BC Education - Mathematics 8 and 9 - INTRODUCTION

RATIONALE

Mathematics is increasingly important in our technological society. Students today require the ability to reason and communicate, to solve problems, and to understand and use mathematics. Development of these skills helps students become numerate.

Numeracy can be defined as the combination of mathematical knowledge, problem solving and communication skills required by all persons to function successfully within our technological world. Numeracy is more than knowing about numbers and number operations. (British Columbia Association of Mathematics Teachers, 1998)

Being numerate involves the application of mathematical understanding in daily activities at school, at home, at work, and in the community. To become numerate, students need to develop the ability to conjecture, reason logically, employ quantitative and spatial information, and apply a variety of mathematical methods to solve problems and make decisions confidently and independently.

The ability to recognize the mathematical demands and possibilities in a situation is an important aspect of numeracy. Numeracy is based on mathematical foundations and requires the application of concepts and skills related to the formal aspects of the discipline of mathematics.

To ensure that students are prepared for the demands of further education and the workplace, the mathematics curriculum:

emphasizes the development of the knowledge, skills, and attitudes relevant to the development of numeracy
supports the creative and aesthetic aspects of mathematics by exploring the connections between mathematics, art, and design
promotes the development of positive attitudes, problem solving, communication, applications, reasoning, and the use of technology

Developing Positive Attitudes

Research, including provincial assessments, consistently indicates that there is a positive correlation between student attitudes and performance. A classroom climate that promotes positive attitudes about the value and relevance of mathematics to students' lives gives them the desire to succeed and the confidence that their efforts are worthwhile. Classroom activities that allow students to apply their learning to practical situations help them see that mathematics is applicable to daily living and valuable to future education and employment.

Becoming Mathematical Problem Solvers

Problem solving is the cornerstone of mathematics instruction. Students working alone and in groups must learn the skills of effective problem solving, which include the ability to:

read and analyse a problem
identify the significant elements of a problem
select an appropriate strategy to solve a problem
verify and judge the reasonableness of an answer
communicate solutions

Acquiring these skills can help students become reasoning individuals able to contribute to society.

As students move through the grades, the curriculum presents them with increasingly diverse and complex mathematical problems to solve. To encourage students' abilities to communicate, explore, create, adjust to changes, and actively acquire new knowledge throughout their lives, mathematical problem solving should evolve naturally out of their experiences and be an integral part of all mathematical activity. Effective problem solving consists of more than being able to solve many different types of problems. Students need to be able to solve mathematical problems that arise in any subject area and to draw upon skills developed in more than one area of mathematics. Becoming a mathematical problem solver requires a willingness to take risks and persevere when faced with problems that do not have an immediately apparent solution.

Communicating Mathematically

Mathematics is a language-a way of communicating ideas. Communication plays an important role in helping students build links between their informal, intuitive notions and the abstract language and symbolism of mathematics. Communication also plays a key role in helping students make important connections among physical, pictorial, graphic, symbolic, verbal, descriptive, and mental representations of mathematical ideas. All activities that help students explore, explain, investigate, describe, and justify their decisions promote the development of communication skills.

The Kindergarten to Grade 12 Mathematics curriculum emphasizes discussing, writing, and representing mathematical thinking in various ways.

Connecting and Applying Mathematical Ideas

Learning activities should help students understand that mathematics is a changing and evolving domain to which many cultural groups have contributed. Students become aware of the usefulness of mathematics when mathematical ideas are connected to everyday experiences. Learning activities should help students relate mathematical concepts to realistic situations and allow them to see how one mathematical idea can help them understand others. Mathematics helps students solve problems, describe and model real-world phenomena, and communicate complex thoughts and information with conciseness and precision.

Reasoning Mathematically

Mathematics instruction should help students develop confidence in their abilities to reason and to justify their thinking. Students should understand that mathematics is not simply memorizing rules. Mathematics should make sense, be logical, and also be enjoyable. The ability to reason logically usually develops on a continuum from concrete to formal to abstract. Students use inductive reasoning when they make conjectures by generalizing from a pattern of observations; they use deductive reasoning when they test those conjectures. To develop mathematical reasoning skills, students require the freedom to explore, conjecture, and validate and to convince others. It is important that their ability to reason is valued as much as their ability to find
correct answers.

Using Technology

The Grades 8 and 9 Mathematics curriculum requires students to be proficient in using technology as a problem-solving tool.

Computers and calculators are tools for learning. They are powerful aids to problem solving. The ability to compute rapidly, analyse data in various ways, and graph mathematical relationships instantly can help students explore mathematical concepts and relationships in greater depth. Students must have access to and use the most appropriate tool or method for a calculation.

It is important to recognize that calculators assist in rote calculation or algorithms, but people accomplish the work at hand. At the same time, access to technology does not eliminate the need for students to learn basic facts and algorithms.

Estimation and Mental Math

Mathematics involves more than exactness. Estimation strategies help students deal with everyday quantitative situations. Estimation skills also help them gain confidence and enable them to determine if something is mathematically reasonable. Although they may have access to calculators from Kindergarten to Grade 12, students need to use reasoning, judgment, and decision-making strategies when estimating. Instruction should therefore emphasize the role that these strategies play.

Note:
The diagram above does not show all possible student transitions between the Applications of Mathematics pathway, the Essentials of Mathematics Pathway, and the Principles of Mathematics pathway.

The course structure for secondary mathematics was designed with the expectation that approximately 50% of students would be registered in Applications of Mathematics, 20% of students in Essentials of Mathematics, and 30% in Principles of Mathematics.

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