Springboard 6: Lessons for use in booster classes

Helping children to do their best in the national tests

Schools have implemented various strategies to help children to do their best in the tests and to demonstrate their mathematical capabilities. Seven effective strategies are described in some detail, together with some test questions to highlight particular points. The strategies described include ways of building revision into ongoing teaching, helping children to help themselves and to demonstrate successfully the mathematics they know, understand and can do.

Seven effective strategies to help children revise are described below.

1 USING PREVIOUS TEST QUESTIONS WHEN TEACHING

An effective revision strategy is to incorporate relevant test questions into the teaching of each unit of work. A number of schools use the QCA Testbase CDROM. Teachers select test items and the corresponding mark schemes from the mental and written (both calculator and non-calculator) tests to use in their lessons.

The advantages for the children include:

the opportunity to discuss and compare different approaches to the questions in order to consolidate a strategy that they feel confident with and can use successfully; a familiarisation with the different question types, including an understanding of what is meant by ‘show your working’ and ‘show your method’ on calculator papers; an understanding of how the mark scheme works for different types of questions, including those with a ‘show your working’ or ‘show your method’ box and those worth more than one mark. Children learn how they can get ‘partial credit’ on these questions; a more systematic development of their confidence in their ability to answer test questions.

2 REFINING AND HONING THE SKILLS FOR EACH OF THE FOUR RULES OF NUMBER

Analysis of recent test papers suggests that a significant proportion of children, when answering test questions involving the four rules of number, use calculation strategies that they are not comfortable with and do not understand fully. Consequently they are unsuccessful. There is evidence that many of these children could have been successful if they had chosen a different method. An effective revision strategy is to review each of the four operations in turn, using a set of different question types for each operation, drawn from the QCA Testbase CD-ROM or elsewhere. For example, the attached revision worksheet concentrates on a variety of subtraction questions.

When sharing and discussing children’s responses to the questions, the aim would be for the children to develop the skills and confidence to:

• use mental methods whenever appropriate, including questions on the written papers;
• examine questions and decide on the most appropriate strategy for each question, recognising that the numbers in the question often help to determine the method they feel most confident in using;
• make estimates and check their answers for reasonableness.

The role of the teacher during such revision sessions is to:

• encourage children to use mental methods as a first resort;
• show children how to record their mental and calculator methods to help with questions that require some explanation or description of the method;
• ensure that children have a secure understanding of place value, which helps them apply their methods successfully;
• enable the children to adopt the strategies they are most secure with by the time of the test;
• monitor children’s methods and answers, and help children with very inefficient strategies to refine their methods as far as possible, ensuring that they understand why these are more efficient methods.

3 CHECKING ANSWERS, INCLUDING APPROPRIATE USE OF THE CALCULATOR

Children need to check their methods. It is a useful strategy to appoint a ‘checker’ when children are working in groups. Checking calculations also needs to be embedded in the teaching so that it becomes ‘second nature’ for the children. An OHP calculator can be used by the teacher to demonstrate ways of checking calculations undertaken using a calculator. In particular, the teacher can model checking strategies using inverse operations. Discussing different strategies that can be used to solve a problem should provide children with alternatives that they can use to check their own solution. This applies to both mental and written methods. For example, the answer to ‘find three-quarters of 360’ can be checked by finding one quarter of 360 and subtracting it from 360.

4 RELATING KEY VOCABULARY AND CONTEXT TO MATHEMATICAL OPERATIONS

In order for children to be successful in test questions such as Question 10, Test B, 2001, it is important that children can identify the key vocabulary and match it to the correct mathematical operation. It is important to note that the key words alone do not lead to the operation; it is also the context of the question that determines the required operation. A useful strategy is to create a display of key vocabulary and the associated operations around the classroom and then refer to this vocabulary and the context as they appear in test questions. ‘How many’ is often associated with addition and multiplication. In this question, because of the context, it should be linked to division.

5 INTERPRETING INFORMATION AND USING ANNOTATIONS

It can be very effective to ask children to read sections of a problem and to use focused questions to establish the information that can be obtained from each section. The children should be encouraged to record this information in a way that is meaningful to them, using shorthand notes, a diagram or a flow chart. Evidence from tests suggests that children are reluctant to draw or write on published material such as test questions, apart from in the designated boxes. It is therefore important to encourage children to annotate and draw on test diagrams, graphs and tables, if it helps them to understand and answer the questions. For example, in attempting the question below, converting the diagram into seven small triangles would help many children to reach a solution. Encourage children to add information to diagrams or tables from the written information provided in the question. For example, questions such as Question 20, Test A, 2001, sometimes include graphs with no scale marked on the axes. Adding information from the question to clarify the scale or to give an indication of the magnitude of the scale often helps children to see how to answer the question.

6 ORDERING NUMBERS

There is evidence that many children need a more secure understanding of the relative size of numbers. Children often have difficulty answering questions that involve the ordering of negative numbers, fractions and decimals, and questions that involve the forming of equivalent fractions. A useful revision strategy is to use visual images, such as a number line, to enable children to see where negative numbers, fractions and decimals fit, and to understand why two representations, fraction or decimal, are equivalent. Remind children that they can draw their own pictures to help them see their way through to a solution.

7 PREPARING FOR THE UNFAMILIAR

Too many children stop working before they reach the end of the test, even though there is still time available for them to attempt the remaining questions. Children need to be encouraged to try questions with which they may not be familiar. If they need to draw any diagrams to help them, they should do so. Emphasise to children that it is better to do that and tackle a question than to sit and think without recording anything. A useful revision strategy is to change the context of particular problems with the children, establish whether this has any effect on the calculation, and if so, why. Getting children to devise problems for others to answer also helps them to interpret the unfamiliar contexts.