College & Dyscalculia

Remedial Students Have Poor Graduation Rates

Unfortunately, the fast pace, large lecture format, and labs with peer support, are rarely sufficient to close the skill gap. The dyscalculic is forced to repeat the remedial courses in the hopes of moving forward, but ends up running into trouble when repeated failure devastates the GPA and results in inadequate academic progress, academic probation, and ineligibility for financial aid and scholarships. Payment for remedial courses also uses up limited financial resources, and results in significant debt accumulation when student loans are used.

Dyscalculia or math learning disability/disorder will prevent you from meeting minimum quantitative reasoning requirements at the college level. For liberal arts majors, this usually means passing a class in College Algebra or Finite Math. Because a dyscalculic student will test into remedial math classes on placement exams, they will be directed to non-college-level refresher courses, like Math 085, Elementary Math Concepts; and Math 095, Pre-Algebra and Elementary Algebra.

The math skills of most adults with dyscalculia are arrested at the 4th grade level; but even when testing at 4th grade, almost all will demonstrate deficient first, second, and third grade skills. At grades 1 through 4, the adult usually knows what to do, but gets problems wrong because of "careless errors." The dyscalculic is not being careless, however, because the dyscalculic has no awareness of their processing problems. These processing errors affect visual-spatial input, auditory input, and touch input.

Like with color blindness and the inability to see or perceive specific color differences, the dyscalculic sees fine, but the brain does not process quantitative information accurately. This results in baffling, frustrating difficulties. A dyscalculic may not be able to add a column of numbers and get the same answer twice because the mind changes the numbers, unbeknownst to the dyscalculic.

The dyscalculic may not process auditory quantitative information accurately, and may not even process tactile quantitative information accurately. Some dyscalculics have difficulty discriminating the difference in size between coins and other objects, and have difficulty comparing groups of items to determine which contains more or less.

The processing glitches present as output errors in counting, decimal point and number alignment, lack of place value awareness, faulty recall of math facts, mixed up and missing signs and numbers, directional confusion during operations, inappropriate preservation of ideas, random number insertions, and abandoned processes.

During processing, working memory is slow and insufficient, the mind switches inputs, acts on erroneous information, omits important information, loses track of operations, confuses sequences, is ambiguous about patterns and the association of meaning to symbols, and blanks out.

The result is a student who is consumed with frustration, anger, and anxiety over the consequences of their inability to perform as expected. An anxiety or panic attack may ensue. After extended traumatic experience with math, the dyscalculic will hate it, avoid it, and may experience an anxiety response at the thought of having to perform.

Because the dyscalculic student can usually perform adequately in all areas except mathematics, they are prone to disgust and disbelief at their mysterious inability to demonstrate math competence. They will attempt to succeed through heroic persistence and determination. After all, they usually excel at reading, writing, and speaking, and most learning tasks come easily. While a positive attitude, diligence, and investment of inordinate time got them mercy grades through elementary and high school math, it rarely works in college. The dyscalculic is stonewalled because professors cannot give grades for effort, and must grade solely on independent, summative exam performance.

See Complete College America's report on dismal college completion rates for students who test into remedial classes.

Remediation, Higher Education's Bridge to Nowhere (2012).

What can be done?

    1. Waive remedial and required quantitative reasoning (QR) courses.
    2. Substitute courses that teach appreciation for quantitative reasoning and the greater world of mathematics, but do not require math calculation and memory of operations. Dyscalculic students can successfully write, speak and create concrete demonstrations of mathematical ideas, and can learn the language of mathematics, but cannot successfully and independently perform on cumulative exams involving calculation. College Examples
    3. Pursue alternate paths to satisfy the College Algebra requirement and allow the use of just-in-time references during exercises and tests or substitute constructive assessments (projects/products) for exams.
    4. Make math accessible to dyscalculic students.
    5. Allow Pass-Fail grading for all courses involving quantitative reasoning.
    6. Substitute constructive assessments for paper exams that measure math skills. The same elements measured by an exam, are measured by a project, which is graded with a rubric. The student creates a product which demonstrates deep understanding of all of the concepts covererd by the exam: vocabulary, concepts, rules, and procedures, and includes the "what, when, where, why, and how" with color-coding and illustrations. The product should be of use to others: a study guide, video demonstration, presentation, graphics, website, e-lesson, or book. Constructive assessments are created outside the classroom and are submitted for evaluation.

Facts to share with the Disabled Student Services Office

Developmental Dyscalculia (Specific Learning Disability in Mathematics, or Mathematics Learning Disorder) Diagnostic code: 315.1

DIAGNOSIS

A comprehensive assessment includes a complete educational history, standardized intelligence and academic achievement tests, personal interviews, and a psychological battery.

A Student meets the criteria for a diagnosis of dyscalculia, AKA specific learning disability in mathematics, when:

(a) Student consistently performs well average or above average on reading and writing tasks, and well below average on math tasks, and

(b) deficits are specific to sequential math memory, math working memory, math fact recall, mathematical reasoning and problem solving, math calculation, and general storage and fluent retrieval of practiced math skills; slow and insufficient working memory; and

(C) deficits are not due to inattention, illness, insufficient interest or motivation, anxiety, educational gaps, poor instruction, poor study skills, socio-economic circumstances, or other environmental causes.

