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Session 2 Making Good Progress in Mathematics Calculation

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Session 2

Making Good Progress in Mathematics

Calculation

- 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.

- 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

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.

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.

- 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.

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

- 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

- 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

67 + 7 +20

154 x 3

2008 – 1996

168 ÷ 4

345 – 257

5.0 – 1.54

- 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?

- Lesson observations
- Book scrutinies
- Pupil conferences
- Planning
- Teacher audits
- Data analysis

- 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