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Mathematics (2020)

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This curriculum policy replaces The Ontario Curriculum, Grades 1–8: Mathematics, 2005. Beginning in September 2020, all mathematics programs for Grades 1 to 8 will be based on the expectations outlined in this curriculum policy.

Assessment and Evaluation of Student Achievement

Growing Success: Assessment, Evaluation, and Reporting in Ontario Schools, First Edition, Covering Grades 1 to 12, 2010 sets out the Ministry of Education’s assessment, evaluation, and reporting policy. The policy aims to maintain high standards, improve student learning, and benefit all students, parents, and teachers in elementary and secondary schools across the province. Successful implementation of this policy depends on the professional judgement of teachers at all levels as well as their high expectations of all students, and on their ability to work together and to build trust and confidence among parents and students.

Major aspects of assessment, evaluation, and reporting policy are summarized in the main “Assessment and Evaluation” section. The key tool for assessment and evaluation in mathematics – the achievement chart – is provided below.

The Achievement Chart for Mathematics

The achievement chart identifies four categories of knowledge and skills and four levels of achievement in mathematics. (For important background, see “Content Standards and Performance Standards”in the main Assessment and Evaluation section.)

Knowledge and Understanding – Subject-specific content acquired in each grade (knowledge), and the comprehension of its meaning and significance (understanding)
Categories Level 1  Level 2 Level 3 Level 4
  The student:
Knowledge of content (e.g., math facts, computational strategies, terminology, mathematical models, money values) demonstrates limited knowledge of content demonstrates some knowledge of content demonstrates considerable knowledge of content demonstrates thorough knowledge of content
Understanding of content (e.g., concepts, theories, procedures, principles, mathematical processes) demonstrates
limited understanding of content
demonstrates some understanding of content demonstrates considerable understanding of content demonstrates thorough understanding of content
Thinking – The use of critical and creative thinking skills and/or processes
Categories Level 1  Level 2 Level 3 Level 4
  The student:
Use of planning skills (e.g., interpreting and expressing problems, identifying unknown(s), making conjectures and estimates, identifying steps to take, considering the use of models and representations, selecting strategies and tools) uses planning skills with limited
effectiveness
uses planning skills with some effectiveness uses planning skills with considerable
effectiveness
uses planning skills with a high degree of effectiveness
Use of processing skills* (e.g., carrying out plans: collecting data, questioning, testing, revising, modelling, solving, inferring, forming conclusions; looking back at solutions: reflecting, evaluating reasonableness, reasoning, justifying, proving) uses processing skills with limited
effectiveness
uses processing skills with some
effectiveness
uses processing skills with considerable
effectiveness
uses processing skills with a high degree of effectiveness
Use of critical/creative thinking processes* (e.g., making and testing conjectures, posing and solving problems, critiquing solutions, providing mathematical reasoning) uses critical/
creative thinking
processes with limited effectiveness
uses critical/
creative thinking
processes with some effectiveness
uses critical/
creative thinking
processes with considerable effectiveness
uses critical/
creative thinking
processes with a high degree of effectiveness
Communication – The conveying of meaning through various forms 
Categories Level 1  Level 2 Level 3 Level 4
  The student:
Expression and organization of ideas and information (e.g., clear expression, logical organization) in oral, visual, and/or written forms (e.g., pictorial, graphic, numeric, algebraic forms; gestures and other non-verbal forms; models) expresses and
organizes ideas and information
with limited effectiveness
expresses and
organizes ideas
and information
with some effectiveness
expresses and
organizes ideas and information
with considerable
effectiveness
expresses and organizes ideas and information
with a high degree of effectiveness
Communication for different audiences (e.g., peers, adults) and purposes (e.g., to generate ideas, present data, justify a solution) in oral, visual, and/or written forms communicates for different audiences and purposes with limited effectiveness communicates for different audiences
and purposes with some effectiveness
communicates for different audiences and purposes with
considerable effectiveness
communicates for different audiences and purposes with a high degree of
effectiveness
Use of conventions, vocabulary, and terminology of the discipline in oral, visual, and/or written forms (e.g., terms, symbols) uses conventions,
vocabulary, and
terminology with
limited effectiveness
uses conventions,
vocabulary, and
terminology with
some effectiveness
uses conventions,
vocabulary, and
terminology with
considerable
effectiveness
uses conventions,
vocabulary, and
terminology with a high degree of
effectiveness
Application – The use of knowledge and skills to make connections within and between various contexts
Categories Level 1  Level 2 Level 3 Level 4
  The student:
Application of knowledge and skills (e.g., representations and computational strategies) in familiar contexts  applies knowledge and skills in familiar
contexts with limited effectiveness
applies knowledge and skills in familiar contexts with some
effectiveness
applies knowledge and skills in familiar
contexts with
considerable
effectiveness
applies knowledge and skills in familiar contexts with a high degree of effectiveness
Transfer of knowledge and skills (e.g., representations and computational strategies) to new contexts transfers knowledge and skills to new contexts with limited effectiveness transfers knowledge and skills to new contexts with
some effectiveness
transfers knowledge and skills to new contexts with considerable
effectiveness
transfers
knowledge and
skills to new contexts with a high degree of
effectiveness
Making connections within and between various contexts (e.g., connections to everyday and real-life situations; connections involving an understanding of the relationships between different measurements; connections among concepts, representations, and forms within mathematics; connections involving use of prior knowledge and experience; connections among mathematics and other disciplines, including other STEM [science, technology, engineering, and mathematics] subjects) makes connections
within and between
various contexts with limited effectiveness
makes connections
within and between various contexts with some effectiveness
makes connections
within and between various contexts with considerable
effectiveness
makes connections
within and between various contexts with a high degree of effectiveness

