The Cambridge View on Mathematics

The study of Mathematics is worthwhile for its own sake, being a key form of intellectual development. It is crucial for the understanding of many other subjects and is essential for functioning within modern society. 

 

Our vision for Maths qualifications for England is to develop a curriculum and assessment model that emphasises the richness and power of Mathematics, is comparable in intellectual rigour to the best in the world, and encourages the continued study of the subject.

 

Our mapping work on international curricula shows that there is not a great difference between the current 14-16 English curriculum content for Maths and notable high-performing jurisdictions and that, therefore, curriculum content is not the cause of any perceived decline in standards. However, our global experience and expertise lead us to conclude that the demand of the assessment in England is lower. We believe that issues of standards should be addressed through a more challenging assessment, including more thorough coverage of high-end topics and skills. We consider that there is scope to alter the balance of question difficulty within current papers to ensure a greater degree of competence for pass candidates, greater preparedness for those studying A Level, and greater discrimination. 

 

However, we are also of the view that it is not educationally desirable (nor technically feasible) to expect all candidates to sit the same un-tiered mathematics examination at the end of the 14-16 stage; the spread of maths ability and learning pace is too wide to take a ‘one size fits all’ approach.

 

We consider it important that students are allowed to progress at a rate appropriate to their skills, thereby increasing their overall attainment level in the longer term. Many high-performing jurisdictions also recognise the need to provide differentiated pathways for their maths students. In the absence of tiering, we would therefore like to see a progression route that allows weaker students more time to cover the curriculum - with defined staging posts. 

 

Experts both in Mathematics and in teaching agree that consolidation and enrichment – as opposed to acceleration and wider content coverage – are the keys to increasing attainment and encouraging the continued study of maths. 

 

In light of this vision there are three points that need to be made about the proposed new 14-16 curriculum. Firstly, the draft indicates an increase in content in some areas; although, for example, topics such as momentum and collisions are important within science, there does not seem to be a justifiable mathematical rationale to their introduction at this stage of mathematics. Their inclusion will increase time pressures on students and teachers without any evident benefit, and could reduce the time available for embedding the core concepts that would lead to a genuine increase in attainment. 

 

Secondly, although the published draft of the National Curriculum sets out the entitlement for all students, in reality we are concerned that it may be beyond the reach of many. A supporting pathway and assessment structure that allows for the full range of ability will be essential. 

 

Thirdly, our research suggests that, in particular, statistics is poorly served within the current 14-16 stage maths exams. We believe statistics is highly important and should be made compulsory within the curriculum, but its assessment should preferably be separate, more flexible, and varied. This would free up essential teaching time to fully address core mathematical areas such as algebraic fluency, numeracy and problem-solving – general skills that HE and employers value – and would allow important statistical skills to be taught, developed, and assessed in a cohesive, valid, and useful way. 

 

We consider that numeracy encompasses both fluency in basic calculation and also the wider definition of functional application of number and quantity in real world contexts. 

 

There is no precedent from high-performing jurisdictions for treating numeracy as anything other than an integral part of Maths. Indeed many do not appear to refer to it explicitly, but nevertheless perform well in international tests designed to assess such skills. We are firmly of the view that numeracy can and should be assessed effectively as an integrated part of the Mathematics assessment, and that neither a hurdle nor a separate unit is appropriate. 

 

All high-performing jurisdictions recognise the importance of sound number sense and understanding of quantity and measure. We believe that increasing the standard of what is currently regarded as a ‘pass’ (Grade C) in the current qualification will help to secure a higher standard of numeracy. We consider the regular practice and thorough testing of non-calculator number work to be important in this regard, as is the regular application of number work within authentic contexts. 

 

We believe that calculators have a valid and important role within a Maths exam – to allow students to demonstrate skills in solving higher order problems without constantly being distracted by arithmetic, as well as being required for specific tasks such as working with trigonometric ratios. We also consider that the assessment should be testing how well candidates understand and use calculators in different contexts, as this is an important skill for the workplace and daily life. Nevertheless, we would recommend that there should be a higher proportion of non-calculator work in 14-16 maths assessments than currently, in order to address concerns regarding overreliance on calculator use in the classroom. 

 

With the possible exception of statistics, we believe that Maths can be examined via 100% external assessment. 

 

For statistics, as a separate assessment, there is a need to engage with large and authentic datasets and to appreciate the full cycle of data handling. It is also important, in order to meet the needs of business, for students to be adept at using computer software to enhance and facilitate the collection, manipulation, display, analysis, and interpretation of data. In order to reflect this in the teaching of statistics, we would recommend that alternative assessment models to traditional written papers are considered.