BC Education - Introduction to Mathematics K to 7

Rationale

Mathematics is increasingly important in our technological society. To succeed in the workplace, students require the ability to reason and communicate, to solve problems, and to understand and use probability and statistics, technology, and measurement. Skills in these areas are also required of all mathematically literate citizens.

Becoming mathematically literate involves developing the ability to explore, to conjecture, to reason logically, and to use a variety of mathematical methods to solve problems. It involves the development of self-confidence and the ability to use quantitative and spatial information to solve problems and make decisions. As they develop mathematical literacy, students generally experience a growth in motivation and self-confidence in mathematics. This growth occurs when they learn to value the importance of mathematics, to develop mathematical habits of mind, and to understand and appreciate the role of mathematics in everyday life.

The provincial mathematics curriculum emphasizes the practical applications of learning and the types of skills needed in the knowledge-based workplace. The new curriculum places greater 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 early years of the mathematics curriculum (K to 7) must help students develop mathematical literacy.

Developing Positive Attitudes

Research, including provincial assessments, always emphasizes the direct association between students' attitudes and their levels of performance. Mathematics activities should engage the interest and imagination of all students so that they are willing to take risks, grow in their tolerance of ambiguity, and achieve high levels of development in their mathematical thinking. Classroom practice and teaching strategies should promote positive attitudes towards mathematics for all students, including those typically underrepresented in careers in mathematics.

Becoming Mathematical Problem Solvers

Problem solving is the cornerstone of mathematics instruction. Students must learn the skills of effective problem solving, including the ability to communicate solutions, so that they will become reasoning, thinking 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. Problem solving requiring mathematical thinking should evolve naturally out of day-to-day activities in the classroom and be an integral part of all mathematical activity, so that students will be able to explore, create, adjust to changes, and actively acquire new knowledge throughout their lives.

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, and mental representations of mathematical ideas. All activities that involve students in exploring, investigating, describing, justifying decisions, and explaining promote the development of communication skills. The K to 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 to relate mathematical concepts to real-world situations and allow them to see how one mathematical idea can help them understand others. This approach emphasizes the usefulness of mathematics in solving problems, describing and modelling real-world phenomena, and communicating complex thoughts and information in a concise and precise manner.

Reasoning Mathematically

Mathematics instruction should help students develop confidence in their ability to reason and to justify their thinking. Students should understand that mathematics is not simply memorizing rules. Mathematics should make sense, be logical, and be enjoyable.

Students' reasoning and logic abilities usually develop 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. Students require the freedom to explore, conjecture, validate, and convince others if they are to develop mathematical reasoning skills. And it is important that their ability to reason well is valued as much as their ability to find correct answers.

Using Technology

New technology has changed the kind of mathematical problems encountered today, as well as the methods that mathematicians use to investigate them. Computers and calculators are powerful problem-solving tools. The power to compute rapidly and to graph mathematical relationships instantly will help students become mathematically self-sufficient. When they are able to use technology, students' growing curiosity can lead to rich mathematical invention.

Calculators and computers are tools that simplify, but do not accomplish, the work at hand, and the availability of calculators does not eliminate the need for students to learn basic facts and algorithms. Students must be

able to select and use the most appropriate tool or method for a calculation. The K to 12 mathematics curriculum puts increased emphasis on the use of available resources, including technology and the mass media.

Estimation and Mental Math

Mathematics involves more than exactness. Estimation skills enhance students' abilities to deal with everyday quantitative situations, and help them gain confidence and become more able to determine if something is mathematically correct. Students need to use reasoning, judgment, and decision-making skills when estimating. Instruction should emphasize an understanding of the value of estimation. It is also important that students develop the ability to mentally calculate simple arithmetic operations when precise answers are required.

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Revised: October 20, 1997

BC Ministry of Education