* Note:
The processing skills and critical/creative thinking processes in the Thinking category include some but not all aspects of the mathematical processes laid out in Strand A: Social-Emotional Learning and Mathematical Processes. Some aspects of the mathematical processes relate to the other categories of the achievement chart.

Criteria and Descriptors for Mathematics

To guide teachers in their assessment and evaluation of student learning, the achievement chart provides “criteria” and “descriptors” within each of the four categories of knowledge and skills.

A set of criteria is identified for each category in the achievement chart. The criteria are subsets of the knowledge and skills that define the category. The criteria identify the aspects of student performance that are assessed and/or evaluated, and they serve as a guide to what teachers look for. In the mathematics curriculum, the criteria for each category are as follows:

Knowledge and Understanding

Thinking

  • use of planning skills (e.g., interpreting and expressing problems, identifying unknown(s), making conjectures and estimates, identifying steps to take, considering the use of models and representations, selecting strategies and tools)
  • use of processing skills (e.g., carrying out plans: collecting data, questioning, testing, revising, modelling, solving, inferring, forming conclusions; looking back at solutions: reflecting, evaluating reasonableness, reasoning, justifying, proving)
  • use of critical/creative thinking processes (e.g., making and testing conjectures, posing and solving problems, critiquing solutions, providing mathematical reasoning)

Communication

  • expression and organization of ideas and information (e.g., clear expression, logical organization) in oral, visual, and/or written forms (e.g., pictorial, graphic, numeric, algebraic forms; gestures and other non-verbal forms; models)
  • communication for different audiences (e.g., peers, adults) and purposes (e.g., to generate ideas, present data, justify a solution) in oral, visual, and/or written forms
  • use of conventions, vocabulary, and terminology of the discipline in oral, visual, and/or written forms (e.g., terms, symbols)

Application

  • application of knowledge and skills (e.g., representations and computational strategies) in familiar contexts
  • transfer of knowledge and skills (e.g., representations and computational strategies) to new contexts
  • making connections within and between various contexts (e.g., connections to everyday and real-life situations; connections involving an understanding of the relationships between different measurements; connections among concepts, representations, and forms within mathematics; connections involving use of prior knowledge and experience; connections among mathematics and other disciplines, including other STEM [science, technology, engineering, and mathematics] subjects)

“Descriptors” indicate the characteristics of the student’s performance, with respect to a particular criterion, on which assessment or evaluation is focused. Effectiveness is the descriptor used for each of the criteria in the Thinking, Communication, and Application categories. What constitutes effectiveness in any given performance task will vary with the particular criterion being considered. Assessment of effectiveness may therefore focus on a quality such as appropriateness, clarity, accuracy, precision, logic, relevance, significance, fluency, flexibility, depth, or breadth, as appropriate for the particular criterion.