students by helping to inform instructional decisions.
SLD-R and SLD-M
SLD-R may be characterized by difficulties with basic reading skills, reading fluency, or reading comprehension. The most common characteristics of an SLD-R in young children are difficulty rhyming words and difficulty learning letter names and sounds of the alphabet, whereas secondary students and adults typically exhibit slowed reading or poor spelling (Mather & Wendling, 2012). In addition, deficits in phonological awareness are considered to be among the most predominant cognitive correlates of an SLD-R (Fletcher, Lyon, Fuchs, & Barnes, 2007). Rapid automatic naming is another cognitive ability associated with poor reading performance, particularly reading accuracy, speed, and comprehension (Wolf, 2007). Finally, individuals with an SLD-R often have stronger oral language and listening comprehension abilities than reading and spelling skills (Mather & Wendling, 2012).
Commonalities also exist with students identified with an SLD-M. For example, children with SLD-M are a heterogeneous group that can be characterized by one or more of the following cognitive/academic profiles: (a) deficits in semantic memory, weak fact retrieval, and high error rates in recall; (b) procedural deficits in numerical calculations and sequencing multiple steps in complex procedures; and (c) dysfunctions in visual-spatial abilities with difficulty representing numerical information spatially (Geary, 2004). This profile may also have poor monitoring of the sequence of steps of formulas (Geary, Hoard, Byrd-Craven, & DeSoto, 2004). Notably, all profiles exhibit weaknesses in long-term memory and retrieval as well as working memory (Swanson & Jerman, 2006).
There are several important differences between students identified with SLD-R and SLD-M, with respect to cognitive profiles, academic achievement, and individual patterns of strengths and weaknesses. For example, a selective meta-analysis of 85 studies related to cognitive profiles showed that children with SLD-R have stronger naming speed and visual–spatial working memory compared with children with SLD-M (Swanson & Jerman, 2006). In a separate study of third-grade students (Compton, Fuchs, Fuchs, Lambert, & Hamlett, 2012), a distinctive pattern emerged of academic strengths and weaknesses on three of the four areas of SLD: (a) Students with an SLD-R exhibited cognitive weaknesses on broad verbal/language functioning (i.e., listening comprehension, vocabulary, syntax), (b) students with an SLD in word reading showed relatively weaker cognitive performance on working memory and oral language, and (c) students with an SLD in applied problem solving had cognitive deficits in abstract reasoning. A distinctive cognitive profile was not found for students with an SLD in calculation.
Differences in academic performance between students with an SLD-R and those with an SLD-M also exist. Willcutt et al. (2013) found that children with SLD-R had lower average grades and poorer overall academic functioning than children with SLD-M. In terms of their respective area of academic weakness, children with SLD-R were significantly more likely to receive extra help compared with children with SLD-M. In addition, children with SLD-R had significantly lower performance on tasks of phonological awareness and naming speed, whereas children with SLD-M had significantly more difficulty on tasks assessing cognitive set-shifting (i.e., shifting attention from a distinct task and/or stimulus to another). Research (Willcutt et al., 2013) indicates that students with an SLD-R experience a greater degree of negative academic consequences, as observed through academic performance, than students with an SLD-M.
Evidence of the academic struggles of students with an SLD-R or SLD-M is plentiful, and one efficient method of clarifying academic differences is to identify the types of errors made by this specific student population. For example, common error types among children who have oral reading problems include omissions (e.g., skipping individual words or groups of words), substitutions (e.g., replacing one or more words in a passage with a more meaningful word), and gross mispronunciations, hesitations, and inversions (e.g., changing order of words in a sentence). Children with reading comprehension difficulties tended to have difficulties recalling basic facts of the story, recalling the sequence of the story, and recalling the main theme of the story (Salvia & Ysseldyke, 1995). In a separate study, common errors among children with word recognition difficulties included omissions, insertions, substitutions, mispronunciations, and transpositions (Gargiulo & Kilgo, 2000).
With respect to math difficulties, McLoughlin and Lewis (1981) identified four error types in math computational analysis: incorrect operation, incorrect number fact, incorrect algorithm, and random error. Other types of errors exhibited by children with SLD-M included careless mistakes, poor handwriting, and deficits in phonological processing (i.e., understanding the phonological features of spoken numbers) or difficulties understanding meaningful number concepts (i.e., number sense; Robinson, Manchetti, & Torgesen, 2002).
