- What is Dyscalculia?
- Who defines dyscalculia and learning disabilities?
- Identifying dyscalculia in the classroom and responses
- Weak Math Learners, Strugglers and Stragglers vs. Math Learning Disabled
- Discrepancy Models in LD Diagnosis
- Dyscalculia Interventions
- RtI / MTSS (Multi-Tier Systems of Support) for Dyscalculia
- Special Education
- Assistive Educational Technology for Struggling Math Students
- Practical Help, Strategies, and Tools for Teachers
- Practical Strategies and Tools for Parents
- Student Resources
What is Dyscalculia?
b. Other difficulties may also be present: Learning Disabilities Checklist
Who defines learning disabilities?
- Specific Learning Disabilities: Definitions and Diagnosis (US DoE)
- How IDEA and ADA (sec. 504) Interact
- ADAAA, 2008 Americans With Disabilities Act
- Disability is a physical or mental impairment that substantially limits one or more major life activities; there is a record (or past history) of such an impairment; or the individual is regarded as having a disability.
- IDEA, 2004 Individuals with Disabilities Education Act (IDEA)
- Specific learning disability is a disorder in one or more of the basic psychological processes involved in understanding or in using spoken or written language that may manifest itself in the imperfect ability to listen, think, speak, read, write, spell, or do mathematical calculations. The term includes such conditions as perceptual disabilities, brain injury, minimal brain dysfunction, dyslexia, and developmental aphasia. The term does not apply to students who have learning problems that are primarily the result of visual, hearing, or motor disabilities; cognitive disability; emotional disturbance; or environmental, cultural, or economic disadvantage.
- State Disability Laws
- Dyslexia Laws by State in the USA (2015) - dyslexia laws are applicable to dyscalculia
- Every Child Succeeds Act, ESSA, 2015
- does not define disability [ NCLD, Impact on SPED] but mandates all students meet rigorous academic standards, prerequisite for college-level courses, and competitive employment (exceptions only for severe cognitive impairments (CI) - even the academic goals for CIs should be challenging and preparatory for work and post-secondary school).
- Mandates: inclusion, Universal Design, MTSS, science-based interventions, specialized instructional support personnel, annual assessments
3. American Psychological Association (APA) in its Diagnostic and Statistical Manual of Mental Disorders
- The DSM-5 (2013) created one overarching category of Specific Learning Disorder with ‘specifiers’ for reading, writing, mathematics.
- After diagnosis, terms like dyscalculia can be used to describe the disorder.
- DSM-V eliminated the IQ-achievement discrepancy requirement
- and replaced it with four essential criteria (A – D):
- have at least 1 of 6 LD symptoms
- persisting at least 6 months despite extra help or targeted instruction
- Academic skills must be well below the average range of scores in
- A. culturally and linguistically appropriate tests of reading, writing, or mathematics, as confirmed by individually administered standardized achievement measures and comprehensive clinical assessment;
- B. and must significantly interfere with academic achievement, occupational performance, or activities of daily living.
- C. onset of problems during the school-age years, although may not fully manifest until young adulthood
- D. must rule out these causes: developmental, neurological, sensory (vision or hearing), or motor disorders, intellectual, mental or neurological disorders, adverse conditions like psychosocial adversity, lack of proficiency in the language of instruction, and inadequate instruction.
Controversy over DSM-V's definition of learning disability.
- Yale University's Opinion: Eliminating terms like dyslexia and dyscalculia in the DSM-V, disregards the respective scientific bodies of knowledge, & prevents respective science-based, targeted interventions.
4. ICD-10 on Math Disorders International Classification of Diseases, Code Book 10 (ICD-10)
IDENTIFYING Dyscalculia in the classroom
- (Video: Dyscalculia Signs & Research)
- cannot keep up with lessons
- uses inefficient and primitive strategies for counting and problem-solving (fingers, tally marks, dots, repeated + or -)
- becomes overwhelmed, tears up, frustrated, anxiety, panic, mental block/ blanks out / can't retrieve learned information
- under-performs in spite of adequate or extraordinary effort and practice
- disorganized: papers, writing, numbers, dots, problem-solving, preparation order of operations, motor planning, etc.
- sequencing difficulties: steps, operations, reasoning, motor planning, manipulatives, speech, recall
- takes an inordinate amount of time to complete work - thinks slowly, works deliberately but with errors
- appears disconnected - not engaged, lost, unable to process and perform as expected
- can repeat patterns, but soon forgets, in spite of typical or extra practice
- accidental number-order and recall errors when copying, writing, reading, speaking, and thinking
- difficulty with time: perceiving and managing time
- difficulty with direction: overwhelmed by directional sequences in arithmetic, changing classes, navigating, geography
- weak pattern recognition, memory and recall; clocks / telling time (visual-spatial weakness, orientation, organization)
- doesn't register all information seen, especially details of fast action (visual processing: speed, perception, processing)
- difficulty repeating demonstrations, difficulty remembering sequences of operations (weak motor sequencing and planning)
- "careless errors": switched operations and signs, borrowing, carrying, alignment, number mixups, omissions, insertions
- loses track when counting, hesitates at pattern transitions (19 to 20),
- can't hold numbers mentally (working memory)
- difficulty memorizing math facts and procedures (inconsistent memory and retrieval)
- easily frustrated or overwhelmed
- avoids math, experiences anxiety
- imperfect retrieval of quantitative information
- limited ability to imagine or visualize abstract concepts or images without seeing them
- lack of number sense, or the ability to estimate or compare quantities
- inappropriately preserves a number, operation, or idea and repeats it erroneously (perseveration)
What to do if you see signs of dyscalculia?
