For Students with Math-Related Disabilities or Math Difficulties, the Successful Educational Intervention is the Same
By David Berg, E.T.
Founder/Director of the Making Math Real Institute
Creator of the Making Math Real Multisensory Structured Methodologies in Mathematics, K-12
The reality for some students that math can be persistently difficult and overwhelming is hardly newsworthy. As educators and parents (and for us as well when we were kids) we continue to experience the exclamations of frustrated students, “I hate math,” “Math is boring,” “I’m dumb, I’m stupid, I’ll never be good at math,” “What’s the point of this stuff – when will I ever need to use parabolas in my life?”
There are numerous valid reasons why students may feel this way, and none of the reasons I know of are the students’ fault, because there is no educational justification for any student to fail in math.
Building literacy and numeracy
Over the last 20 years in our educational system, there has been a valuable focus on literacy development in our country. Some of the significant improvements made during this time include:
- Increased understanding of research connecting neurodevelopment with specific instructional practices
- Increased use of multisensory structured reading and language programs
- Improved professional development for teachers to help expand understanding and application of more comprehensive and inclusive programs
- Improved assessment to help teachers address specific educational needs of students
The results of our nationwide focus on literacy have been an important and much needed step in the right direction, yet there is still much to do in continuing this positive development. However, in our cultural focus on literacy, have we forgotten something? What about math? Math has been the neglected curriculum for far too long. For example, according to the Educational Resources Information Center (ERIC), research on reading and language far exceeds the research on math. In the 34 years I have been an educator I have witnessed the money, time, and energy spent on professional development, programs, and materials for reading and literacy far exceed the expenditures for math. In numerous districts and schools I have observed across the country, the time allotted each day for reading far exceeds the time devoted to math.
The development of numeracy is of equal importance and value as is the development of literacy. Numeracy means being literate with numbers and math. As literacy refers to the ability to read for meaningfulness, to interact critically with the literature, so too, does numeracy refer to the ability to interact critically with the mathematics with depth of comprehension, not the mere memorization of procedural steps. In my opinion, the development of literacy and numeracy should be the focal points of K-12 education in our nation today. As parents and educators, we need to guarantee our high school graduates are both literate and numerate.
Math difficulty or disability?
Since there has been significant research in the area of reading, there are definitions of and widespread agreement on the nature of learning disabilities in reading, specifically, dyslexia. However, there has been relatively little research in the area of math (despite the recent upsurge since 2005), and consequently, there is no current consensus on the core deficits including definitions, or means of identifying math-related disabilities, specifically, dyscalculia. Regardless of the current lack of consensus in determining the precise nature of math disability, the existence of math-related learning disabilities is indisputable.
Furthermore, researchers are attempting to distinguish between students with math-based learning disabilities versus those struggling with “math difficulties.” All of the ongoing research in mathematics is highly worthwhile and will continue to provide all of us with valuable information as developments in research progress. However, it is essential to understand that the successful intervention and remediation for students with math-based learning disabilities or math difficulties are the same. Both populations require an explicit, developmental, comprehensive, and multisensory-structured methodology in mathematics. The intervention and/or remediation must be provided by highly trained educators, thoroughly knowledgeable of the content, and capable of delivering the curriculum prescriptively in alignment with students’ individual and/or collective processing styles. Therefore, from a practical and educational standpoint it is not crucial to distinguish between math disability and math difficulty. All students need the most appropriate and most prescriptive interventions we can provide.
Many struggle with math basics
Over the last 34 years I have worked across the country with more than 10,000 students of all ages and processing styles. According to my experience and research, at least half of our students nationwide are experiencing some degree of math difficulty. One of various indications of this widespread challenge in math is the conservative estimate that 40 – 60% of students nationwide are failing algebra I. The repeated concerns I have received from middle school, high school, community college teachers, and parents is the following: “Our students have not learned the math basics such as the multiplication facts, fractions or place value.” Representing one of many sources confirming this ongoing national problem in mathematics comes from the State of California Department of Education’s California Basic Educational Data System, retrieved December 8, 2008. According to this statewide data collected from 2003 -2008, the highest level of achievement overall for California algebra students has only been 22% scoring at proficient or higher.
In addition, my research, assessment data, and experience have shown me that students with math disabilities and students who struggle do not lack the intelligence or the motivation to be successful in math. Typically, they lack the underlying perceptual and associative processing tools that enable all of us to successfully process numbers and math. In essence, processing means information in, information out, i.e., how we receive information, make sense of it, store it, retrieve it, and express it. These processing tools, known as sensory-cognitive development (“cognitive” refers to processing), help us to express what we know – they provide a direct conduit in both directions connecting processing to intelligence.
Building mathematical sensory-cognitive skills is key
Sensory-cognitive development for math refers to the specific ability of using the visual, auditory, and kinesthetic-motoric senses to engage and support the successful processing of numerical and/or mathematical symbols. Students with under-developed sensory-cognitive abilities often have limited access to memory and are characteristically challenged by learning, retaining, and applying the math facts, recalling formulas and definitions, remembering the sequences and structure of multi-step problem solving, integrating concepts with their respective procedures, and managing all the details in their procedural work.
