College & Dyscalculia

California Law to Increase College Completion (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

ACCOMMODATIONS

Given a dyscalculic's limitations, it is only reasonable to

(A) Waive college algebra and all remedial and prerequisite math courses for which the dyscalculic is developmentally unprepared and academically incapable. If the required math courses are not integral to the degree, the university may elect course waivers and substitutions.

AND / OR

(B) Substitute- in place of college algebra and traditional "remedial or developmental" refresher math courses- a UDL practical universal math literacy course.

Developmentally appropriate instruction should utilize tools that minimize cognitive load and demand for rote and procedural fluency. Instruction is modular, student-paced, skill and deficit driven. with practical experiences and exercises that result in deep understanding and which the student can reasonably complete in the time allotted. As students demonstrate mastery of objectives, a permanent seal is earned, which allows for course interruption and resumption.

(C) Authentic Assessments (AA) replace traditional cumulative, timed assessments. Students actively, dynamically, and creatively demonstrate (teach) the concepts being measured. The instructor establishes the topics, criteria, and grading rubric for the project. The student chooses how to teach or demonstrate the key concepts (e-submission, live demonstration, explainer video, illustrated guide, etc.). Focus is on key language and the who, what, when, where, why, and how. AAs are used in all instances requiring quantitative reasoning and calculation. Extra time may be needed to accommodate slow processing and the creative process. LD students usually require additional time to progress through the curriculum.

Accommodation Option B - SUBSTITUTE FOR COLLEGE ALGEBRA & REMEDIAL MATH

2-PART MATH LANGUAGE FLUENCY COURSE

A series of two or combination of 2 UNIVERSAL PRACTICAL MATH COURSES designed to satisfy the Quantitative Reasoning (QR) Breath and Depth Requirements for a non-STEM Bachelor degree.

UDL Universal Math Literacy or Math Appreciation course outcomes:

  • Student will successfully teach decimal system basics, numeration, digits, and recognizable number patterns.

  • Student will explicitly teach logical verbal reasoning and model LVR for decoding, interpretation, reasoning, translation, and encoding.

  • Student will independently demonstrate the use of a full SI place value chart to orient to the decimal point, identify the unit, and to successfully interpret visual-spatial, directional, sequential information.

  • Student will independently demonstrate the use of a full SI place value chart to readily perform conversions among monetary units.

  • Student will independently demonstrate the use of a full SI place value chart to readily perform conversions among metric units.

  • Student will demonstrate all metric units of measurement.

  • Student will demonstrate common US units of measurement.

  • Student will demonstrate conversion between metric and US units with the use of apps.

  • Student will consistently demonstrate the use of maps, diagrams, and other visual-spatial aids, to establish. locaton, directionality, orientation, organization, movement, and sequencing.

  • Student will demonstrate practical strategies and tools for visual-spatial awareness and orientation.

  • Student will demonstrate competency in planning and executing navigation in a variety of situations.

  • Student will demonstrate math language fluency through the efficient use of digital and tangible full SI place value charts, Dyscalculia Stack of SI Money (Dysc$), and apps to visually organize, experience, model, manipulate, reason, calculate, document, and demonstrate understanding and problem solving with negative and positive integers.

  • Student will demonstrate math language fluency through the efficient use of a complete SI digital and tangible place value chart, Dysc$ money, and apps to model fractions, decimals, mixed numbers, and equivalency, and to problem-solve and manipulate fractions in multiple forms.

  • Student will use Dysc$ money to model numeration, number, decimal system relationships, and to perform operations (addition, multiplication, factoring, division, subtraction) to solve practical relevant problems in context.

  • Student will use Dysc$ money to model ideas and relationships represented as equations, addition and multiplication facts, digits, and metric and US unit conversions, across the SI decimal chart.

  • Student will use Dysc$ money to model properties, rules, order of operations, and algebraic principles.

  • Student will consistently solve algebra problems using digital tools: Goegebra, Algebra Touch, DragonBox Algebra, MathWay, PhotoMath, OneNote, and MathType Extension in Google Docs.

  • Student will demonstrate expedient access to math references for concept illustrations, demonstrations, and interactive tools, using MathAntics, and MathIsFun.

  • Using canonical number patterns and kinesthetic strategies, student will fluently mentally combine, subtract, divide, multiply, and will retain the result long enough to communicate it in speech or writing.

  • Student will demonstrate the fluid ability to reason about and figure with fractions, percents, tips, taxes, discounts.

  • Student will demonstrate math language fluency by efficiently expressing any number in a variety of ways: Unit identification, Spoken Words, Written Words, Standard Notation, Scientific Notation, Prime Factorization, International System Prefix (SI), SI Symbol, Model with Dysc$ Money, Expanded Notation, Equivalents (Unit Conversions), Equation, Algebra, Fraction, Mixed Number, Decimal, and Percentage.

  • Student will explain 3 historical facts about mathematics in context, with impact on culture, science, and philosophy.

  • Student will always explain the context, practical utility, and personal relevance of math concepts.

  • Student will explicitly and consistently demonstrate and employ visual references (maps, diagrams, illustrations), graphs) to contextualize information about location, position, direction, action, distance, and to make predictions.

  • Student will consistently utilize visual resources (ex. maps) to establish context and to annotate, establish the facts, orient to the situation, and determine how to problem-solve.

  • Student will explain the naming logic for each period (section) of the full decimal place value area covered by the International System SI (metric system).