Error Identification and Analysis in Reading and Math
Identifying the types of errors made by students is not enough to gain clarity into the meaningful differences between the reading and math SLD groups. A formal investigation into quantifying and investigating the error patterns, that is, error analysis, is also necessary. Error analysis is a widely utilized, well-supported, and effective strategy used to inform research and practice in various realms of academic learning (Greenberg, Ehri, & Perin, 2002; Leu, 1982; Radatz, 1979). The process of error analysis has been utilized to gain insight into individual learning processes, develop an understanding of SLDs and other obstacles to learning, create academic curricula, remediate errors and misunderstandings in students’ learning, and develop more effective instructional practices.
For more than 40 years, error analysis has provided insight into how individuals learn to read and the different strategies that they rely upon to navigate challenges in their reading (Leu, 1982; see Greenberg et al., 2002). In addition, error analysis has played a significant role in planning instructional interventions (Greenberg et al., 2002). In fact, Greenberg et al. (2002) used error analysis to identify differences in the way adults and children learn to read, and they concluded that adults and children utilized different cognitive processes and approaches in their reading, thereby warranting different interventions. A subsequent study, focusing on children’s use of strategies (McGeown, Medford, & Moxon, 2013), showed that different cognitive skills underlie their strategy use. Through analyzing children’s errors, they found that different cognitive skills predicted reliance upon different strategies. For example, if children had more well-developed decoding skills, they were more likely to rely upon a phonological strategy to read new words and less likely to rely upon an orthographic (visual) strategy. These researchers concluded that, by using error analysis, educators may be able to identify which specific type of strategy a child is relying upon to read, which can then provide the educator with valuable information for reading instruction and intervention.
Researchers have been using error analysis for math as far back as the early 20th century, and this effort was reignited in the late 1970s with a growing emphasis on individualization and differentiation in education (Radatz, 1979). More recently, studies involving analysis of math errors indicate the importance of differentiating between reasoning errors in mathematics versus careless oversites (Herholdt & Sapire, 2014) and using error analysis as a means to provide timely information to teachers about student’s abilities so that instruction can be better adjusted to meet individual needs (Ketterlin-Geller & Yovanoff, 2009). Furthermore, identifying differences between math errors caused by difficulties with language versus those caused by a deficiency in prerequisite math skills helps to establish the most effective intervention (Radatz, 1979).
In summary, error analysis has helped researchers advance theories of learning and identify common systematic errors and misconceptions, enabling the development of more effective instructional materials and curricula, which are aligned with the typical learning process and address common learning challenges (Radatz, 1979; Riccomini, 2005). Taken together, these findings suggest that the process of error analysis in mathematics and reading has significant value in the diagnosis of SLDs, identification of academic difficulties, and providing support for the development of effective remediation strategies and informing the instructional practices of educators (Herholdt & Sapire, 2014; Ketterlin-Geller & Yovanoff, 2009; Radatz, 1979; Riccomini, 2005). Therefore, we posit that utilizing error analysis will facilitate a better understanding of the error types and patterns of students with SLD-R and SLD-M. This information can then be utilized to identify more effective educational interventions and instructional practices.
Purpose of the Study
The purpose of the present study was to analyze the types of errors made on the Kaufman Test of Educational Achievement–Third Edition (KTEA-3; Kaufman & Kaufman, 2014) by students with SLDs in reading/writing (SLD-R/W) compared with students with SLD-M. The authors were also interested in how these differences compare with their typically achieving peers. We hypothesized that the SLD-R/W and the SLD-M samples in our study would be significantly more prone to making achievement errors in comparison with the control group.
Method
Data
Data for this study were obtained from a larger normative sample of students who were tested during the standardization and validation of the KTEA-3 (Kaufman & Kaufman, 2014) between August 2012 and July 2013. Specifically, three subsets of data—or groups of students—were selected. The two clinical samples1 included students with an SLD-R/W and students with an SLD-M. The third group served as a control and included students who did not have SLD-R/W or SLD-M.
