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How maths teaching has changed -

the new order of learning

 

A Summary

Recent changes in maths teaching are:

  1. The maths curriculum has much more content.
  2. There is more emphasis on using and applying mathematical knowledge, skills and understanding.
  3. Addition and subtraction facts have to be learnt as well as multiplication tables.
  4. Computers and calculators are used to enhance children's learning.
  5. There is much more emphasis on mental methods of calculation and strategies for mental methods are taught and discussed.
  6. Written methods of calculation are introduced later than they were and, at the time of writing, any efficient method can be used.

League tables based on the results of national tests have put pressure on schools to achieve high standards.

 

The National Curriculum

In 1989 the National Curriculum was introduced for all schools in England and Wales. This sets out the learning objectives for each level of development in all subjects.

Before then the content of, and amount of time spent on, each subject varied greatly from school to school, which made transfer to a new school difficult for children and resulted in varying standards.

 

The National Numeracy Strategy

Along with the National Curriculum came standard attainment tests (SATs) which all children take towards the end of Key Stages 1, 2 and 3 in English, Mathematics and Science.

After several years it was discovered that standards were not improving in maths and English, despite the National Curriculum, and in 1999 The National Numeracy Strategy was introduced for primary schools. This uses the National Curriculum content (as detailed below), but goes beyond it by setting out how maths should be taught through whole class teaching in daily maths lessons.

Each lesson should begin with about 10 minutes on oral work and/or mental calculation, followed by a direct teaching session on a particular aspect of maths which children then practise, often at their own level of attainment. The lesson ends with a plenary session in which learning is drawn together, key facts summarised, links made to other areas of the curriculum or where the methods pupils have used to solve problems are discussed and explained etc.

Children are taught how to use calculators in terms of the technical skills required, but use them in activities designed to help them to understand numbers and how our number system works. They are not expected to use them as a calculating tool unless they are working on a realistic problem in which the numbers are well above their mental ability or their known written methods of calculation.

 

Calculating methods

The National Curriculum requires schools to focus on mental methods of calculation in the primary school. Written methods of calculation are not required until children begin level 4, which for children of average attainment is around year 5. Until this level children can use a calculator for any realistic problems in which the calculations are beyond their mental ability, just as most adults do in real life. The knowledge, skills and understanding required for mental calculation and for using a calculator are detailed through the levels in the National Curriculum.

Written methods of calculation are used when children are confident in using mental methods for calculations involving 2-digit numbers and are developed from those mental methods. There is no requirement for any particular written method and children are encouraged to choose an efficient method which they understand appropriate for the calculation.

For example 246 + 325 might be worked out through a written method as 500 + 60 + 11 = 571 or as a conventional vertical sum using a carrying figure. Similarly 348 x 23 could be done using conventional long multiplication or by using the grid method. described in 'The new methods' in the parents' section of mad4maths.

 

Maths Content- The National Curriculum


The areas of maths which have to be taught in the National Curriculum are:

Using and Applying mathematics
  1. Using maths as a tool for solving everyday problems, for making things and for investigating mathematical ideas;

  2. Using mathematical vocabulary to communicate and interpret information;

  3. Applying all aspects of mathematical knowledge in problem solving activities;

  4. Developing the skills needed for mathematical reasoning, i.e. predicting, testing, generalising, concluding and justifying findings.

Number
  1. Understanding numbers, including negative numbers and decimals, in terms of counting, reading, writing, ordering and understanding place value;

  2. Using addition, subtraction, multiplication and division in solving realistic problems;

  3. Learning addition and subtraction facts within 20 (e.g. 8 + 7, 18 - 12) and multiplication and division facts to 10 x 10;

  4. Interpreting a calculator;

  5. Developing skills in mental calculation;

  6. Using written methods of calculation;

  7. Understanding and using fractions, decimals, percentages and ratio;

  8. Using estimation and approximation in numbers, calculations and a range of measurements;

  9. Using metric units of measurement for length, capacity and weight, reading time on analogue and digital clocks, using standard units of time, understanding Imperial units still in use, solving problems involving measures.

Algebra
  1. Exploring and using number patterns;

  2. Using symbols, simple formulae and equations;

  3. Understanding and using co-ordinate representation.


Shape and Space
  1. Knowing the names and properties of 2-D and 3-D shapes, including angle and symmetry, and using knowledge to build, draw and describe them.

  2. Understanding and describing position and direction using common words e.g. forwards, backwards, left, right, clockwise and anticlockwise, using compass bearings and co-ordinates;

  3. Understanding types of movement and giving instructions for movement, including using angle as a measurement of turn;

  4. Measuring shapes, including lengths of sides, perimeters, areas, volumes and angles

Handling Data
  1. Sorting and classifying objects;

  2. Collecting, recording and processing information, including the use of data collection sheets, tables, lists, tally charts, frequency tables and a computer database;

  3. Representing and interpreting data including the use of diagrams, frequency tables, bar charts, pictograms and line graphs;

  4. Understanding and using averages, including mean, median and mode;

  5. Understanding and using appropriate words to identify and describe likelihood;

  6. Discussing the probability of events, including those with equally likely outcomes, (e.g. the probability of rolling a six using a dice).

Mary Ruddle 2007