It is an accepted truism that “what you test is what you get” and that assessment is a key lever in defining students’ classroom experiences of mathematics. This is perhaps hardly surprising in many European classrooms when measures of performance increasingly ensure more centralised control over what is learned and how it is taught (Ball, 2003). Consequently the design of well-informed national assessment is crucial. If we want to ensure that students are engaged in meaningful mathematical activity it is essential that we understand how the assessment we use frames pedagogy and learning. This is particularly important in many European nations as curriculum design is being influenced by national performance in international studies such as PISA (OECD, 2002) and TIMSS. The European key competences (EU, 2007) promote the development of quantitative literacy as necessary preparation for work and active citizenship. The research we report here has been conducted as part of a national evaluation of work currently underway in England that is remodeling the 14-19 curriculum and piloting new qualifications to support a range of mathematics learning pathways. An initial systematic scrutiny of hundreds of assessment components for 16-18 year olds was carried out using a comprehensive framework that builds on the work of Burkhardt and colleagues (see for example, Bell (1992)) who sought to understand “balanced assessment”. To allow mapping of the fullest range of possible assessment tasks the framework has domains covering (i) structure (the degree of scaffolded support), (ii) content (concerning topic areas) (iii) process skills (recognising the phase(s) of problem solving covered) (iv) Task type (covering sub-domains of context, complexity, unfamiliarity). Additionally any potential barriers, for example due to language, and the required use of resources (such as graphic calculators) are identified. This framework indicates the potential mathematical activity that might result for students and the next step is to investigate, from the students’ perspective, how this translates into classroom experiences. We are particularly interested in the potentially different mathematical experiences of students following two such pathways, e.g. the traditional academic mathematics route and an alternative “applications” or “use of” mathematics route. The different designs of the qualifications situates the former so that vertical mathematisation might be expected to dominate and lead to horizontal mathematisation (in the sense of Freudenthal and colleagues (see for example, Treffers (1987)), whereas in the case of the latter route the reverse might be expected to be the case.

Our analytic framework indicates in detail the potential mathematical activity that might result for students; the next step is to investigate, from the students’ perspective, how this translates into individual experiences. Our focus here, therefore, is not on the “implemented curriculum”, of which we have detailed accounts from a parallel research project (see for example, Wake, 2007) but rather the “attained curriculum”. We investigate with students the demand of assessment items by recording their written mathematics together with their spoken commentary as they work through assessment examples. We use an analytical frame that builds on our scrutiny framework and connects with the analysis of mathematical understanding of Sierpinska, 1996.

At the time of submission the second phase of our research is incomplete, however, by the time of our presentation the totality of our scrutiny of assessment and explorations with students will help us understand how assessment drives student mathematical experiences and learning in greater depth than was possible through our initial scrutiny work. Of particular importance is the insight we will gain into how assessment of mathematics in context makes different demands of students to assessment of mathematics that is more abstract in nature. Better understanding of these principles will be of benefit to curriculum and assessment designers throughout Europe.