Membership in the two clinical samples was confirmed by diagnoses that followed the Diagnostic and Statistical Manual of Mental Disorders (4th ed., text rev.; DSM-IV-TR; American Psychiatric Association, 2000) or IDEIA criteria. Membership in the SLD-R/W group required (a) a one standard deviation difference between a test of cognitive ability and a test of reading or written expression (excluding spelling subtests) and (b) a reading and/or writing score below 85 coupled with a score above 90 in another achievement area. The same criteria were required to be classified with an SLD-M. However, instead of using reading and writing, math was the deciding factor. Overall, about 15% of students in the SLD-M group also had an SLD-R but were excluded from the SLD-R/W group (Kaufman, Kaufman, & Breaux, 2014).
Efforts were made to ensure comparability between the three groups, given the available data, which allowed for matched-group comparisons. Specifically, background data indicated that the two SLD samples were closely similar on the variables of age, grade in school, gender, and region, and reasonably similar in ethnicity and parent’s education. In addition, a control was selected to match the grade distributions of both the SLD-R/W and SLD-M samples and to approximate the gender, ethnicity, and parent’s education distributions of the two SLD samples (see Table 1 for the demographic distributions of the three groups).
|
Table 1. Demographics for the Experimental and Control Samples.
Measures
KTEA-3
The KTEA-3 (Kaufman & Kaufman, 2014) is a measure of academic achievement for children aged 4 to 25. The KTEA-3 also includes an error-analysis component that allows the administrator to document the types of errors made by the examinee and to identify consistent patterns of errors made within and across subtests. The present study utilized error analysis from the following subtests: Reading Comprehension, Phonological Processing, Letter and Word Recognition, Nonsense Word Decoding, Spelling, Written Expression, Listening Comprehension, Oral Expression, Math Concepts and Applications, and Math Computation.
Analysis
A multi-step process was used to investigate the relationship between students with SLD-R/W and SLD-M and their corresponding KTEA-3 error scores on tasks of academic achievement. First, curriculum experts identified error types within and across 10 of the KTEA-3 subtests. Next, the error patterns were quantified via factor analyses. Specifically, the derivation of factor scores for math, reading decoding, and spelling subtests were based on exploratory factor analyses (EFAs; O’Brien et al., 2017), and the derivation of factor scores for tests of reading comprehension, oral language, written expression, and phonological processing were based on principal components analysis (PCA; Choi et al., 2017; Hatcher et al., 2017). Factor groups, or areas in which errors are made, were then derived using EFA and PCAs. Related to the current study, three error factors were extracted for the Letter and Word Recognition and Math Concepts and Applications subtests, and two error factors were identified for the Reading Comprehension, Phonological Processing, Nonsense Word Decoding, Spelling, Written Expression, Listening Comprehension, Oral Expression, and Math Computation subtests.
Second, we examined differences in achievement errors for students with SLD-R/W and SLD-M via multivariate analyses of the factor scores within each subtest and across the three groups. To adjust for crystallized knowledge (Gc), the KTEA-3 Oral Language Composite was used as a covariate in the analyses related to three of the seven subtests: Reading Comprehension, Phonological Processing, and Math Concepts and Applications; thus, we used MANCOVA with subtest factor scores as dependent variables and a grouping variable (SLD-R/W, SLD-M, matched control) as the independent variable. One-way MANOVAs were used in the analyses related to the remaining seven subtests: Listening Comprehension, Oral Expression, Letter and Word Recognition, Nonsense Word Decoding, Spelling, Written Expression, and Math Computation.
Results
First, descriptive statistics (means and standard deviations) were calculated for the factor scores related to each error factor within the 10 subtests. The error factor scores were scaled to have a mean of 10 and a standard deviation of 3. Higher factor scores indicate a greater ability (an accumulation of fewer errors) for each error factor. At face value, it is reasonable to expect the control group to have the greatest factor scores (less errors) than the SLD groups. In addition, it is reasonable to anticipate the SLD-R group to have lower “reading-related” error factor means compared with the SLD-M group and for the SLD-M group to have lower “math-related” error factor means compared with the SLD-R group. Interestingly, this was not always the case. The Expository–Literal factor means from the Listening Comprehension subtest and the Geometric concepts factor means from the Math Concepts and Applications subtest are similar across the three groups. Also noteworthy is the fact that the SLD-M group error factor score means are lower compared with the SLD-R/W in both Written and Oral Expression (see Table 2).
|
Table 2. Group Means and Standard Deviations on Error Factors for Each Subtest.
