Access to Math

MAKING MATH ACCESSIBLE TO STUDENTS WITH MATH LEARNING DISABILITY

Renee Hamilton-Newman, President, Dyscalculia.org
UNDERSTANDING DYSCALCULIA: Sequential memory is very limited and working math memory is too short to hold complex chunks of information and instructions. Most cannot even keep track when counting 100 pennies. Most cannot count by 3 beyond 12 without manually adding 3 to each increment. Because they cannot consistently recall addition, subtraction, multiplication and division facts, even simple tasks become complex efforts of manual calculation. This is why it is mandatory that Math LD students master the use of a calculator appropriate to their academic level.

Since math LD students suffer with directional disorientation, they get extremely disoriented when
doing operations like long division, multiplication, fractions and equations because of all of the computational directions involved.

Again, the math LD student is probably unsure of the meaning of simple math terms like numerator, denominator, product, etc. While the math LD student experiences ease in acquiring information in other subjects, their ability to acquire math information is retarded by poor storage and recall of: math vocabulary, visual-spatial orientation, sequences, operations, formulas and basic facts. For this reason, it is essential that math LD students be practiced in the use of uncluttered reference charts and colorful, illustrated handbooks.

In addition to the difficulties mentioned above, the LD-Math student will verbalize incorrectly and will reason mistakenly without noticing, even about facts and concepts they are sure of. They are unaware of “careless” mistakes made when copying numbers or when writing dictated numbers. They will even on occasion write a different number than they tell you they are writing.

COLLEGE PROGRAM RECOMMENDATIONS: Math LD students should receive a personal curriculum. The required math courses must be replaced by equally rigorous courses within their capabilities. Given their history of limited success in high school math courses taught in small groups with a qualified teacher, it is unreasonable and unrealistic to expect that they will succeed in larger classes at the college level and pace. 

Poor performance in college math courses will significantly impact the grade point average, likely resulting in the loss of standing, scholarships, and other privileges. Such consequences amount to discrimination that is the direct result of a student's severe learning disability in mathematics.

Math memory problems and difficulties with visual-spacial perception and orientation, make
math achievement very difficult. A computer tutorial method has the best chance of success if all
concepts are illustrated with multimedia animation with full redundancy of information displayed
with sound, text, images and motion with a strong emphasis on the concepts, symbols,
vocabulary, syntax and translation of the language of mathematics. 

A program should present information sequentially, in small chunks immediately followed with opportunities to manipulate, prove, apply, practice and master the concepts. Such programs will track progress and mastery of the curriculum and will not allow advancement without requisite mastery. Credit should be given for completion of the established curriculum. All math courses are taken on a PASS/FAIL basis.

TUTORING: Classroom instruction and tutoring by someone unskilled in the treatment of learning disabilities, is NOT advised. Typical instruction will only frustrate the instructors and students alike.
Math LD students need to prove concepts with hands-on applications and linguistic reasoning.
They have limited visualization ability but exceptional verbal reasoning ability, and must strongly
associate math concepts with familiar spoken and written language.

In light of the facts presented above, repeating a failed math class with student tutorial assistance, will not result in efficient mathematical processing in a person with a specific learning disability in mathematics. Even if the dyscalculic achieves procedural success with a tutor, it is very likely that the student will fail the exam because of math memory deficiencies. It is possible for dyscalculics to repeat patterns/algorithms successfully; but knowledge of the supporting facts, processes and reasoning is not stored in memory for future retrieval. This explains why these students can perform well enough with a tutor or teacher or on homework, but then fail examinations miserably.

RECOMMENDATIONS:

(1) All classes involving math, should be taken on a Pass/Fail basis so that math disability does
not penalize and stigmatize the student by severely diminishing the grade point average. 

(2) Unlimited time and use of a calculator and reference handbook on all quizzes and exams.

(3) Utilize multimedia computerized instruction whenever possible to minimize transcription
errors, provide tracking, & allow for review, practice and mastery at the student's pace.

