traditional vs. authentic
by Renee M. Newman, Founder, Dyscalculia.org, Published February 26, 2020
Timed, paper tests are inappropriate for LD students. To mitigate processing difficulties, have the student demonstrate mastery actively by creating something of value that can be used to communicate the concepts to others. The student produces a lesson with rich instructional elements: visuals, physical demonstrations, and verbal explanations. The student creates on their own time, and can present live, one-on-one with the instructor, or can submit a video of themselves confidently teaching someone. This way, the student can experience concepts until they understand deeply, and can practice teaching the concepts until they can deliver the ideas with confidence and enthusiasm. This series of exercises will lead to permanent experiential learning that is readily accessible for fluid quantitative reasoning and advanced learning.
Authentic Assessment is the difference between building a circuit and explaining all of its elements and their relationships, versus merely answering questions about circuits. Actually doing a thing to prove that you can do it, is superior to reading about it and then answering questions about what you read. Authentic constructive assessments validate capability, whereas traditional assessments measure the ability to memorize, and are "false proofs" of mastery. Authentic Assessments are often graded with a rubric.
DYSCALCULIA IN THE CLASSROOM
Students experience difficulties in several cognitive areas essential for quantitative reasoning and math learning: The degree of difficulty varies by circumstance and individual.
- visual-spatial perception, processing, and memory
- directional-sequential perception, processing, and memory
- working memory (like RAM in a computer)
- processing speed (like clock speed or operations per second in a computer)
- digit-span / verbal short-term memory (normal = memory of 5 to 7 to 9 numbers or elements in sequence)
- fluid recall of learned facts, rules, and procedures (speed of access and retrieval of stored information)
Manifestations of processing deficits:
- unable to keep up with instruction
- engagement is interrupted when unable to connect new information to existing knowledge
- unable to readily hook new knowledge to prior knowledge due to impaired recall and faulty reasoning
- unconscious number and word mix-ups
- sequencing errors when reading, writing, speaking, thinking, and moving
- recall and production errors when reading, thinking, speaking, writing, and moving
- random sign, symbol, and operation errors
- a result of overwhelmed working memory
- losing track
- and the inability to hold all essential bits of information in mind
- faulty reasoning
- perseveration (the inappropriate retention of an idea)
- attempting problem-solving without complete understanding
- distress and anxiety, due to impaired functioning
- the result of an overwhelmed processor
- unable to handle simultaneous demands for rapid problem-solving
- especially under timed conditions
- task demands compound to exceed capacity and impair performance across domains:
- recall of facts, rules, formulas, and procedures
- visual reasoning
- verbal reasoning
- quantitative reasoning
- translation of quantitative ideas into appropriate words and symbols in thought, speech, and writing
- encoding (communication in spoken and written language)
- overall speed of performance
The dyscalculic student learns differently and must demonstrate mastery actively. If adequately instructed and accommodated in basic math classes, the student can achieve course outcomes and fulfill program requirements.
If the student is not allowed to adequately experience in order to learn and understand deeply, and is not practiced in communicating ideas through creative demonstrations and teaching, they will never acquire fluency in the language of mathematics and will not be able to benefit from standard instruction - thus, they will not meet course outcomes, and will not satisfy program requirements.
Where students have not acquired fluency, but are required to progress through the curriculum, the student must be accommodated with supports, like a calculator and use of instant references and step-by-step examples.
LD students should be given ample time and opportunity for active experiences; to reason aloud verbally and to focus on the language involved; to reason visually with illustrations, graphic organizers, and aids for visual discrimination (masking, isolating, tracking, graph paper for alignment).
LD students need a hypertext syllabus or course schedule that details content with links to excellent resources for experiencing demonstrations, interactions and practice, visualizations and animations, verbal explanations, and opportunities to create,
Struggling students are pulled through the curriculum, without securing foundational skills and functional independence, in spite of interventions. For example, we read the test to students, instead of teaching them to read, we help them do their worksheets, but don't have the time to impart the skills needed to complete the work independently.
Employ appropriate instruction and assessments that fully engage and empower students to learn through ample, authentic and relevant experiences, and to demonstrate functional independence by richly and effectively teaching and producing learning assets.
Students become producers of information, not merely passive consumers.
Students are in control of their learning, instead of being victimized by inadequate and inappropriate methods.
Accommodate the student by doubling the time allowed for learning and course completion.
The student must reason slowly and carefully in order to mitigate unconscious glitches in several areas: visual-spatial-directional-sequential processing; visual discrimination; visual memory; perseveration; fluid recall of facts, rules, and procedures; overwhelmed cognitive load- and the natural mental static, anxiety, and dysfunction that result.
The student must experience and prove concepts by doing, with explicit focus on the language involved (spoken, in print, written). The student must practice until they are confident and capable. Practice in the form of deep experience. Instead of doing 40 problems, explain (teach) how to do 4 while color-coding, focusing on the language involved, explaining the logic, the why and how of procedures.
Timed paper quizzes and tests are replaced with projects and authentic demonstrations of mastery, like the successful teaching of a concept, or the creation of a learning asset. The student can submit a video demonstration of themselves explaining a concept with illustrations, color-coding, rationale, and focus on the language involved (words, symbols, syntax, and context).
STUDENT AS TEACHER:
Lastly, the student must teach the concept successfully and enthusiastically to others, 4 times, using explicit language that is defined and illustrated, and with physical demonstrations, verbal explanations, and examples or illustrations.
The student should produce a durable instructional reference that showcases key ideas with vocabulary defined and illustrated, and the identification and illustration of facts, rules, and procedures.
- Possible forms of communication: study guide, presentation, website, multimedia lesson, movie, animation, book, article, podcast with a visual supplement, poster, etc.
Reasonable and Appropriate Accommodations Justified by Functional Limitations
- To access the curriculum and benefit from instruction, accommodative strategies must be employed that
- lessen cognitive load
- allow for the methodical identification, organization, and interpretation of elements, conditions, and demands
- and allow sufficient time and opportunity to employ specific strategies and tools necessary for accurate problem-solving, translation, and encoding
- The student must experience the concepts in authentic and relevant contexts and must deeply understand all of concepts, language (symbols and words), and images presented.
- The student needs the time and opportunity to
- reason aloud,
- visually isolate and organize - ex. mask, color-code, and annotate
- and illustrate
- in order to accurately identify, decode, and interpret the language of mathematics -
- symbols, vocabulary, syntax, morphology, context
- and visual-spatial-directional-sequential information
Like missed stitches when knitting, failure to readily connect new knowledge to prior knowledge ruins the learning experience. The LD student chronically misses stitches, so has a weak foundation, and achieves only shallow learning. Although they may be able to repeat simple patterns long enough to complete worksheets, later, they cannot readily access the memory, and must relearn because they never acquired deep understanding.
When cognitive load exceeds capacity, working memory becomes overwhelmed, and new information is not processed optimally, thus learning and performance are impaired.
Reduce cognitive load, and thus free up capacity, by physically experiencing, verbally reasoning, visually illustrating, and teaching others.
To mitigate retrieval difficulty, have instant access to references and physical or virtual manipulatives.
To mitigate visual-spatial difficulties, use tools to mask, isolate, organize, track, and align elements.
To mitigate slow processing, supply instructional redundancies (UDL) : teacher notes, video of lectures, step-by-step examples, access to excellent resources that provide background information, prerequisite knowledge. illustrations and demonstrations, and practice exercises.
algebra tiles illustrate binomials