Développement cognitif de l'enfant

Introduction to Dyscalculia

• Dyscalculia is a specific learning disability focusing on mathematical cognition.
• Less widely known than dyslexia, it emerged later in research.
• Affects approximately 6% of children, similar to the prevalence of dyslexia.
• Exclusively impacts mathematical skills, unlike other learning disabilities which affect multiple areas.
• Current research emphasizes the role of cognitive processes in mathematical difficulties, rather than just calculation.
• Cognition encompasses all brain activity in reflection and information processing. It includes mental operations used in understanding, learning, and problem-solving.

Who are Children with Mathematical Difficulties?

• DSM-5 Criteria:
  • Difficulty accessing the meaning of numbers: Difficulty linking a number to the corresponding quantity (e.g., understanding that "36" represents 36 objects).
  • Difficulty constructing the number sequence.
  • Lack of mental representations: Constant need for concrete supports to grasp concepts.
  • Issues understanding statements: Related to poor oral language, vocabulary, or sentence structure.
  • Anxiety about mathematics: Leads to avoidance of the subject.
• Diagnostic process: Oral and written language tests are routinely used to eliminate other potential causes of difficulty.

Key Components of Mathematical Abilities

• Semantic domain: Understanding the quantitative value of numbers, accuracy decreasing with larger numbers.
• Approximate Number System (ANS): Natural ability to roughly estimate quantities. ANS underdevelopment is common in dyscalculia.
• Logical operations: Include skills like seriation, classification and logical reasoning.
• Symbolic system: Understanding that numbers are arbitrary symbols that need to be interpreted.
• Positional system (base 10): Understanding the progression from units to tens.
• Arithmetic operations: Skills in addition, subtraction, multiplication and division.
• Arithmetic problems: Ability to analyze and solve complex problems.
• Related domains: Language, memory, executive functions, and visuospatial reasoning also play a crucial role.
• Types of dyscalculia: Primary (limited to mathematical cognition) and secondary (linked to underlying issues like language or attention).

How to Diagnose and Treat Dyscalculia

• Standardized tests: Used to compare performance with a control group.
• Qualitative and Quantitative analysis : Identify specific weaknesses.
• Diagnostic process: Exclusion of secondary causes to confirm primary dyscalculia.
• Planning: Establish short- and long-term objectives based on assessment results.
• Collaboration: Involve parents, teachers, and other professionals.
• Evidence-Based Practice: Using scientific evidence for interventions.
• Individualized interventions: Tailored to the specific needs of each student.

Cognitive Models of Number Processing

• McCloskey model: Describes how humans understand and use numbers symbolically. It includes:
  • Oral input: Number is spoken.
  • Visual input: Number is shown as Arabic numerals.
  • Comprehension and Production: Understanding and expressing numbers symbolically.
  • Verbal system: Syntactic (order of words/numbers to convey quantity) and lexical (written/spoken number names).
• Phonological system: Invented words to orally name numbers
• Arabic number system (Lexical): Specific number classes (units, tens, etc.).
• Syntactic System: Order of digits determines value.
• Semantic representation: Clear idea of quantity.
• Procedural knowledge: Steps of calculations
• Storage for basic arithmetical facts: Memorization.

Models for the Development of Numerical Skills

• Von Aster & Shalev Model: Focuses on stages of numerical development.
• Analogical representation of quantity (pre-school): Subitizing (rapid quantity recognition), approximating and comparing quantities
• Verbal system (preschool): Counting, oral number skills
• Arabic code (early elementary): Learning written number and calculation skills
• Numerical line (mid-elementary): Using the mental representation of a line to solve problems
• Various additional concepts: Size/separation, distance/spatial, sequence/order and magnitude.

Application and Practice

• Testing: Use the funnel principle for assessing numerical line skills.
• Remediation: Address specific weaknesses directly.
• Comorbidities: Evaluate the presence of other conditions (e.g., language issues).

Classifications and Categorization

• Classification: Grouping items with common attributes. This includes various types and ways of classifying elements (disjoint, overlapping sets, classes included within other classes).
• Development Stages:
  • Sensory-motor
  • Preoperational
  • Concrete operational
  • Formal operational

Serial ordering and Construction

• Important for many everyday tasks (e.g., sorting clothes).
• Underpins logical structures.
• Transitivity: Understanding relationships between elements (if A<B and B<C, then A<C).

Important developmental stages.

Conservation

• Understanding that quantity remains constant despite changes in appearance (e.g., a ball of clay that is flattened).
• Stages of development.

Types of Quantities

• Continuous (e.g., weight, length).
• Discontinuous (e.g., countable objects)
• Importance: Critical for strong mathematical reasoning.
• Development progression.

Inclusion Principle

• Understanding that a set can include subsets. (e.g.: within 10 are 1, 2, 3, 4...)
• A fundamental concept in subtraction.
• Important for understanding number relationships.

Additive Decomposition

• Strategies to make calculations easier by breaking down numbers into smaller parts.

Arithmetic Operations

• Addition
  • Properties (commutative, associative, identity element)
  • Strategies (manipulation, counting, memorized facts)
  • Common errors
• Multiplication
  • Properties (commutative, associative)
  • Strategies (repeated addition, memorized facts)
  • Common errors
• Division
  • Concept of equal partition
  • Strategies (mental calculation, written procedures)
  • Common errors

Problems in arithmetic

• Problems with phrasing influence problem understanding.
• Problem type variations (change, combination, or comparison).
• Unknown elements.
• Operations that are needed for completing the problem.

Cognitive Functions Involved in Math

• Perception: receiving and registering information
• Memory: working memory (manipulating info) and long-term memory (storing facts)
• Comprehension: decoding written/spoken language
• Reasoning: using logic and explanations
• Other executive functions

Resolution and Control

• Self-checking: comparing the desired outcome with the obtained response
• Error identification and prevention
• Support tools for struggling students

Types of Arithmetic Problems

• Change problems (initial state and change of state)
• Comparison problems (relating two quantities).
• Combination problems (finding the total quantity)
• Equalizing problems (adjusting one quantity to equal another)
• Proportional simple: Problems like finding the unit value and multiplicative comparison.

Specific Difficulties and Symptoms

• Problems with numerical sense/estimation
• Problems with numerical patterns
• Difficulty with counting strategies
• Poor mental processing
• Weak concept of place value

Math Anxiety

• Fear and avoidance of mathematical tasks.

Rationale and Impact

• Impact on math performance (classroom, academic, and life situations)
• Impact on overall learning
• Long-term consequences: Affects future opportunities.

Dyscalculia

• Definition and characteristics
• Prevalence and neurodevelopment considerations
• Symptoms and associated difficulties
• Diagnostic criteria and considerations

Formal System of numbers

• Historical perspective on number systems
• Principles of a system based on base-10
• Understanding the role of place value in a base-10 system.
• Explanation of Arabic numeral system.
• Different types of calculation: verbal, arabic number systems, etc
• Importance when dealing with larger numbers.

Ce quiz explore les différentes étapes du développement cognitif chez l'enfant, y compris la classification, la conservation et la sériation. Les questions abordent les âges clés et les capacités essentielles à chaque stade. Testez vos connaissances sur la manière dont les enfants développent leur compréhension numérique et logique.