- Keep regular notes on the child's inefficient reasoning, and remarkable performance and behaviors.
- Refer a parent to dyscalculia.org, the dyscalculia checklist, the learning disabilities checklist, and dyscalculia screeners.
- Direct the parent to email the school principal requesting testing for a specific learning disability in mathematics.
- Implement the strategies in Topic 9 below, and keep notes on the results.
- Email Renee Newman with questions.
- Is poor math performance the result of environmental causes?
- Stress at home or school: child cannot concentrate, is distracted, is distressed, lost motivation
- Illness: impaired ability to attend to lessons, missed instruction
- Absences: too much lost instruction, work not made up, missed essential instruction
- Barriers: poverty, lack of transportation, lack of technology, unmet basic needs, lack of home support, language or cultural barriers
Weak Math Learners, Strugglers and Stragglers vs. the Math Learning Disabled
- CAUSES of Math Learning Disorder
- Developmental Math in K-8 vs. Developmental Math at College
- (WV - slides 32-33)
- If dyscalculia affects 6% to 22% of the general population, how many of your students are likely dyscalculic?
- The entire population of students could benefit from the strategies that work with dyscalculic students, since the majority of all studnents struggle with achieving math proficiency.
- Should we try to sort them?
- Not every child has every characteristic of dyscalculia.
- Not all researchers agree on the set of characteristics that describe dyscalculia, and many subdivide dyscalculia into types based on specific skill deficits.
- We cannot always discern the causes of poor math performance (neurological vs. environmental).
- Formal diagnosis is time-consuming and costly in terms of instructional time and staff resources.
- Staff, inexperienced with dyscalculia, are reluctant to attempt diagnosis, instructional planning, or remediation.
- ESSA says all students, even LDs, must meet same grade-level academic standards, and all weak students get intervention.
Discrepancy Models in LD diagnosis
- IQ Score vs. Academic Achievement Achievement Scores (Overall and Specific Skills)
- IQ: Average = 100
- Diagnosing Dyscalculia
- No Evidence that Discrepancy Model leads to accurate LD diagnosis (Kaufmann, p.5)
MONEY TEACHES BASIC NUMBER CONCEPTS
- Tips to address core skill weaknesses in:
- memory, automaticity, sequencing, directional awareness, processing speed, working memory, retrieval, visual-spatial discrimination and reasoning, rules and operations and procedures, auditory processing, articulation, penmanship, fluency, logic, and generalization.
- Remediation (30-minutes per day as RtI or MTSS)
- Money Lessons: Money Teaches Place Value, Base 10 & Basic Math Concepts
- Our Lessons | Number Notes | Halves
- Access to Math
- Best Math Tools
- Place Value Parking Lot with Money - $100-million to Hundredth
EXCITE WITH REAL MONEY
GENERALIZE to PLAY MONEY with KEY NUMBER INFORMATION
- Do not wait to see improvement. Either the child learns with the method immediately or they do not.
- Do not persist with unsuccessful methods or tools.
- (Adults rarely persist for longer than a minute with an ineffective tool or strategy.)
- First validate that the child has all prerequisite skills and knowledge.
- Give accommodations or tools to mitigate the skills he lacks.
- Thoroughly explain and demonstrate a concept by focusing on math language, real applications, and the 6 w's.
- Have the child explain the who, what, when, where, why and how of it.
- Initially offer scaffolding, but have the student independently demonstrate and teach concepts 4+ times successfully.
- If the child cannot achieve independent demonstration, try a different method.
- There is much talk of a growth mindset, persistence in the face of challenges, and development of grit. Develop persistence, and positive attitudes about learning, with effective experiential activities that demonstrate and prove concepts.
- Do this by encouraging students to try different ways of thinking and doing until they find what works for them. No method works for every child. If a method does not work, it does not mean the child cannot learn; it means the child must LEARN DIFFERENTLY.
- The teacher and student must persist until they find the keys to understanding and performance.
- Be careful not to discourage students by insisting they persist at ineffective practices that result in frustration, failure, anxiety and avoidance.
RtI / MTSS (Multi-Tier Systems of Support)
Learning Disabled in Mathematics - Reasoning and or Calculation: identification and treatment
What does US Federal Education Law say about Specific Learning Disability?
