Mental Mathematics

1. Mental Mathematics

2. Aims • To consider the purpose of the starter in the daily maths lesson • To consider possible content of the starter • To look at some starter activities

3. Background and context • Concern that children’s mental calculation skills and recall of facts were generally weak. • Framework referred to the first part of the lesson as: • • Oral work and mental calculation (about 5 to 10 minutes) (Whole-class work to rehearse, sharpen and develop mental and oral skills) • Focus was on strengthening children’s oral and mental skills through regular daily practice. • 1999 Framework lists a number of activities that might form part of this oral work and mental work. • Oral and mental ‘starter’ and was often judged by Ofsted to be the strongest part of mathematics lessons. • Successful starters were short, focused activities that prepared the children for the main teaching activity by getting them to think mathematically. • These ‘starters’ were objective-led activities that supported children’s learning and moved it on.

4. Current situation • Range of purposes and related activities has increased. • Focus on oral and mental calculation has widened and become a vehicle for teaching a range of mathematics. • Too often, the ‘starter’ has become an activity extended beyond the recommended 5 to 10 minutes. • In these situations, there can be more teacher talk than there is oral and mental work • Some evidence that the focus on oral and mental calculation has been lost and needs to be reinvigorated. • The ‘starter’ to a lesson remains an effective way of engaging children at the start of a lesson through a brisk, well-focused activity that helps to secure children’s knowledge and sharpens their skills. • Some evidence that mental work is only done in the starter • Some evidence that teachers see mental mathematics as giving children a test

5. Starter • Activities may continue to be rehearsal activities. • Rehearsal and practice are designed to strengthen knowledge and skills. • Important that children have sufficient opportunity to consolidate all the mathematics teaching they have received. • Mental work fulfils many other purposes.

6. The six Rs of oral and mental work • Rehearse • Recall • Refresh • Refine • Read • Reason

7. Rehearse • Practise and consolidate existing skills. (usually mental calculation skills, including using and applying) • Vocabulary and language of number • Properties of shapes or describing and reasoning.

8. Recall • To secure knowledge of number facts, (developing speed and accuracy) • Recall quickly names and properties of shapes • Recall quickly units of measure or types of charts or graphs to represent data.

9. Refresh • To draw on and revisit previous learning • To assess, review and strengthen children’s previously acquired knowledge and skills • Return to aspects of mathematics with which the children have had difficulty • Draw out key points from learning.

10. Refine • To sharpen methods and procedures • Explain strategies and solutions • Extend ideas; develop and deepen the children’s knowledge • Reinforce their understanding of key concepts • Build on earlier learning so that strategies and techniques become more efficient and precise

11. Read • To use mathematical vocabulary • To interpret images, diagrams and symbols correctly • To read number sentences and provide equivalents • To describe and explain diagrams and features involving scales, tables or graphs • To identify shapes from a list of their properties • To read and interpret word problems and puzzles • To create their own problems and lines of enquiry.

12. Reason • To use and apply acquired knowledge, skills and understanding • To make informed choices and decisions • To predict and hypothesise • To use deductive reasoning to eliminate or conclude • To provide examples that satisfy a condition always, sometimes or never and say why.

14. Activities for Mental Work?

17. Useful Strategies for developing mental skills • Ensure children have understood a question by: -repeating the question more slowly -rephrasing the question -presenting the question visually -asking the children to put the question into their own words -giving an example of a possible answer -give them thinking time • Help all children to answer by asking them to: -say an answer in unison -show an answer with their fingers -point to a number on a grid, target board or line -asking questions with a range of possible answers -waiting before expecting an answer -getting the children to tell their partner the answer -giving children digit cards to hold up -writing answers on personal whiteboards -taking an answer but asking the children to discuss whether it’s correct

18. Key messages • Cover all areas of maths • Think of the 6Rs • Involve all children • 2 or 3 sessions in a week should be to do with your target area in maths • Counting and rapid recall should occur every day