Second, seven MANOVAs, three MANCOVAs, and appropriate post hoc tests were conducted to identify significant error differences between groups for the 10 subtests. Significant differences were found for all 10 analyses, and the collection of significant findings is presented below (see Table 3 for multivariate analysis results).
|
Table 3. MANCOVA and MANOVA Results Summary by KTEA-3 Subtests and Error Factors.
Reading
The first of four reading subtests, Reading Comprehension, included two error factors: (a) Expository–Literal and (b) Narrative–Inferential, and significant differences were detected (Wilks’s λ = .930), F(4, 580) = 5.32, p < .001). Specifically, the SLD-R/W group made significantly more Expository–Literal errors compared with the control group, and the SLD-M group made significantly more Narrative–Inferential errors compared with the control group.
The second reading subtest, Phonological Processing, included two error factors: (a) basic phonological awareness and (b) advanced phonological processing, and significant differences were detected (Wilks’s λ = .915), F(4, 574) = 6.53, p < .001. Specifically, the SLD-R/W made significantly more basic phonological awareness errors compared with both the SLD-M and control groups and significantly more advanced phonological processing errors compared with the control.
The third reading subtest, Letter and Word Recognition, included three error factors: (a) contextual vowel pronunciation, (b) intermediate letter sound knowledge, and (c) consonant pattern knowledge. Significant differences were detected (Wilks’s λ = .749), F(6, 624) = 16.20, p < .001. For each of the three error factors, the control group made significantly fewer errors compared with the two SLD groups, and no significant differences were detected between SLD-R/W and SLD-M.
The fourth reading subtest, Nonsense Word Decoding, included two error factors: (a) letter sound knowledge and (b) basic phonic decoding. Significant differences were found (Wilks’s λ = .801), F(4, 536) = 15.69, p < .001. Specifically, the SLD-R/W group made significantly more letter sound knowledge errors than the SLD-M and control groups, and the SLD-M group made significantly more errors than the control group. No significant differences between groups were discovered for the basic phonic decoding error factor.
Writing
Spelling and Written Expression subtests comprised this category. Significant differences were found within the Spelling subtest (Wilks’s λ = .708), F(4, 548) = 25.79, p < .001, and the Written Expression subtest (Wilks’s λ = .708), F(4, 634) = 29.82, p < .001. The Spelling subtest consisted of two error factors: (a) sound to letter mapping and (b) phonological awareness, and the control group made significantly fewer errors compared with both SLD groups. In addition, the SLD-R/W made significantly more sound to letter mapping errors compared with the SLD-M group. The Written Expression subtest consisted of two error factors: (a) General and (b) Mechanics, and the control group made significantly fewer General and Mechanics errors compared with the SLD groups. No significant differences were identified between the SLD-R/W and SLD-M.
Language
Language subtests comprised Listening Comprehension and Oral Expression. In both cases, significant differences were found, Wilks’s λ = .888, F(4, 528) = 8.08, p < .001, and Wilks’s λ = .855, F(4, 634) = 12.89, p < .001, respectively. The Listening Comprehension subtest consisted of a Narrative–Inferential and an Expository–Literal error factors. The control group made significantly fewer Narrative–Inferential errors than the SLD groups, whereas no significant differences in Expository–Literal errors were detected between groups. Oral Expression consisted of an oral expression grammar error factor and a general oral expression error factor. Again, the control group made significantly fewer errors in both categories than the SLD groups. No differences were identified between SLD-R/W and SLD-M.
Mathematics
The first mathematics subtest, Math Concepts and Applications, consisted of three error factors: (a) math calculation, (b) geometric concepts, and (c) complex math problems, and significant differences were detected, Wilks’s λ = .868, F(6, 526) = 6.42, p < .001. Specifically, the control group made significantly fewer math calculation errors than the SLD-M group. No significant differences between groups related to the geometric concept errors. Finally, the control group made significantly fewer complex math problem errors compared with the SLD groups, with no significant differences between the two SLD groups.