Processing exists as a means for all of us to express what we know. If the mathematical processing tools are not developed, then it appears as if we do not know the math. Just as carpenters express their craft through the practiced and developed use of tools: hammers, saws, drills, etc., we also use sensory-cognitive processing tools to express what we know about math. Imagine the carpenter with an empty tool belt. How does the carpenter express his/her craft without the tools? It is the same for students with math-related learning disabilities or who struggle in math. Without developed processing tools, they are not able to express what they know. Unfortunately, students with underdeveloped sensory-cognitive tools may be misperceived as less intelligent and less capable than their peers who, by fortune of genetic makeup, possess developed processing tools. Therefore, it is eminently possible to be highly intelligent despite the developmental lack of certain mathematically-based processing tools.
A case study of a client I worked with several years ago presents a strong example supporting the distinction between processing development and intelligence. The client was 42 years of age, a graduate of M. I. T. and currently worked for NASA. According to assessment, this individual’s overall intelligence was in the 99th percentile and he presented as someone extremely accomplished, if not brilliant. However, until the moment of our work together, he had never learned the math facts. My assessment of his sensory-cognitive development for learning and retaining the math facts did indicate extreme underdevelopment. When I asked him how he managed the academic demands of rigorous math and science courses throughout his school career, he responded by telling me how he used his intelligence to create compensatory methods to solve calculations with the math facts. He also confirmed that he benefited from his strong ability to understand the concepts easily, but his compensatory methods for calculation tended to slow him down relative to his peers, and he also felt he had to work much harder than his peers, which in turn made him feel less intelligent than his peers.
This client’s experience, despite the years of stress and anxiety he felt throughout school, is most unique. Through tenacity and determination he was able to endure and succeed without the benefit of a prescriptive intervention to develop the sensory-cognitive development for learning and retaining the math facts. His experience is not representative of the larger group. I have worked with thousands of students who, until receiving prescriptive interventions and remediations for developing their sensory-cognitive tools, had given up on math and furthering their integration of numeracy.
In alignment with my experience and research, it is important to note that regardless of the 42-year-old client’s high intelligence and strong work ethic, his sensory-cognitive tools remained underdeveloped until he received prescriptive interventions as an adult. In other words, these sensory-cognitive tools are not maturational. They do not develop on their own as we get older. They do not develop simply because we are determined and work hard. They develop because an experienced educator has assessed that these processing tools are underdeveloped and has addressed the development of these sensory-cognitive tools with prescriptive methods.
As with the 42-year-old brilliant client, I have frequently observed students express their confusion and frustration when they know they are as smart as their peers, yet have to struggle constantly in math while some of their peers make math seem effortless. According to my experience, the two strongest indications for successful remediation are 1) the delivery of math curriculum specifically designed to support and develop these crucial processing tools, and 2) the delivery of math curriculum in alignment with students’ individual processing styles to ensure they successfully process the curriculum. NOTE: Every time individuals process successfully, their processing tools get stronger and more developed.
Since there is not yet a specific determination of dyscalculia, it is difficult to ascertain an accurate percentage of the population with this math-related learning disability. In my opinion and experience, it is not of primary importance to quantify the number of people specifically identified with dyscalculia or any other form of math-related learning disabilities separate from students who struggle in math. The issue of real importance is providing prescriptive help for all these students – and the methods for helping all these students is the same. However, if these students do not receive interventions that directly address the development of the math-based sensory-cognitive processing tools, the likelihood of negative outcomes increase sharply whether or not students have math-related learning disabilities or consistently struggle with math.
For students who do not get their educational needs met in mathematics I have repeatedly observed an ongoing subtractive development not only in the area of math which directly underlies the pervasive and increasing gap in achievement for these students, but far more seriously in their ability to trust their own mathematical sense. As I observe these students when confronted with any component of math, I note significant anxiety in their affect and behavior. Frequently, these students do not know if their solutions are right or wrong. They cannot trust their own mathematical problem solving ability. This horrible feeling and experience, if not addressed appropriately, may lead to academic wounding. Academic wounding is the internalization of the personally based myth of the pre-conception of failure: “I hate math,” “Math is boring,” “I’m dumb, I’m stupid. I’ll never be good at math.” Academic wounding can affect all students, with or without learning disabilities. If not appropriately addressed, academic wounding may persist indefinitely into adulthood until such time as the individual repeatedly experiences authentic and indisputable success.
I have personally encountered thousands of adults experience powerful releases of emotion upon realizing they were not actually “stupid,” and they could have been successful in math. These same people frequently breakdown weeping in the pain, loss, and sorrow for having believed in a most inaccurate and unnecessary personal myth. The good news is that the successful development of numeracy can begin or continue developing at any time of life.