Task 3: Summary of the Progression of Learning Mathematics document

The following is a list of the other subject areas that have learning progressions: English Language Arts, Francais (langue seconde – Programme de base), Francais (langue seconde – Programme d’immersion), Mathematics, Science and Technology, Geography, History and Citizenship, Drama, Visual Arts, Dance, Music, Physical Education and Health, Ethics and Religious Culture (

Structure[MK1] of the Document:

  • The document is divided into 6 sections: Introduction, Arithmetic, Geometry, Measurement, Statistics, Probability, and Examples of Strategies
  • Helpful for lesson planning as it shows when the mathematical topic/concept/skill should be introduced, how it progresses over each cycle, and the point at which it should be mastered.
  • Document provides clear links to the content taught in each grade and cycle
  • Document shows a gradual development of learning. For example, in cycle 1 students learn to count numbers that are less than 1000, in cycle 2 students learn to count numbers that are less than 100,000, and in cycle 3 students learn to count numbers that are less than 1,000,000
  • Introduction:
  • Strong numeracy skills can be developed through the effective use of all the concepts outlined in the Quebec Education Program (2001) and the Progression of Learning Mathematics (2009) document, which is a complementary document to the Quebec Education Program (2001)
  • Progression of Learning Mathematics (2009) document “provides additional information on the knowledge and skills student must acquire throughout elementary school with respect to arithmetic, geometry, measurement, statistics, and probability” (pg. 3)
  • Five Strands:
  • The aforementioned five content strands are addressed separately within the document in the following order: arithmetic, geometry, measurement, statistics, and probability.
  • “Each strand covers the knowledge to be acquired as well as the actions to be performed in order for student to fully assimilated the concepts presented” (pg. 3)
  • The 5 sections (one for each content strand) include the following information:
  1. Introduction
  • An overview of the progression of learning
  • Helpful suggestions. For example, in the Arithmetic section, the authors note that “care must be taken not to progress too quickly from one concept to another” (pg. 5)
  1. Content tables
  • Divided into topics and specific expectations corresponding to each topic. For example, “Natural numbers less than”, a topic within the Arithmetic Strand, is comprised of 14 specific expectations.
  • Mathematical symbols and vocabulary are included at the end of each topic after the specific expectations. Vocabulary and symbols are grouped based on the cycle and grade in which they are introduced and applied.
  • Left Column of the table  topics and corresponding specific expectations
  • Right column of the table  divided into three cycles and six grades.
  • Tables show gradual development/progression of learning with arrows, stars, and shaded boxes. The arrows indicate when a concept/specific expectation is introduced and when students construct knowledge with teacher guidance. The stars indicate when a concept/specific expectation is applied. The shaded boxes indicate when a student is required to recall and use the skills learned in the previous cycle or grade

Details on Content:

Arithmetic Section:

  • Very important stand as the content learned is the building blocks for all strands in mathematics
  • Learning content is divided into three categories: 1. Understanding and writing numbers, 2. Meaning of operations involving numbers, and 3. Operations involving numbers
  • Stresses that the latter two categories should be taught simultaneously

Understanding and Writing Numbers / Meaning of Operations Involving Numbers / Operations Involving Numbers
  • Students study natural numbers first then progress to rational numbers, which includes decimals and integers
  • Progression from counting groups to place value
  • Student use manipulatives to grasp the meaning of numbers
  • Topics addressed: A. Natural numbers less than…, B. Fractions (using objects or drawings), C. Decimals up to…, and D. Integers
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  • Learn the importance of operations, to recognize different operations, and the appropriate use of each operation
  • Students use concrete, semi-concrete or symbolic means to learn the meaning of operations
  • Topics addressed: A. Natural numbers less than…, B. Decimals up to…, and C. Fractions
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  • Both conventional and developed processes to perform numerical operations
  • Calculators are used as a learning tool
  • Topics addressed: A. Natural, B. Fractions (using objects or diagrams), C. Decimals, and D. Using Numbers

Geometry Section:

  • Activities and manipulatives aid in learning geometry
  • Two-dimensional and three-dimensional figures
  • Locate, compare, identify, describe, classify, construct
  • Progression from concrete to abstract
  • Topics addressed: A. Space, B. Solids, C. Plane figures, and D. Frieze patterns and tessellations.

Measurement Section:

  • Calculation of direct and indirect measurements
  • Topics addressed: A. Lengths, B. Surface areas, C. Volumes, D. Angles, E. Capacities, F. Masses, G. Time, and H. Temperature

Statistics Section:

  • Display, interpret and compare data
  • Progression from bar graphs to circle graphs

Probability Section:

  • Conduct and observe random experiments
  • Progression from experimental probability to theoretical probability reasoning

“Examples of Strategies” Section:

  • Suggested strategies, which foster in the development and use of the three competencies
  • Organized into a table with the type of strategy on the left and the suggested reflection prompts on the right
  • Separated into 2 Categories:
  • 1. Cognitive and Metacognitive Strategies
  • Includes: Planning, Comprehension, Organization, Development, Regulation, Generalization, Retention, Development of Automatic Processes, and Communication
  • 2. Other Strategies
  • Includes: Affective Strategies and Resource Management Strategies

[MK1]Add a list of the other subject areas that have LPs as well as the link for the webpage where you found the info.