Session 2

Making Good Progress in Mathematics

Calculation

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.

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

Obstacles to progressIn 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.

Other significant findingsPupils:• 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.

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.

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.

Dealing with the issues – related facts

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

Issues – lack of strategies

197 - 48

Take 40 off to make 157Then 8 off to make 149

Subtract 50 to make 147 then add 2 back to make 149

Add 2 to 48, to make 50Then add 50 to make 100. Then add 90 to make 190. Then add 7 to get 197.2+50+90+7 = 149

8

1917- 48149

52 90 7

__________48 100 190 197

52 + 90 + 7 = 149

WhichMethod..?

Which strategy…?

67 + 7 +20

154 x 3

2008 – 1996

168 ÷ 4

345 – 257

5.0 – 1.54

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?

Identifying the issues

• Lesson observations

• Book scrutinies

• Pupil conferences

• Planning

• Teacher audits

• Data analysis

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