Qualitative or Quantitative Differences? Latent Class Analysis of Mathematical Ability for Special Education Students

Students with disabilities comprise a protected population for which particular educational and instructional interventions are expected to be provided. Ideally, remedial interventions should be individualized to each student's need. This is the goal of the Individuals with Disabilities Education Act of 1990 (IDEA) and embodied in the Individualized Education Program (IEP) process, but complete individualization is usually impossible due to limited resources and the need for teachers trained to provide services tailored to specific groups, such as mobility training or Braille for students with visual impairment. As a result, students who meet categorical eligibility criteria specified in IDEA and further delineated by relevant state special education laws and procedures are sometimes grouped for instruction rather than receiving individual attention. The disability categories defined by IDEA and state laws were formed on historical and political, rather than empirical, foundations. Categories are typically defined on the basis of such characteristics as type of impairment (e.g., perceptual, language, physical, cognitive) or etiology (e.g., traumatic brain injury). Emotional/behavioral disorders are defined by mal-adaptive behaviors and moods that differ from the norm for age peers, and specific learning disabilities are defined by differences among abilities and achievement within the individual. The current article investigates whether the mathematics achievement of students in special education can be used to identify those who share common cognitive skills that may not be in concordance with their disability labels. Latent class analysis of a comprehensive test of mathematics taken by fourth-grade students with various disabilities reveals that a model with 2 latent classes is adequate to characterize the latent structure of the data. A parallel relationship of response profiles across the 2 classes suggests differences in the levels of mathematical ability (quantitative), rather than differences in the type of mathematical ability (qualitative), between the 2 latent classes in terms of generic mathematical proficiency. Cross-validation on a separate data set with careful matching of content areas within the math test verified this conclusion. Although a significant relationship exists between the identified latent classes and various disabilities, the analysis also found common mathematical problem-solving behaviors across disability categories. Implications for intervention and limitations of the current study are discussed. health impairment, physical disabilities) cover a range of diagnostic conditions. Several broad categories defined by IDEA and state law (e.g., noncategorical identification, developmental delay, other health impairment) are used as catch-alls for students who clearly display impairment but cannot be assigned a definitive …