David Mills, Ph.D., M.A. (physics, psychology)

Math learning difficulties and disabilities.  More than three in every ten students in school today have significant difficulties learning math.  This is on average ten students in every classroom. 

The largest fraction of these students suffer from inadequate learning of the subject at earlier stages.  Several factors contribute to this situation, including 1) poor instructional techniques, especially in grade school; 2) trying to teach a subject to a student before the student is developmentally ready, 3) negative socio-economic factors; 4) negative parent and elementary school teacher beliefs about the "natural difficulty" of math, resulting in expectations of poor achievement.

The group of students affected is quite diverse:  difficulties may range from poor understanding of basic number concepts; incomplete knowledge of addition or multiplication tables; not understanding or being unable to manipulate fractions, ratios and percentages; as well as a variety of difficulties with more advanced math concepts encountered in algebra and calculus.  

It is my observation that incomplete early learning can underlie problems experienced by many advanced students, even those, for example, now finding themselves in AP calculus.   For this reason, it is essential that tutoring at all levels be done by a professional who is as comfortable with assessing and teaching of elementary operations as he/she is in teaching advanced concepts.

Mathematics is inherently a sequential and increasingly complex subject, and failure to adequately learn the subject at any stage -- for whatever reason -- can mean continuing trouble when later stages are attempted. 

Many teachers and parents are unaware of the existence of specific math learning difficulties.  Reading difficulties have received more than fifty times the amount of attention among researchers, funding agencies and educational institutions.  This is in spite of the fact that the numbers of people affected by each are estimated to be the same.  As a consequence, math learning difficulties and disabilities are often not diagnosed and affected students not given the early attention needed.

This disparity appears due to the perception that learning math is not as important as learning to read.  However, the argument that a basic foundation in mathematics is required to function in a modern society has been receiving increasing support.  In consequence, the requirements for achievement in math have correspondingly been increased, e.g., as a condition for graduating high school and/or entering college. 

My Approach:  I have found that most students with mathematical learning difficulties can be maintained in regular classrooms with adequate support, and many can raise their grades into the "A" level.

In general, tutoring begins with helping the student in whatever way the student desires and finds most helpful, assisting with homework or test preparation, etc.  

● As we work together, one of my tasks will be to identify specific difficulties which stem from inadequate comprehension of earlier material.

● Specific methods and procedures, tailored for each student, are worked into regular tutoring sessions to assist students improve comprehension and usefulness of earlier material.  

If symptoms of dyscalculia appear present, a diagnostic test is used to confirm its presence.  If this specific disability is confirmed there is a specialized treatment which can provide significant improvement.    Similarly, math problems complicated by dyslexia also require a specialized approach.  Finally, extreme math anxiety can be ameliorated using methods similar to the treatment of phobias.  Each of these causes and cures are discussed in more detail in the relevant section.

● If motivation is an issue, applications of homework and materials are tailored to fit the student's interests or goals.

● I also determine the ways the student learns most easily, and which concepts or processes provide the most difficulty. Every student has strengths that can be called upon, if they can be identified and used appropriately.  

Because there is no single cause for math learning difficulties, a successful approach has to be tailored to the needs of each individual student.  My approach is a general one which can be applied to any difficulty in learning mathematics, at any grade level.  Specific approaches applicable to math learning disabilities, math anxiety, and other conditions are discussed separately in the relevant posts (list at right). 

My background has allowed me to develop the treatment of math difficulties from a unique perspective: I have a doctorate in physics, with the equivalent of a Master's degree in mathematics, but I also have an M.A. in Clinical Psychology, with a specialization in working with children, adolescents and families. I have had extensive experience tutoring students in grade school, high school and college.


Sources for the discussion above can be found in the collection of review articles, "Why is Math So Hard for Some Children?   The Nature and Origins of Mathematical Learning Difficulties and Disabilities," by Berch and Mazzocco, Eds (2007). 

Another excellent resource, especially in translating research findings into practical teaching approaches, is "How the Brain Learns Mathematics," by David A. Sousa (2008).

Note:  All original material on this site and linked websites © D. Mills 2011.

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