The second mathematics subtest, Math Computation, consisted of two error factors: (a) basic math concepts and (b) addition, and significant differences were detected, Wilks’s λ = .821, F(4, 512) = 13.19, p < .001. In basic math concepts, the SLD-M preformed significantly lower than both the SLD-R/W and control groups. Although there was no significant difference between the two SLD groups in addition, SLD-M had significantly more errors than the control group.
Discussion
Some differences and many more similarities were found between the two clinical groups. Out of the 22 types of errors in reading, writing, language, and mathematics, only four were significantly different between the SLD-R/W group and the SLD-M group. Two were significantly different between all three groups. Within the clinical groups, basic phonological awareness (in Phonological Processing) was significantly lower for the SLD-R/W group than the SLD-M group, whereas basic math concepts (in Math Computations) was significantly lower in the SLD-M group than in the SLD-R/W group. Letter and sound knowledge (Nonsense Word Decoding) and sound to letter mapping (Spelling) were significantly different for all groups, with SLD-R/W being significantly lower than SLD-M and SLD-M being significantly lower than the matched control. In the other 18 error types, there were no significant differences between clinical groups. However, in 10 of those error types, both clinical groups were significantly lower than the control: contextual vowel pronunciation, intermediate letter sound knowledge, consonant pattern knowledge, phonological awareness, general, mechanics, inferential–narrative, oral expression grammar, general oral expression, and complex math problems. Three error factors showed no significant differences between any of the groups: basic phonic decoding (Nonsense Word Decoding), Expository–Literal (Listening Comprehension), and Geometric concepts (Math Concepts and Applications).
Implications for Diagnosticians
As predicted, the SLD-R/W and the SLD-M samples in our study performed significantly lower than the control group on the error factors directly related to their area of weakness. In other words, the performance of the SLD-M sample was significantly lower than that of the control group on the error factors directly related to the development of math skills. Similarly, the SLD-R/W sample group scored significantly lower than the control group on the error factors directly associated with the development of reading and/or writing skills. What is interesting is that out of the 22 error factor scores, only four were found to be significantly different between the SLD-R/W and SLD-M samples.
Overall, there were more similarities than differences between the SLD-R/W and SLD-M samples. For example, both of the samples scored significantly lower than the control group on errors that required working memory. This finding is consistent with previous studies regarding the role of working memory in the identification of SLD-M (Hale et al., 2008) and SLD-R (Evans, Floyd, McGrew, & Leforgee, 2001; Hale, Fiorello, Kavanagh, Hoeppner, & Gaither, 2001; McGrew & Woodcock, 2001).
It is crucial to note that both of the SLD-R/W and SLD-M samples performed significantly lower than the control group on many of the factors that are generally associated with reading and/or writing skills only. This finding is extremely important as it indicates that students with SLD-M may benefit from interventions designed to address typical SLD-R/W challenges. At the same time, students with SLD-R/W may need support in certain areas of math as can be seen from the complex math problems error factor. This should not be interpreted as support of a “one size fits all” approach, but rather support for diagnostic evaluation and monitoring of reading and writing performance in addition to mathematics for students with SLD-M.
The same level of performance (i.e., the same score) does not always equate to the same pattern of performance (i.e., the same cognitive processes utilized). Children might use a wide range of cognitive processes to complete any task. The input and output are measurable and observable, but understanding “the underlying neuropsychological processing demands [is] essential,” for helping children with learning and behavioral challenges (Hale & Fiorello, 2004, p. 130). Results of this study preliminarily suggest that a deficit in the same underlying psychological or neuropsychological processes may be manifested in different types of learning disabilities. For example, children with weakness in simultaneous processing might experience difficulty solving math problems that require procedural steps because they focus too much on each of the steps and find it hard to sequentially organize these individual steps. The same children would be typically expected to struggle with inferential reading comprehension due to their difficulty putting different pieces of information from text in perspective or interpreting implicit language. However, their overall performance on reading tests might not be low enough to signal anything unsettling because their literal/textual comprehension is generally intact, and they might qualify to receive services only in the area of mathematics. It is important for school psychologists and other practitioners to design and conduct a comprehensive evaluation in a way that would tease out which basic psychological processes might contribute to each individual’s presenting academic challenge and to consequently make it possible for the problem-solving team to develop a highly individualized educational plan that specifically addresses the individual’s specific learning needs.
