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In part two of The TES guide to the curriculum review Sarah Cassidy tackles mathematics

Mathematics is one of the subjects which sees the greatest changes under proposals for a new national curriculum for the 21st century. But schools should be well-equipped to deal with the biggest reform by the time it is introduced in September 2000.

The primary maths curriculum looks radically different after being rewritten to correspond with the National Numeracy Strategy. But by the time the new programmes of study are introduced the strategy will be at least a year old and the renewed focus on mental arithmetic will be familiar to every primary teacher.

Primary schools can satisfy all the requirements of the new maths curriculum by implementing the numeracy strategy in full, according to Education Secretary David Blunkett's proposals.

The curriculum and the strategy were developed in tandem to ensure they aligned. Unsurprisingly there is much more emphasis on mental arithmetic for five, six and seven-year-olds. Basic counting and number patterns are to be reinforced to ensure children understand the concept of number.

Calculators will also play a much smaller role in primaries. Currently, the curriculum requires five-year-olds to learn how to use a calculator. In future, however, they will only be introduced to seven to 11-year-olds and then only for "calculations involving several digits, including decimals".

If a sum can't be done in your head, use a pen and paper, is the message.

Some advanced material has been removed from key stage 1, including simple fractions, decimals and negative numbers. They are now introduced to juniors with a syllabus which focuses on mental calculations, fractions and decimals.

At secondary level, the current joint key stage 3 and GCSE programme has been split into separate programmes of study. GCSE -level itself has also been divided into a foundation programme putting maths in real-life contexts for disaffected students and a higher programme to stretch brighter students.

The foundation section is packed with non-statutory examples of how to use maths topics: diet sheets, VAT, shop discounts, maps and scale drawings.

The higher level goes much further and includes simultaneous and quadratic equations, exponential functions and more complex 3D geometry.

Those pupils who follow this advanced curriculum for 14 to 16-year-olds will be able to"use proportional reasoning with fluency...use short chains of deductive reasoning and begin to understand the importance of proof". All programmes of study contain much more detail than the current curriculum - the key stage 3 curriculum alone is nine pages long.

At all levels the "Using and Applying Mathematics" section has been merged with the other programmes of study.

It does however remain as an attainment target, which should ensure the application of maths to real life problems is covered.

National tests will be changed to reflect the new emphasis.

Key stage 1

* Learn to count, read, write and order numbers to 100 and beyond.

* Develop a range of mental calculation skills.

* Use developing mathematical language to explain reasoning when solving problems.

Key stage 2

* Extend competence and confidence with numbers, moving to security in calculating.

* Explore features of shape and space and develop measuring skills.

* Discuss reasoning using a wider range of mathematical language, diagrams and charts.

Key stage 3

* Increasingly make connections between different aspects of maths.

* Extend calculating skills to fractions, percentages and decimals, and begin to understand the importance of reasoning about proportion.

* Begin to develop facility in the use of algebraic techniques and symbols.

* Study linear functions and their corresponding graphs.

* Progress to using definitions and reasoning to understand geometrical objects.

* Undertake practical data handling work, introducing a quantitative approach to probability.

Key stage 4 (foundation)

* Increasingly make connections between different aspects of maths.

* Consolidate skills in calculating with fractions, percentages and decimals.

* Use proportional reasoning in simple contexts.

* Develop facility in the use of basic algebraic techniques and symbols.

* Use definitions and reasoning to describe and understand geometrical objects.

* Undertake practical handling data work, using a range of skills and techniques.

Key stage 4 (higher)

* Refine calculating skills to include powers, roots and numbers expressed in standard form.

* Use proportional reasoning with fluency.

* Develop facility in using algebraic manipulation and simplification

* Solve a range of equations, including those with non-integer coefficients.

* Use short chains of deductive reasoning and begin to understand the importance of proof.

* Use definitions and formal reasoning to describe and understand geometrical objects and logical relationships between such objects.

* Undertake practical data handling work, using a broader range of skills and techniques, including those relating to sampling.

* Develop an appreciation of maths' importance as an analytical tool for solving problems.

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