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RTI and Special Education

Please, if possible send me more information about unexpected underachievement, RTI, within the discipline of mathematics. What types of comprehensive tests should my students take to determine an LD issue?


Response from David Allsopp, Ph.D., Professor of Special Education in the College of Education at the University of South Florida:

Please, if possible send me more information about unexpected underachievement, RTI, within the discipline of mathematics. What types of comprehensive tests should my students take to determine an LD issue?

To begin, there is no consensus on how educators can best determine whether or not a student has a mathematics learning disability (LD). In part this is due to the lack of confidence most professionals have related to the traditional discrepancy method for identifying learning disabilities generally, where students were identified if the discrepancy between a cognitive IQ score and one or more achievement scores was at a designated threshold (e.g., 1.5 Standard Deviations). Mostly, the discrepancy model is no longer being used for LD identification in PK-12 education.

As I am sure you are aware, Federal law now requires that LD identification cannot be considered unless a student is shown to have persistent lack of response to well documented evidence based instruction within a tiered instruction system (e.g., Response to Intervention/Multi-Tiered System of Supports). States differ on what if any other criterion or criteria are needed for identification after lack of response to intervention is met. Some states require additional testing or allow school districts to determine what additional measures they will use for LD identification. One approach is to administer a battery of achievement and cognitive process assessments for the purpose of looking for a pattern of strengths and weaknesses that denote specific areas of difficulties while also denoting specific areas of strengths in areas of learning (e.g., math, reading, writing) and cognitive processing (e.g., central auditory processing, working memory, visual motor processing, etc.). When a particular pattern or set of patterns is demonstrated, then identification for a Learning Disability might be considered. A general rule that still stands is that students who are identified with a Learning Disability cannot also qualify for identification for Intellectual Disability. Other exclusion factors include environmental stressors such as poverty, culture diversity, linguistic diversity, and "poor teaching." Also, a learning disability cannot be the result of a psychiatric/social-emotional/behavioral disorder (although students can have a learning disability and also have an emotional/behavior disorder).

Specific to research on mathematics learning disabilities, there is some information that might be of help with your question but unfortunately, it is not "absolute." First, there do appear to be several indicators of a possible Math LD (i.e., that often are present when students experience persistent difficulties with mathematics). They include:

  1. Persistent deficiency in math test performance over time (e.g. K-3)

  2. Lack firm grasp of numerosity, recognizing quantities, identifying missing numbers in a sequence (number & number sense). A key is that these students have difficulty with these things at an age when most peers succeed

  3. Lack of conceptual mastery

Students who have a math LD may also demonstrate difficulties with particular types of cognitive skills. However, if a student has difficulties in these areas, then it does not necessarily mean that they have a math LD. Language difficulties related to number and quantity may occur. An example of this might be when a student has difficulty remembering the answer to a math problem due to the need to utilize linguistic processing (the need to efficiently process language based information that represents quantity and numerical associations). Sometimes students with math LDs have spatial skill difficulties which might include estimation of quantity/number (e.g., an approximate solution, determining equality using proportional manipulatives, aligning numbers when doing calculations, etc.). Difficulties with memory can also be present with math LDs, particularly with working memory, which requires the deliberate review, reliance on, and application of information during a task like keeping digits in mind and their relative values when performing a math operation. This relates to a student's ability to take in new information, relate it to information they know, make connections, and utilize these connections to learn or perform a particular task "realtime."

Other factors that can contribute to difficulties in mathematics are difficulties in other academic areas not specific to math such as reading, writing, and spelling. Interestingly, students with reading difficulties or ADHD tend to have more difficulties with mathematics than those without these conditions. Of course interrupted mathematics instruction across time and negative attitudes about mathematics communicated by teachers and students in the classroom (math anxiety) can also affect mathematical success of students.

Unfortunately there is no one assessment or measure that will reveal whether or not an individual has a mathematics learning disability. So, at this point, I can only give you my personal thoughts about the approach I would take. So, please understand that what follows is my opinion based on my read of the literature and my experience with struggling learners:

  1. I would first determine whether or not a student has actually received research supported effective mathematics instruction in cases where they are not responding. This includes whether Tier 1 instruction incorporates these practices and the extent to which additional tiered instruction has actually been targeted to address foundational concept/skill gaps utilizing explicit mathematics instruction practices (e.g., explicit systematic instruction, use of visuals, concrete-representational-abstract instruction, communicating mathematical ideas, teaching math problem solving strategies, etc.)

  2. I would verify that the exclusion factors mentioned above are not interfering with the student's mathematics success.

  3. I would use the 3 indicators described earlier to determine whether or not additional assessment is warranted. If a student demonstrates each of the 3 indicators, then I would suggest moving to a more extensive set of assessments that pair mathematics and reading achievement batteries with cognitive process batteries that specifically evaluate working memory, central auditory processing, linguistic processing, and visual-spatial processing.

  4. From the results from these assessments, I would look for distinct patterns of strengths and weaknesses. If the student demonstrates general patterns of weaknesses across the board, then it is more likely that the student's difficulties are the result of a more global set of issues rather than a math specific disability. If a student shows specific patterns of weakness with reading and mathematics, and one or more of the cognitive processes, then it I'd be more inclined to think that difficulties with mathematics are linked to difficulties with reading/linguistic processing (i.e., a reading disability), particularly if language is an area of weakness. When patterns of weakness are central to mathematics (i.e., not in reading) and include one or more of the cognitive processing areas then I would be more inclined to suspect a mathematics LD.

I hope that my response to your question helps. I wish I had a more straightforward answer but this is where we are at this point in terms of our understandings of/identifying mathematics learning disabilities. Please refer to an article written by Michele Mazzocco for a nice review of mathematics learning disabilities that helped me in structuring my response: Mazzocco, M. (March/April 2007). Early predictors of mathematical learning difficulties: Variations in children's difficulties with math. Exchange, 40-47. Also, an excellent in-depth book on mathematics difficulties/disabilities is: Why is Math So Hard for Some Children? The Nature and Origins of Mathematics Difficulties and Disabilities?, edited by Dr. Mazzocco and colleagues, published by Brookes Publishing.

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