RATIONALE
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)
Becoming numerate involves developing the ability to explore, conjecture, reason logically, and use a variety of mathematical methods to solve problems. It also involves the development of self-confidence and the ability to use quantitative and spatial information in problem solving and decision making. As students develop their numeracy skills and concepts, they generally grow more confident and motivated in their mathematical explorations. This growth occurs as they learn to enjoy and value mathematics, to think analytically, and to understand and appreciate the role of mathematics in everyday life.
The provincial mathematics curriculum emphasizes the development of numeracy skills and concepts and their practical application in higher education and the workplace. The curriculum places emphasis on probability and statistics, reasoning and communication, measurement, and problem solving. To ensure that students are prepared for the demands of both further education and the workplace, the graduate years of the mathematics curriculum (Grades 11 and 12) help students develop a more sophisticated sense of numeracy. At the same time, the curriculum investigates the creative and aesthetic aspects of mathematics by exploring the connections between mathematics, art, and design.
Developing Positive Attitudes
Research, including provincial assessments, consistently indicates that there is a positive correlation between student attitudes and performance. Mathematics activities should be interesting and engaging, so that students will be more likely to take risks to develop their mathematical thinking. Classroom practice and teaching strategies should promote positive attitudes toward mathematics for all students.
Becoming mathematical Problem Solvers
Problem solving is the cornerstone of mathematics instruction. Students must learn the skills of effective problem solving, which include the ability to:
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 therefore help students relate mathematical concepts to real-world situations and allow them to see how one mathematical idea can help them understand others. This approach emphasizes that 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, validate, and convince others. It is important that their ability to reason is valued as much as their ability to find correct answers.
Using Technology
The Grade 10 to 12 Mathematics curriculum requires students to be proficient in using technology as a problem-solving tool. New technology has changed the level of sophistication of mathematical problems encountered today as well as the methods that mathematicians use to investigate them. Graphing tools such as computers and calculators are powerful aids to problem solving. The power to compute rapidly and to graph mathematical relationships instantly can help students explore many mathematical concepts and relationships in greater depth. When students have opportunities to use technology, their growing curiosity can lead to richer mathematical invention. It is important to recognize that calculators and computers are tools that simplify, but do not accomplish, the work at hand. The availability of calculators does not eliminate the need for students to learn basic facts and algorithms. Students must have access to and be able to select and use the most appropriate tool or method for a calculation. In each of the mathematics courses, technology is used extensively to assist in the investigation and exploration of mathematical concepts.
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. Even though 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:
To simplify this diagram, not all possible student transitions between the Applications
of Mathematics Pathway, the Essentials of Mathematics Pathway, and the Principles
of Mathematics Pathway have been shown.
©
2000 Copyright. All Rights Reserved. BC MOE Standards Department.
Maintained by: Mathematics Coordinator
Revised: November 28, 2000
Next
page
Ministry of Education Home Page