Session 2 Making Good Progress in Mathematics Calculation

1. Session 2 Making Good Progress in Mathematics Calculation

2. Objectives • To examine the characteristics of pupils making slow progress in mathematics. • To identify and discuss the obstacles to progress in calculation. • To consider implications for managing mathematics in school.

3. Pupil characteristics • Often girls • Viewed mathematics as either right or wrong • Judged how good they were by the number of ticks or crosses • Didn’t like answering questions – saw this as a risk • Tended to work on their own – when they worked with others this was to align answers • Their work was neat

4. Obstacles to progress In number and calculation, pupils: • Have difficulty identifying related facts from known facts. • Were reluctant to use mental calculation skills. • Used formal written methods in preference to mental methods as they believed formal methods were better. • Relied on one fixed method to get a correct answer. • Lacked images and models to help with visualising mathematics.

5. Other significant findings Pupils: • Lacked opportunities for talk during mathematics lessons with their teacher, teaching assistant and peers. • Experienced a low level of challenge and tended to work within their comfort zone. • Developed a low appetite for risk-taking Teachers: • Some believed that children would be more self-confident if they always got the right answers, but this often led to routine and low-level work.

6. What do pupils need? • Structured and guided opportunities to develop a range of mental calculation strategies. • Experience of different ways to approach a problem or to do a calculation and to be able to compare their methods and ideas with others. • Support and modelling from adults to help them to work on more open approaches, to decide how and what to record.

7. Issues – related facts • Children had difficulty finding related facts from known facts. • Children viewed multiplication facts as unrelated facts they needed to memorise, and found this difficult.

8. Dealing with the issues – related facts

9. Issues – lack of strategies • Sustained teaching and learning of strategies and use of models and images to support • Frequent use and application of known facts to derive new ones • Understanding by teacher and pupil of the building blocks which are needed for calculation – e.g., place value, partitioning, structure of the number system • Frequent revisiting of strategies – discussion and evaluation of effectiveness and efficiency

10. Issues – lack of strategies • 8 • 1917 • 48 • 149 Subtract 50 to make 147 then add 2 back to make 149 Which Method..? 197 - 48 • 52 90 7 • __________ • 100 190 197 • 52 + 90 + 7 = 149 Add 2 to 48, to make 50 Then add 50 to make 100. Then add 90 to make 190. Then add 7 to get 197. 2+50+90+7 = 149 Take 40 off to make 157 Then 8 off to make 149

11. Which strategy…? 67 + 7 +20 154 x 3 2008 – 1996 168 ÷ 4 345 – 257 5.0 – 1.54

12. Issues – use of formal methods • Are formal methods the first resort for children in calculations using larger numbers? • Do children stop using jottings/number lines once they have been introduced to formal methods? • Do children make choices about the methods of calculation they use?

13. Identifying the issues • Lesson observations • Book scrutinies • Pupil conferences • Planning • Teacher audits • Data analysis

14. Key Outcomes • Every child, unless there is a barrier to cognition and learning, is entitled to reach national expectations or better at the end of each key stage. • Every child should make good progress through a key stage. • All children are in a school/setting that enables this to happen. • Every child has the right to teaching and learning which enables them to reach the national expectations. • Every child expects and is expected to be involved in the process