Your shopping cart is empty

Good practice in primary mathematics: evidence from 20 successful schools

November 2011, 110140

The following information has all been taken from the Ofsted report Good practice in primary mathematics: evidence from 20 successful schools which can be downloaded here

Background Information

This survey was conducted following a ministerial request for Ofsted to provide evidence on effective practice in the teaching of early arithmetic. All of the schools visited are successful institutions, as reflected in their most recent inspection reports. While many other highly effective schools might have been visited, the 20 schools selected for the survey span a wide range of contextual characteristics, such as size and location, as well as being educationally diverse due to their maintained or independent status and varying attainment on entry to the school. Results of national Key Stage 2 mathematics tests (taken at age 11, Year 6) for the maintained schools, show their pupils’ progress has been significantly above the national average, and often outstanding, for at least the last four consecutive years.


One school has recently adopted the Singapore curriculum, which emphasises the consistent use of visual representation to aid conceptual understanding. For instance, ‘bar models’ are used to represent the relative sizes of quantities and fractional parts. The images below show use of bar models in solving addition and subtraction problems in Year 2.

Figure 18: Pupils’ use of visual representation in solving problems.

The Singapore textbooks and teachers’ guides draw on multiple images when developing calculation skills, including illustration of base-10 apparatus as well as partitioning numbers, as shown in the extract from a teachers’ guide in figure 19 below.

Figure 19: The left hand illustration shows one 10 being exchanged for 10 ones in the subtraction of 38 from 54, with addition being used as a check. The right hand illustration models column subtraction with partitioning of 62 into 50 + 12 as a prompt in the second question.

Download the complete document