Limitations
There were a few limitations within the study. First, as mentioned above, 15% of the SLD-M group also had an SLD-R/W. This may have affected reading scores for some of the students in the SLD-M group. Second, this study was a retrospective study. As such, the authors were not able to control the data collection process or control for certain variables. Because we used a pre-existing data set, our research questions were limited. For example, we would have liked to compare errors between the SLD-R/W group and those students who had language learning disabilities. However, due to missing data and small sample sizes, we were prohibited from making this comparison. Future research in the area can be created with certain groups in mind to understand not just their differences but their similarities as well.
Acknowledgements
The authors thank NCS Pearson for providing the standardization and validation data for the Kaufman Test of Educational Achievement–Third Edition (KTEA-3). Copyrights by NCS Pearson, Inc., used with permission. They also thank Alan and Nadeen Kaufman for their supervision of the comprehensive error analysis research program.
Authors’ Note
Tawnya Knupp was at UConn working as a statistation when the study started. She is currently not affiliated with any University. Melissa Root was a professor at UConn when the study was conducted. She now has her own priviate practice Root Success Solutions. Matthew Pagirsky was a student at St. John’s University and has since graduated. He is currently working on his postdoctorate.
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.
Notes
1.
Demographic data for the two clinical samples are provided in the Kaufman Test of Educational Achievement–Third Edition (KTEA-3) Technical and Interpretive Manual (Kaufman, Kaufman, & Breaux, 2014).
References
|
American Psychiatric Association . (2000). Diagnostic and statistical manual of mental disorders (4th ed., text rev.). Washington, DC: Author. Google Scholar | |
|
Choi, D., Hatcher, R. C., Langley, S. D., Liu, X., Bray, M. A., Courville, T., . . . DeBiase, E. (2017). What do phonological processing errors tell about students’ skills in reading, writing, and oral language? Journal of Psychoeducational Assessment, 35(1-2), 25-47. Google Scholar | SAGE Journals | |
|
Compton, D. L., Fuchs, L. S., Fuchs, D., Lambert, W., Hamlett, C. (2012). The cognitive and academic profiles of reading and mathematics learning disabilities. Journal of Learning Disabilities, 45, 79-95. Google Scholar | SAGE Journals | ISI | |
|
Evans, J. J., Floyd, R., McGrew, K. S., Leforgee, M. H. (2001). The relations between measures of Cattell-Horn-Carroll cognitive abilities and reading achievement during childhood and adolescence. School Psychology Review, 31, 246-262. Google Scholar | |
|
Fletcher, J. M., Lyon, G. R., Fuchs, L. S., Barnes, M. A. (2007). Learning disabilities: From identification to intervention. New York, NY: Guilford Press. Google Scholar | |
|
Gargiulo, R. M., Kilgo, J. L. (2000). Young children with special needs: An introduction to early childhood special education. Albany, NY: Delmar. Google Scholar | |
|
Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37, 4-15. Google Scholar | SAGE Journals | ISI | |
|
Geary, D. C., Hoard, M. K., Byrd-Craven, J., DeSoto, M. C. (2004). Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability. Journal of Experimental Child Psychology, 88, 121-151. Google Scholar | Crossref | Medline | ISI | |
|
Greenberg, D., Ehri, L. C., Perin, D. (2002). Do adult literacy students make the same word-reading and spelling errors as children matched for word-reading age? Scientific Studies of Reading, 6, 221-243. doi:10.1207/S1532799XSSR0603_2 Google Scholar | Crossref | |
|
Hale, J. B., Fiorello, C. A. (2004). School neuropsychology: A practitioner’s handbook. New York, NY: Guilford Press. Google Scholar | |
|
Hale, J. B., Fiorello, C. A., Dumont, R., Willis, J. O., Rackley, C., Elliott, C. (2008). Differential ability scales–Second edition: (Neuro)psychological predictors of math performance for typical children and children with math disabilities. Psychology in the Schools, 45, 838-858. doi:10.1002/pits.20330 Google Scholar | Crossref | |
