Why is Math So Hard for Some Children? The Nature and Origins of Mathematical Learning Difficulties and Disabilities
by Daniel B. Berch, Michelle M. M. Mazzocco, Foreword by Robert Siegler. Paul H. Brookes Publishing Co., Baltimore, MD, 2007, 488 pp, $49.95 Hardcover.
This text starts the clean-up of another messy area of learning disability (LD). It is said to be the first of its kind, collating historic and recent research in the field of Math LD. Authors are from wide-ranging fields: neurology; neuroscience; epidemiology; behavioral genetics; cognitive, developmental and educational psychology; and mathematics and special education. While their attempt is commendable, they fail to achieve consensus on either the components of Math Learning or the nature of Math Learning Difficulty/Disability (MLD).
In the text, the editors divide the material into three parts: Part I. Characterizing Learning Disabilities in Math – historical perspective, MLD prevalence, and theories about math acquisition. The editors try to define a structure of mathematical acquisition, by providing differing theories. The authors discuss elementary and higher order components of math learning including: number sense, working memory, phonologic processing, visuo-spatial thinking, conceptual understanding, and procedural knowledge.
Part II. Neuropsychologic Factors – math deficits particular to a variety of genetic and neurodevelopmental disorders with reference to newer brain imaging and genetic studies. And, Part III- including Additional Influences on Math Disabilities (anxiety, gender, ethnicity and motivation) and Instructional Interventions. Within these parts, related chapters are organized into sections. The editors preface each section with an introduction explaining the contribution of each chapter. Related sections are followed by a commentary.
Despite the editors' ambitions to “establish a common language” and organize math processing into a framework, I feel they failed. I had trouble both “mapping out” what individual authors were saying and further difficulty relating proposed theories to one another because the authors used inconsistent terms. The editors attempted to clarify these in the commentary sections but weren't wholly successful. Methodologically, I was also concerned that populations compared were too loosely defined (we're not told if they were matched for IQ, language skills, specific reading issues, socioeconomic status etc). When trying to finally define MLD, the editors admit “MLD is a biologically based, behaviorally defined condition for which no consensus definition exists” … and for which there is no consensus in either symptom complex or theoretical basis. (Maybe their next book will be; “A First Definition of MLD.”)
The editors could have addressed these issues by imposing “a common language.” Within such a framework, authors still could have expressed divergent views but their points of agreement (and disagreement) would have been clearer. Visuals would also have enhanced the text. Theories of Mathematics learning could have been presented as schematic maps with “at risk” components marked to show where and what type of difficulty a child might encounter. Tables listing relative strengths and weaknesses found in the different disabled groups discussed (Traumatic Brain Injury, Turner Syndrome, Fragile X, Spina Bifida/ Myelomeningocele, Reading Disabled, Specific Language Impaired, and ADHD) would have aided understanding.
As a Developmental/Behavioral Pediatrician, I see the most affected students: the ones schools have so far failed. I see patterns in what kids and their parents report, evaluation reports they bring in and in the interventions they receive. I've developed theories over time, so a text of this intent, was of major interest to me. Unfortunately, I'll have to wait for upcoming editions to gain clarity.
Knowing that mathematics teachers want to reach all kids, they need to know what a student's failure means. I was curious if this text would be of help to a high school mathematics teacher. I asked Norma Gordon, M.Eng, Lexington Public Schools, MA to comment:
Math teachers/specialists identify students with MLD, then develop and deliver individualized modifications – which often requires “breaking down” (scaffolding) content/instruction. The authors could have looked at the National Council of Teachers of Mathematics (NCTM) Principals and Standards for School Mathematics (which breaks curriculum into Content1 and Processes2 components) and identified likely areas where an MLD student might falter. This in turn would potentially direct the teacher to where instructional models could be most effective. Furthermore, standards not addressed would highlight future research needs.
1Content: Number and Operations, Algebra, Geometry, Measurement, Data Analysis and Probability.
2Processes: Problem Solving, Reasoning and Proof, Communications, Connections.
In summary, I feel the authors have made a solid contribution by compiling and editing this book, and in turn have confirmed that there is no single nor easy answer to the question, “Why is Math so Hard for Some Children?”
Doreen Karoll, MD
Franciscan Hospital For Children