The Mathematics Curriculum in Primary and Lower Secondary Grades
In 2005, the Ministry of Education released the revised Ontario Curriculum, Grades 1 to 8 Mathematics, and Le curriculum de l’Ontario—Mathématiques, de la 1re à la 8e année.9,10 The revised curriculum recognizes student diversity and is based on the belief that all students can learn mathematics. The curriculum supports equity by promoting the active participation of all students and by identifying the knowledge and skills students are expected to demonstrate in every grade. It recognizes different learning styles and sets expectations that call for the use of a variety of instructional strategies and assessment tools. Further, it aims to challenge all students by including expectations that require them to use higher order thinking skills and to make connections among related mathematical concepts and among mathematics, other disciplines, and the real world.
The French-language curriculum is developed, implemented, and revised in parallel with the English-language curriculum. A distinct feature of the French-language education system is the Aménagement Linguistique policy, which is intended to promote, enhance, and expand the use of the French language and culture in a minority setting and in all spheres of activity.11
The revised mathematics curriculum includes five strands or major areas of knowledge and skills: Number Sense and Numeration, Measurement, Geometry and Spatial Sense, Patterning and Algebra, and Data Management and Probability. Seven mathematical processes also are identified—Problem Solving, Communicating, Reasoning and Proving, Reflecting, Representing, Connecting, and Selecting Tools and Computational Strategies—that describe the practices students need to learn and apply in all areas of their mathematics studies. In Grades 1 to 12, students engage actively in applying these mathematical processes throughout their programs of study.
Problem solving is central to learning mathematics. By learning to solve problems and by learning through problem solving, students connect mathematical ideas and processes, and develop conceptual understanding. Problem solving allows students to use the knowledge they bring to school, and helps them connect mathematics with situations outside the classroom. It gives meaning to skills and concepts in all strands. It provides opportunities for students to reason, communicate ideas, make connections, and apply their knowledge and skills, and it promotes collaboration, the sharing of ideas and strategies, and the discussion of mathematics.
In fourth grade mathematics, students are expected to develop knowledge and skills in each of the following five strands:
- Number Sense and Numeration—Work with whole numbers, decimal numbers, and simple fractions; understand magnitude; and solve problems and use proportional reasoning
- Measurement—Use strategies to estimate, measure, and record length, perimeter, area, mass, and volume; and determine relationships among units and measurable attributes
- Geometry and Spatial Sense—Learn about the geometric properties of quadrilaterals and three-dimensional figures, compare angles, construct three-dimensional figures, and identify and describe the location of objects
- Patterning and Algebra—Learn about numeric and geometric patterns and predictions related to patterns and repeating patterns, and understand equality between pairs of numeric expressions
- Data Management and Probability—Collect and display discrete data, interpret data, and make predictions related to simple probability experiments; conduct experiments; and compare predictions to results
In eighth grade mathematics, students are expected to develop knowledge and skills in each of the following five strands:
- Number Sense and Numeration—Use equivalent representations for numbers, including positive exponents; solve problems using whole numbers, decimal numbers, fractions, and integers; and use proportional reasoning in meaningful contexts to solve problems
- Measurement—Learn about applications of volume, relationships among units, and measurable attributes, including the area of circles and volume of cylinders
- Geometry and Spatial Sense—Learn about the geometric properties of quadrilaterals and circles; develop relationships and solve problems involving lines, triangles, and polyhedra; and use the coordinate plane to represent transformations
- Patterning and Algebra—Use graphs, algebraic expressions, and equations to represent linear growth patterns; model linear relationships, both graphically and algebraically; and solve and verify algebraic equations
- Data Management and Probability—Collect and organize data, explore data relationships, and use probability models to make predictions about real life events