Primary Matters Spring 06

Feb 18, 2006

Miles Berry

As part of my ‘watching brief’ on primary matters for the IMA‘s Schools and Further Education committee, I write a termly report attempting to summarize developments in primary maths education, focussed principally on provision in England. What follows is my report for the spring term.

National Curriculum Test Analysis

Detailed analysis of pupil performance in the 2005 Key Stage 1 and 2 tests is available from QCA’s website, together with summary guidance on ‘implications for teaching and learning’. At Key Stage 1, QCA report increased confidence amongst pupils tackling the tests, but suggest several areas in which problem solving skills might be better developed, particularly when interpreting a range of contexts, and tackling two stage problems. They also encourage teachers to represent problems in different ways, and develop visualization and reasoning for shape or space problems. Amongst level 5 pupils in Key Stage 2, they report success in solving problems involving ratio and geometrical reasoning, and interpretation of pie charts. Again improved performance would come from attention to problem solving skills, notably through checking answers are reasonable within the question’s context. They also advocate more opportunity for pupils to work with fractions, visualization and spatial reasoning.

Primary National Strategy

The review of the National Strategy Numeracy Framework continues, with an expectation that a draft of the new version will be available for Easter. There will be clearer age-related expectations for outcomes, and an overall scaling up of expectations for each year group, as well as better use of the web to present and support the framework. Suggestions from the consultation exercise have included clearer linkage between objectives and expectations, broadening the application of ‘pace’ from lessons to learning, clearer focus on calculation and application, more room for personalization, and embedded assessment.

The National Strategies team have also pulled together material focussed on learning and teaching using ICT, including a ‘practical support pack’ featuring a number of video case studies linked to specific areas of the programme of study.



HMCI’s annual report on primary mathematics recorded a continuing rise in standards, with learning and teaching good or better in more than 70% of schools, although concern was raised over a relatively high proportion of less satisfactory lessons in the foundation stage. Use of ICT has improved, particularly through use of interactive whiteboards, but assessment and the wider application of mathematics remain cause for concern. The subject is generally well led.

These conclusions are in part mirrored by OFSTED’s evaluation of the Primary National Strategy, which warns that “there is still much that needs to be done to improve standards in mathematics”. Again, one area highlighted is the relatively limited provision for mathematics through other subject areas, although ICT is again singled out as an area in which there has been significant improvement. The report suggests that schools’ use of assessment data lacks rigour, with factors affecting poor performance not being identified or remedied sufficiently early.


Some Academic Research**

Hwang, Chen and Hsu [1] have had positive evaluations from use of a web-based ‘whiteboard’ system in teaching division.  Fiori and Zuccheri [2] have conducted a comparative study of written subtraction algorithms, and suggest that the choice of algorithm is more significant than cultural differences. They further emphasize the need to teach mental arithmetic and checking. In another comparative study, Moseley [3] has demonstrated benefits, including more interconnected and viable understanding, from introducing rational numbers through diverse perspectives. Okazaki and Koyama [4] discuss the use of both inversion and reciprocity as concepts to help overcome difficulties in division with decimals.

[1] Wu-Yuin Hwang, Nian-Shing Chen and Rueng-Lueng Hsu, Development and evaluation of multimedia whiteboard system for improving mathematical problem solving, Computers & Education, Volume 46, Issue 2, February 2006, Pages 105-121.

[2] Fiori, Carla and Zuccheri, Luciana, An Experimental Research on Error Patterns in Written Subtraction, Educational Studies in Mathematics, Vol 60 No 3, pp323-331

[3] Moseley, Bryan, Students’ Early Mathematical Representation Knowledge: The Effects Of Emphasizing Single Or Multiple Perspectives Of The Rational Number Domain In Problem Solving, Educational Studies in Mathematics Vol 60 No 1, pp37–69

[4] Okazaki, Masakazu – Koyama, Masataka, Characteristics of 5th Graders’ Logical Development Through Learning Division with Decimals, Educational Studies in Mathematics, Vol 60 No 2, pp217-251