- Dyscalculia.org's Legal Docs Folder (Fed files are in this folder)
- Eligibility for Special Education and Response to Intervention Services
- Federal DOE Guidance on Dyslexia, Dyscalculia, & Dysgraphia and IEPs (Oct. 2015)
- Federal DOE Guide: IEP Goals Must Align with the Current Grade-level Content Standards
- Video US. Dept. of Special Ed & NCLD: Using dyslexia, dyscalculia, & dysgraphia in schools.
Assistive Educational Technology for Struggling Math Students
Practical strategies & tools for teachers
Strategies to address dyscalculia in the classroom with individualized instruction and best-practices:
- Give parents a schedule of lessons with examples and resources
- Reduce number of practice items
- Meet with child before or after school to preview lesson
- Get to know each child's interests & talents and relate to those when teaching. (differentiation)
- Assign a game to teach or practice the skill or prerequisite skills (see FIX, Tools)
- Penmanship problems: students get digital version of textbooks, e-exercises, e-assessments, projects vs. written assignments
- Use ModMath app or other digital math environments to mitigate bad penmanship.
- Also assign apps to practice formation of numbers and symbols.
- Require students to color-code operations (red-subtract, green-add, blue-multiply, black-divide)
- Require students to use graph paper to align columns and rows of numbers, and to illustrate work.
- Require students to use a ruler or card to isolate numbers to reduce errors when copying and reading.
- Explicitly teach strategy for decoding decimal numbers (head = decimal point, stronger right is for parts, weaker left = wholes)
- Explicitly teach place value (parking lot, base 10).
- Explicitly teach conical pattern recognition (dice).
- Explicitly teach counting and fact families using conical patterns, and discourage use of fingers.
- See our video lessons linked in the V-A-L-U-E Table in the middle of the Money page.
- Examples: #2 Count from .01 to .25 (video) | #21 Count by 5s to 100 (video)
- Deliberately teach the language of mathematics.
- Example: Cap=head, capital, per capita, capitalization, captain, capture, captor, captive, captivate, capitalism, capable
- Professor Mahesh Sharma's IDEAL MATH LESSON PLAN
- Chunk information into small bits, and build with them (facts, steps); creatively relate new to known.
- Allow an overwhelmed student to take a time-out for physical activity, resume later with instructional scaffolding
- Universal Design: Instructional redundancies- visual illustrations & demonstrations (print + video), text and oral explanations (audio), physical practice / student demonstrates and teaches concept (activity), documentation (journal, movie).
- Offer video or static illustration of steps that can be reviewed as often as necessary to gain understanding.
- When checking papers, avoid discouraging red marks and lack of explanation.
- Write encouraging notes explaining errors and offer strategies to increase accuracy.
- Failure: discretely record results in a bottom corner and put "see me."
- Allow use of multiplication or fact charts, handbooks, and references to mitigate memory and retrieval problems.
- Talking calculators provide extra aural feedback of entries to help catch mistakes.
- Teach student to use any calculator, app, tool or program (ex. Kidspiration) proficiently.
- Encourage students to reason aloud and talk through problem-solving and arithmetic.
- Have student articulate transitions & rationale for action; deliberately point out what to watch for.
- 1:1 Assessments for severe students to observe & point out unconscious errors & offer strategies to increase accuracy.
- Organization: color-code classes & supplies; schedules on top of all books; directions to next class; time; locker combo; plan.
- Substitute activities for worksheets: demonstrating expedites problem-solving, use illustrations or money to visualize.
- Allow use of money to visually reason through problems & mitigate retrieval difficulties with rules, operations, and procedures.
- Teach cardinal directions; develop directionality with the sun, maps, geography & navigation games; illustrate procedures.
- Teach time: telling, visualizing; use visual timers & clocks (color clock); planners / calendars; task analysis & estimation.
Practical strategies & tools for parents
- Manage It | Conquer It | Fix | To Do | Remediation | Accessing Math | Appreciating Math | Best Math Tools
- Pattern Recognition: Decimal Stack 1 & 5
- Conical Patterns - Dots, Dice, Dominos
- Chunking in Conical Patterns when counting, organizing, thinking, visualizing, adding, subtracting, multiplying, dividing.
- Language: morphology
- Using money to learn K-8 math concepts
- Teaching the language of mathematics - Focus on Developing Math Language Competence
- Math Terms Menu Poster
- Aggregate and Disaggregate (Halloween Candy Theme)
- Prefix UNI- means 1 (Trace and Talk)
- Prefix bi- means 2 Word List Practice (Trace and Talk)
- Prefixes Dec-, Deca-, Deci- (10, tenth) Illustrated [36 pages]
- Prefix DEC- 10 [18 pages]
- Prefix Cent and Half (Cent- Words Illustrated, Halves Illustrated, .05 to half-trillion)
- Math Lessons
- Number Prefixes & Symbols
- Appreciating the world of mathematics