  • Student will be able to fluently create and label the 19 periods (main sections) on the SI decimal place value chart, and will include rows containing the period and column word labels, powers of 10, prime factorization, SI prefix, other common prefixes, SI symbol, number, and a word that exemplifies the place value location (ex. megawatt, nanogram).

  • Student will demonstrate the functional use of math affixes, symbols, vocabulary, syntax, and decimal system encoding (numeration, place value, the International System Prefixes and SI symbols, equations, graphical representations, and basic decimal system patterns.

  • Student will demonstrate the ability to fluidly use the SI Decimal Place Value Chart to convert metric units between the maximum and minimum values represented in the 53 columns ,or value places, covered by the International System.

  • Student will always concretely experience and demonstrate math concepts with Dysc$, chart, or other means.

  • Student will first experience concepts and prove truths concretely, while describing with appropriate language, before representing ideas mathematically (symbolic expression becomes intrinsically associated with the ideas represented, and "rules and procedures" are logical extensions of demonstrations).

  • Students will immediately teach or share a mastered idea with others, >three times (with talk of context, relevance, concrete demonstrations, symbols, written language, and illustrations).

  • Student will demonstrate mastery of the language of mathematics in spoken and written forms by successfully decoding, interpreting, reasoning, evaluating, translating, and communicating (encoding in speech, concrete active demonstrations, illustrations, and written forms) quantitative information randomly accessed from a variety of domains (science, news, travel, finance, statistics, civics, business, trades, culture, etc.)

  • Student will confidently interpret numbers between 10^26 to 10^-26 culled from the news.

  • Students will perform metric unit conversions without arithmetic using the Full SI Decimal Chart.

  • Students will solve math problems using verbal reasoning without manual computation (ex."The famous centenarian lived just 2 years after her milestone. She lived to be 102.").

  • Students will confidently and competently perform activities of daily living: handling cash, banking, shopping (discounts, sales tax, rebates, tips, insurance, warranties, cost of ownership, incentives, interest, closing costs, penalties, points, bonuses, tax write-offs, investments, stock trading, savings, and taxes - sales, property, income, luxury, probate, estate, inheritance, and capital gains).

  • Students will demonstrate financial literacy and critical thinking with adequate interpretation, research, comparison, consideration of multiple variables, and intelligent decision-making on these scenarios: marriage-work-childcare; housing; transportation; savings for education, retirement, investment, emergencies, gifts, charity, investments, business, major expenses; family budget; and starting a business.

  • Student will perform bookkeeping functions, budgeting, and accounting, for an individual, family, and small business.

  • Student will solve practical geometrical problems involving: building planning, measuring, calculating, estimating, purchasing, installation, systems (flooring, wall coverings, floor coverings, roofing, plumbing, electrical, tile, heating and cooling, storage, appliance capacity and load, furnishings, landscaping, driveways, sidewalks, steps, doors, windows, insulation, lighting, security, communication and security systems, and the use of tools to perform work.

  • Student will solve healthcare problems involving consideration of multiple variables: medication dosing and dosing calculations and conversions based on age and weight; ideal vs dangerous health metrics (blood pressure, weight, heart rate, oxygen level, BMI, blood sugar); obtaining health insurance coverage for an individual and a family; managing healthcare (premiums, disease, accidents, illness, preventative care, prescriptions, planning for expenses, copays, deductibles, out-of-pocket expenses, reimbursements, health spending accounts, matching, incentives, penalties, elective vs necessary care, experimental vs standard care).

  • Student will competently interpret statistics and communicate using statistics on current events: pandemic reporting, measures of intelligence, brain function, and academic achievement.

  • Student will competently solve a variety of occupational problems involving research, documentation, and consideration of multiple variables: cost of education and training, cost of living, compensation and related benefit and expense scenarios, taxes, fees, aid, debt, and budgeting.

  • Student will competently solve a variety of functional problems involving needs assessment, research, documentation, and consideration of multiple variables: cost of obtaining transportation and attendant costs, (down payment, interest, lease, fees, mileage, insurance, tax incentives, rebates, credit costs, taxation, licensing, registration, traffic infractions, credit rating, and cost-benefit analysis.

  • Student will plan and demonstrate behavior that results in building a favorable credit rating, and will explain the components of credit ratings, and qualitative and quantitative consequences of rating classifications.

  • Student will document intelligent shopping for common communication and productivity equipment and services: cell phones and mobile plans; internet; infotainment; software and apps; computers; televisions; security systems; GPS and navigation; smart home systems.

College Examples of Substitution of College Algebra and Remedial Math Solutions

(1) Michigan State University Eliminates Remedial Math - 2018

(2) Wayne State University in Detroit Eliminates Math Requirement - Inside Higher Ed 2016

(3) Retooled Courses Help Students Avoid a Remedial-Math Roadblock to College - EdWeek 2018

(4) Carnegie Math Pathways - Quantway 1 - Quantway 2 - Statway - Online 2020

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

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

(6) Math Appreciation

(7) 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 devastation, scheduling ineligibility, barriers to academic progress in the course of study, and puts financial aid, academic standing, scholarship and job eligibility in jeopardy. 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.

Remedial Students Have Poor Graduation Rates

80% of remedial math students, fail to pass college math within 3 years (Community College Research Center, Columbia University, 2010)

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 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.

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.

Dyscalculic learners experience frustration in ALEKS when once-mastered concepts (indicated by progress on the pie chart) is lost on assessments that spiral back on learned concepts. Students lose momentum and confidence when their progress indicators reset and show that they must relearn once mastered material.