Aim and Goals of K-12 Mathematics Education
Many of the topics and problems in a mathematics classroom can be initiated by the children themselves. In a classroom focused on working mathematically, teachers and children work together as a community of learners; they explore ideas together and share what they find. It is very different to the traditional method of mathematics teaching, which begins with a demonstration by a teacher and continues with children practicing what has been demonstrated. (Skinner, 1999, p. 7)
The K-12 aim of Saskatchewan's mathematics program is to help students develop the understandings and abilities necessary to be confident and competent in thinking and working mathematically in their daily activities and ongoing learnings and work experiences. The mathematics program is intended to stimulate the spirit of inquiry within the context of mathematical thinking and reasoning.
The four K-12 goals for mathematics in Saskatchewan are broad statements that identify the characteristics of thinking and working mathematically. At every grade level, students' learning should be building towards their attainment of these goals. Within each grade level, outcomes are directly related to the development of one or more of these goals. The goals in boldface font in the list of outcomes indicate a stronger connection to the related outcome. The instructional approaches used to promote student achievement of the grade level outcomes will, therefore, also promote student achievement with respect to the goals.
Mathematics as a Human Endeavour
Developing an understanding of mathematics as a human endeavour requires students to engage in experiences that:
- value place-based knowledge and learning
- value learning from and with community
- encourage and value varying perspectives and approaches to mathematics
- recognize and value one's evolving strengths and knowledge in learning and doing mathematics
- recognize and value the strengths and knowledge of others in doing mathematics
- value and honour reflection and sharing in the construction of mathematical understanding
- recognize errors as stepping stones towards further learning in mathematics
- require self-assessment and goal setting for mathematical learning
- support risk taking (mathematically and personally)
- build self-confidence related to mathematical insights and abilities
- encourage enjoyment, curiosity, and perseverance when encountering new problems
- create appreciation for the many layers, nuances, perspectives, and value of mathematics.
Logical Thinking - Through their learning of K-12 mathematics, children will develop and be able to apply mathematical reasoning processes, skills, and strategies to new situations and problems. This goal encompasses the processes and strategies that are foundational to understanding mathematics as a discipline. These processes and strategies include:
- inductive and deductive thinking
- abstracting and generalizing
- exploring, identifying, and describing patterns
- verifying and proving
- exploring, identifying, and describing relationships
- modelling and representing (concretely, visually, physically, and symbolically)
- hypothesizing and asking "what if " (mathematical play)
Number Sense -Through their learning of K-12 mathematics, children will develop an understanding of the meaning of, relationships between, properties of, roles of, and representations (including symbolic) of numbers and apply this understanding to new situations and problems. Key to developing number sense is students having ongoing experience with:
- decomposing and composing of numbers
- relating different operations to each other
- modelling and representing numbers and operations(concretely, visually, physically, and symbolically)
- understanding the origins and need for different types of numbers
- recognizing operations on different number types as being the same operations
- understanding equality and inequality
- recognizing the variety of roles for numbers
- understanding algebraic representations and manipulations in terms of extending numbers
- looking for patterns and ways to describe those patterns numerically and algebraically.
Spatial Sense - Through their learning of K-12 mathematics, children will develop an understanding of 2-D shapes and 3-D objects, and the relationships between geometrical shapes and objects and numbers, and apply this understanding to new situations and problems. Development of a strong spatial sense requires students to experience:
- construction and deconstruction of 2-D shapes and 3-D objects
- investigations into relationships between 2-D shapes and 3-D objects
- explorations of how number (and algebra) can be used to describe 2-D shapes and 3-D objects
- exploration of the movement of 2-D shapes and 3-D objects
- exploration of the dimensions of 2-D shapes and 3-D objects
- exploration of different forms of measurement and their meaning
Mathematics as a Human Endeavour -Through their learning of K-12 mathematics, students will develop an understanding of mathematics as a way of knowing the world that all humans are capable of with respect to their personal experiences and needs. Students should be encouraged to challenge the boundaries of their experiences, and to view mathematics as a set of tools and ways of thinking that every society develops to meet their particular needs. This means that mathematics is a dynamic discipline in which logical thinking, number sense, and spatial sense form the backbone of all developments and those developments are determined by the contexts and needs of the time, place, and people.
Kindergarten Mathematics Education
Kindergarten mathematics provides children with an understanding of quantity, shape, and space in their environment. Children require opportunities for reflection, exploration of both patterns and relationships, sharing ideas and problems, and decision making. Opportunities for children to communicate through representing will be part of the learning experiences in Kindergarten. Kindergarten children will have opportunities to achieve the mathematics outcomes through play and inquiry.
For additional information, refer to http://www.education.gov.sk.ca/math-curricula.