Download Quebec Education Program

TASK 2:
Summary of The Quebec Education Program: Preschool Education
and Elementary School Education
Organization of the Document:
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A seventeen page section titled “Mathematics” within the Quebec Education Program
document.
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The document is divided into five sections: 1. Competencies 2. Essential Knowledges 3.
Cultural References 4. Vocabulary and 5. Suggestions for Using Information and
Communication Technologies
The education program for mathematics is divided into three competencies:
o The first competency focuses on solving situational problems
o The second competency involves mathematical reasoning
o The third competency refers to using mathematical language to communicate
effectively
All three competencies are inherently connected as they all examine arithmetic,
probability, geometry, measurement, and statistics. The difference between the
competencies is “the emphasis placed on different facets of mathematical thinking”, such
as solving problems, reasoning, and communication (Gouvemement du Quebec:
Ministere de l’Education, 2001, 141).
Each competency contains three cycles. Cycle 1 refers to grades 1-2, cycle 2 refers to
grades 3-4, and cycle 3 refers to grade 5-6
Elementary School in Quebec extends from grade 1 to grade 6 inclusively
A section titled “Essential Knowledges” is addressed after the three competencies on
page 150. This section is divided into the five strands of mathematics, which are:
arithmetic, geometry, measurement, probability, and statistics. Each strand indicates the
sub-strands taught in each of the three cycles.
The next section indicates which components of mathematics in each cycle is culturally
referenced
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Content Information: Competencies
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Contains three competencies
o Each competency covers three cycles, which represent grades 1-2, grades 3-4, and
grades 5-6
Each competency has key features, end-of-cycle outcomes, and evaluation criteria
Competency 1: Solving Situational Problems Related to Mathematics
 Skill that is used to solve everyday challenges
 Students work independently or in groups and are encouraged to be creative
 A situational problem “requires the use of arithmetic, geometry, measurement, statistics,
and probability” (Gouvemement du Quebec: Ministere de l’Education, 2001, 142).
 Situational problems can be pure mathematics or have a real-life context
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Key Features: “decode the elements of the situational problem, model the situational
problem, apply different strategies to work out a solution, validate the solution, and share
the information related to the solution” (Gouvemement du Quebec: Ministere de
l’Education, 2001, 143)
Mathematical progression from Cycle 1 to Cycle 3
o Cycle 1: The students are given complete information to solve situational
problems. The students decide which task they are going to perform and use any
representation to gather information. Their solution is completed in one to two
steps and they use basic mathematical language to communicate their solution in
writing or orally.
o Cycle 2: The students are more careful in choosing which type of representation
to use to solve the situational problem provided because they include more than
one type of information. The students work out the solution in several steps and
are capable of anticipating the desired results. They use more complex
mathematical language than cycle 1 to validate and explain their solution orally or
in writing.
o Cycle 3: The students can appropriately choose which representations to use to
organize and display the various types of information in the problem. Their
solution involves several steps. The students use accurate mathematical language
to validate and explain their solution orally or in writing.
Competency 2: Reasoning Using Mathematical Concepts and Processes
 “engaging in mental activities such as abstracting, coordinating, differentiating,
integrating, constructing, and structuring” (Gouvemement du Quebec: Ministere de
l’Education, 2001, 144).
 Key Features: “define the elements of the mathematical situation, mobilize mathematical
concepts and processes appropriate to the given situation, apply mathematical processes
appropriate to the given situation, and justify actions or statements by referring to
mathematical concepts and processes” (Gouvemement du Quebec: Ministere de
l’Education, 2001, 146)
 Mathematical progression from Cycle 1 to Cycle 3
o Cycle 1: Students attempt to devise their own method to add and subtract natural
numbers. They also create flat figures and solids, measure time and length with
instruments provided.
o Cycle 2:
 The students continue to “develop their understanding of the number
system” (pg .145)
 Add and subtract natural number and decimals using conventional
approaches
 “Describe and classify geometric objects” (pg. 145)
 Create patterns from reflections
 Interpret problems involving chance and probability
o Cycle 3:
 Generate their own processes and master conventional processes to
adding, subtracting, multiplying, and dividing whole and decimal numbers
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“Add and subtract fractions and multiply fractions by natural numbers”
(147)
Classify flat figures, work with nets, and estimate and calculate
measurements such as lengths, surface area, volume, time, temperature,
angles, and capacities
Create patterns with reflections and translations
Examine the difference between theoretical probabilities and experimental
probabilities
Interpretation of circle graphs
Justify the use of technological tools and can accurately determine if
technology should be used for a given problem
Competency 3: Using Mathematical Language to Communicate
 Key Features: “become familiar with mathematical vocabulary, make connections
between mathematical language and every language, interpret or produce mathematical
messages” (Gouvemement du Quebec: Ministere de l’Education, 2001, 149)
 Mathematical progression from Cycle 1 to Cycle 3
o Cycle 1: Simple terms and symbols. One or more of the following mathematical
representations: drawings, tables, graphs, symbols, objects or words
o Cycle 2: Complex mathematical terms and symbols. More than one type of
mathematical representation
o Cycle 3: Precise mathematical language used in solution and explanation. Several
types of mathematical representations used.
Content Information: Essential Knowledges
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Is divided into five strands: Arithmetic, Geometry, Measurement, Statistics, and
Probability
Information under each strand/category/topic is organized in chart form and categorized
into each of the three learning cycles.
Arithmetic is further divided into THREE categories:
1. Understanding and Writing Numbers, which examines the topics of natural
numbers, decimals, fractions, using numbers, integers.
2. Meaning of Operations Involving Numbers, which examines the topics of
natural numbers, decimals, fractions
3. Operation of Numbers, which examines the topics of natural numbers,
decimals, fractions
o Decimals are introduced in cycle 2
o Using numbers and integers only appears in cycle 3
o Fractions are introduced in cycles 1 and 2,but manipulation only occurs in cycle 3
Geometry is divided into four topics: 1. Space 2. Solids, 3. Plane Figures, and 4. Frieze Patterns
and Tessellations
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Measurement is divided into eight topics: 1. Lengths, 2. Angles, 3. Surface Area, 4. Volumes, 5.
Capacities, 6. Masses, 7. Time, and 8. Temperature
o Time and Lengths are topics covered in all three cycles
o Angles, Surface Area, and Volume appear in cycles 2 and 3
o Capacities, Masses, and Temperature are only addressed in cycle 3
Statistics is one topic in itself
 The progression from cycle 1 to cycle 3
Interpret bar graphs
and pictographs
Interpret brokenline graphs
Interpret circle graphs
and calculate means
Probability of
events
Theoretical vs.
experimental probability
Probability is one topic in itself
Listing outcomes of
simple experiment
Content Information: Cultural References
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Numbers, Operations, Geometric Figures, and Measurements, which have a cultural
reference are categorized into each of the three learning cycles
Content Information: Vocabulary
 Mathematical words and phrases are categorized into the three learning cycles
Content Information: Suggestions for Using Information and Communication
Technology
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Technological tools are categorized into the three learning cycles.
Overlap of all three cycles and overlap of cycle 2 and cycle 3
Cycle 3 is the only cycle that uses memory function on the calculator, uses computer to
explore integers, and explores interactive mathematics websites
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