(4) According to Dyscalculia expert, Professor Mahesh Sharma, math instruction should incorporate both of the methods below in this order:  

FIRST: (a) Explain the linguistic aspects of the concept; (b) Introduce the general principle, truth or
law that other truths hinge on; (c) Let students use investigations with concrete materials
to discover proofs of these truths; (d) Give many specific examples using concrete
materials; (e) Have student talk about their discoveries about how concepts work; (f) Then
show how these individual experiences can be integrated into a general principle or rule that
pertains equally to each example. 

SECOND: g.) Reemphasize the general law, rule, principle, or truth that other mathematical truths hinge on; h.) Then show how several specific examples obey the general rule; i.) Have students state the rule and offer specific examples that obey it; j.) Have students explain the linguistic elements of the concept.

(5) REMEDY PAST DISCRIMINATION: Where math classes were taken without accommodations
and failed, remove grade from factoring of grade point average: adjust grade to P (pass) or
F (fail) without grade points, then recalculate GPA.

(6) Use graph paper to organize numbers on the page; use of guides to isolate rows and
columns of numbers; use of colored erasable pens/pencils to color-code operations
(+/-/*/÷) (subtraction=red, addition=black, multiplication=blue, division=green), reference
sheets for math facts, rules, vocabulary, sequences; allow area to illustrate problems; allow
dyscalculic to talk through math processes and reasoning; assign a TA or partner to listen
and look for dyscalculic errors and to provide appropriate correction and direction.

(7) Provide waivers and substitutes to math course requirements in college.

(8) Provide literary or project-based substitutes for math-intensive assignments.

(9) Reduce by 75%, purify/simplify math problems on tests and assignments.

(10) Provide one-on-one testing and instruction whenever possible.

(11) Teach math as a foreign language.

(12) The vocabulary of math must be taught explicitly, reinforced daily, used matter-of-factly,
and synonyms used interchangeably and fluently.

(13) Read children’s math books: write about, illustrate & teach the concepts.

(14) All instructors of a Math LD student should be educated about dyscalculia.

(15) MATH TEST SUBSTITUTIONS: (a) student creates own tests and test keys; (b) student creates a
presentation on the lesson & presents it as a review lesson to the class or to the teacher.

(16) Student should regularly engage in visual-spatial exercises. Some suggestions follow:
     a) Tangoes Tangram Puzzle game
     b) Library of Virtual Math Manipulatives: http://nlvm.usu.edu/en/nav/vlibrary.html
     d) GeoGenius software: http://www.littlefingers.com
     f) KarisMath.com

(17) Math LD students must rely upon their strengths in reading and verbalizing to become fluent in the
language of mathematics.

(18) Math LD students should learn everything with a sensory integrative method. They must 
must employ their strengths in verbalizing to speak about, demonstrate, and illustrate the
concepts simultaneously. Math LD students will not do well with passive learning methods. Even with Cari
teaching the concepts to others, several repetitions of the teaching exercise will be required
for Cari to move the information into long-term memory that is easily accessible for future
recall and application. Periodic repetition over time will be required to facilitate recall. Cari
will require visual supports and visual discrimination training that is tactile with auditory and
verbal components.

(19) Math LD students must assume the role of teacher for themselves. They must do whatever talking, explaining, drawing, building, writing, and demonstrating that is necessary to absolutely convince
themselves of the logical facts they must learn. Then they must convince others of these facts.
While these may seem like daunting orders, we must assume that the dyscalculic will not adequately
retain information for future use unless they achieve deep and experiential learning.
Superficial, quick, passive, rote, one-dimensional presentations of concepts will not be
effective. Where these inferior methods are the only exposure to material, students should
receive accommodations.

(20) Standard accommodations for memory disabilities include: untimed tests, open book
exams, projects substituted for tests, reference charts, heavier weighting of assignments
and review activities, multi-sensory and interactive computer instruction, review and game
exercises; and electronic or oral presentations/demonstrations substituted for tests.

(21) Teaching/learning must occur in a tight framework of properly sequenced scaffolding, as in
the CLSO (concepts, language, symbols, operations) system [see karismath.com], and the
student and instructor must be skilled in the identification and mitigation of dyscalculic
tendencies. Proper methodology must be used and daily exercises performed to achieve a
working mathematical processing faculty. Dyscalculia is essentially a cognitive impairment in
mathematical ability.

 (by Renee M. Newman)