ATYPICAL BRAIN

Research has proven developmental dyscalculia results from cortical abnormalities in regional neural organization in the left angular gyrus, particularly a reduction in grey matter in the left intraparietal sulcus; whereas acquired dyscalculia results from brain damage (stroke, injury, etc.)

PROGNOSIS

Student cannot overcome these cognitive impairments with typical approaches like tutoring and studying harder, alone, as these cannot lead to permanent math learning, math memory, and math facility.

While the MLD student may be capable of executing guided practice, and demonstrating mastery through extended exercises; the dyscalculic is incapable of consistent retention of math material in long-term memory, and must relearn the concepts at each attempt.

The dyscalculic can learn of the nature of their mental glitches and the errors that result. They can utilize tools and strategies to minimize the impact of these cognitive inefficiencies and mistakes of speech, reading, writing and demonstrating quantitative ideas. They cannot, however, eliminate the condition entirely, or control the natural stress response that occurs when diligent effort does not result in success.

ACCOMMODATIONS

Given a dyscalculics limitations, it is only reasonable to require:

(A) waiver of the math courses that require calculation and for which the dyscalculic is developmentally unprepared; AND / OR

(B) substitution of required math classes with courses that expose the dyscalculic student to math concepts, math language, math history, and math literacy, without the need for exercises and exams involving calculation; OR

(C) constructive assessments to measure a dyscalculic's understanding of required math concepts, as opposed to typical instruction, practice, and exams. The instruction must be developmentally appropriate (modular, student-paced, prerequisite skills dictate content, student can reasonably complete all topics in the alloted time, a pretest indicates the student has the foundation to benefit from and advance through the curricculum).

Option A

If the required math courses are not integral to the degree, the university may elect course waivers and substitutions.

Option B

Substitute a Math Literacy or Math Appreciation course for College Algebra. For examples, see

the courses listed below. College Examples

(1) Introduction to Mathematical Thinking by Dr. Keith Devlin, Stanford Univ. via Coursera

(2) Learning How to Learn by Dr. Barbra Oakley, Univ. of California-San Diego via Coursera

(3) Math Appreciation

(4) Overview of Statistics

Option C

Most colleges do not have a course, or even a series of courses, that take a dyscalculic student through mastery of fourth-grade math content (multiplication, division, fractions, decimals, etc.), all the way through college algebra. Even if a series of comprehensive review courses exist, the college lacks instructors and tutors, trained in dyscalculia and the specific strategies and methods needed to successfully teach the disabled learner.

It is unethical to force students to take a series of remedial courses, for which they are developmentally unprepared. Repeated failure results in student debt, GPA devistation, scheduling ineligibility, barriers to academic progress in the course of study, and puts financial aid, academic standing, scholarship and job eligibility in jeapordy. It is also frustrating, depressing, and demoralizing, and can lead to health problems and drop-out.It is unethical to require College Algebra for graduation for a math-learning-disabled student.

It is unreasonable to expect that a college can remediate a disabled student's significant math deficiencies in a fast-paced, large-class, independent-learner format, given failure of 12 years of daily, slow-paced, small-group, circular, supported instruction by certified teachers.

Where pretesting demonstrates that the student is developmentally ready to benefit from the course material and the instructional format, it may be appropriate for the dyscalculic student to cover required course material in a programmed format with with essential features. The math program tracks exposure and practice; requires demonstrated mastery of perquisite skills before introducing new concepts; does not require performance on a cumulative final assessment; is student-paced; has just-in-time help for vocabulary definitions and concept demonstrations; provides instant feedback; has ample scaffolded practice until independence is achieved; has instant interactive tools for visualizing, measuring, calculating, and converting; allows drag-and-drop; has graphic organization tools for aligning numbers, grouping, highlighting, and color-coding elements, operations, and like-terms; and contains instructional redundancies (audio, visual, and kinesthetic).

Full course credit should be given for complete progression through the established curriculum, on a pass-fail basis (not calculated into GPA).

California Law, Fall 2019

Assembly Bill 705, requires community colleges to maximize the likelihood that students will complete college-level Math and English within 1 year by instituting these recommendations from Complete College America:

    1. reduce the number of required remedial/developmental/non-college-level math courses
      • compress all into 1 comprehensive course;
    2. offer simultaneous enrollment in college-level math and supplementary math;
    3. substitute Statistics for College Algebra for liberal arts/humanities majors;
    4. customize curricula to each program of study; and
    5. offer modular courses, divided into discrete math competencies.
ALEKS course progress pie

ALEKS

The ALEKS program used by the University of Wisconsin-Madison for distance education and independent learning, attempts to use AI to assess student mastery and to only present new concepts when a student has the prerequisite skills. It is modular, and uses visual feedback to track progress and motivate students.

ALEKS Higher Ed Success Stories

ALEX Frustration: Students with dyscalculia experience frustration when periodic cumulative testing resets their progress because they have forgotten "learned" concepts. For example, a student may have mastered 100% of the content on fractions.The student may miss some questions on fractions on a random pop-quiz covering mastered material. Students become discouraged when their colored pie slice for fractions, now indicates 80% instead of 100%. The student must relearn the forgotten concepts.

Dyscalculics are daunted, frustrated, and aggravated by frequent forgetting of learned facts and procedures, inconsistent recall, impaired math reasoning, visual-spatial-sequential confusion, and occassional number mixups when reading, thinking, and writing.