|
Hale, J. B., Fiorello, C. A., Kavanagh, J. A., Hoeppner, J. B., Gaither, R. A. (2001). WISC-III predictors of academic achievement for children with learning disabilities: Are global and factor scores comparable? School Psychology Quarterly, 16, 31-55. Google Scholar | Crossref | ISI | |
|
Hatcher, R. C., Breaux, K. C., Liu, X., Bray, M. A., Ottone-Cross, K. L., Courville, T., . . . Dulong Langley, S. (2017). Analysis of children’s errors in comprehension and expression. Journal of Psychoeducational Assessment, 35(1-2), 58-74. Google Scholar | SAGE Journals | |
|
Herholdt, R., Sapire, I. (2014). An error analysis in the early grades mathematics—A learning opportunity? South African Journal of Childhood Education, 4, 42-60. Google Scholar | Crossref | |
|
Individuals With Disabilities Education Improvement Act . (2004). 20 U.S.C. § 1400 et seq. Google Scholar | |
|
Kaufman, A. S., Kaufman, N. L. (2014). Kaufman Test of Educational Achievement–Third Edition. Bloomington, MN: NCS Pearson. Google Scholar | |
|
Kaufman, A. S., Kaufman, N. L., Breaux, K. C. (2014). Kaufman Test of Educational Achievement–Third Edition (KTEA-3) (Technical & interpretive manual). Bloomington, MN: Pearson. Google Scholar | |
|
Ketterlin-Geller, L. R., Yovanoff, P. (2009). Diagnostic assessments in mathematics to support instructional decision making. Practical Assessment, Research & Evaluation, 14, 1-11. Google Scholar | |
|
Leu, D. (1982). Oral reading error analysis: A critical review of research and application. Reading Research Quarterly, 17, 420-437. Google Scholar | Crossref | ISI | |
|
Mather, N., Wendling, B. J. (2012). Essentials of dyslexia assessment and intervention. Hoboken, NJ: John Wiley. Google Scholar | |
|
McGeown, S. P., Medford, E., Moxon, G. (2013). Individual differences in children’s reading and spelling strategies and the skills supporting strategy use. Learning and Individual Differences, 28, 75-81. Google Scholar | Crossref | |
|
McGrew, K. S., Woodcock, R. W. (2001). Woodcock-Johnson III (Technical manual). Itasca, IL: Riverside. Google Scholar | |
|
McLoughlin, J. A., Lewis, R. B. (1981). Assessing special students: Strategies and procedures. Columbus, OH: Merrill. Google Scholar | |
|
National Center for Education Statistics. (2015, May). Children and youth with disabilities. Retrieved from http://nces.ed.gov/programs/coe/indicator_cgg.asp Google Scholar | |
|
O’Brien, R., Pan, X., Courville, T., Bray, M. A., Breaux, K. C., Avitia, M., Choi, D. (2017). Exploratory factor analysis of reading, spelling, and math errors. Journal of Psychoeducational Assessment, 35(1-2) 8-24. Google Scholar | |
|
Radatz, H. (1979). Error analysis in mathematics education. Journal for Research in Mathematics Education, 10, 163-172. Google Scholar | Crossref | |
|
Riccomini, P. (2005). Identification and remediation of systematic error patterns in subtraction. Learning Disability Quarterly, 28, 233-242. Google Scholar | SAGE Journals | ISI | |
|
Robinson, C. S., Menchetti, B. M., Torgesen, J. K. (2002). Toward a two-factor theory of one type of mathematics disabilities. Learning Disabilities Research & Practice, 17, 81-89. Google Scholar | Crossref | |
|
Salvia, J., Ysseldyke, J. E. (1995). Assessment. Boston, MA: Houghton Mifflin. Google Scholar | |
|
Swanson, H. L., Jerman, O. (2006). Math disabilities: A selective meta-analysis of the literature. Review of Educational Research, 76, 249-274. Google Scholar | SAGE Journals | ISI | |
|
Willcutt, E. G., Petrill, S. A., Wu, S., Boada, R., Defries, J. C., Olson, R. K., Pennington, B. F. (2013). Comorbidity between reading disability and math disability: Concurrent psychopathology, functional impairment, and neuropsychological functioning. Journal of Learning Disabilities, 46, 500-516. Google Scholar | SAGE Journals | ISI | |
|
Wolf, M. (2007). Proust and the squid: The story and science of the reading brain. New York, NY: HarperCollins. Google Scholar |