Merely having another set of data in the form of benchmarking, targets and progress reports that ‘name and shame’ schools leads to resentment and compliance but not to improvement of learning and teaching (Earl & Fullan, 2003; McNeil, 2000). In South Africa, Kanjee (2007) sums up the challenge:

For national assessment studies to be effectively and efficiently applied to improve the performance of all learners, the active participation of teachers and schools is essential. … Teachers need relevant and timeous information from national (as well as international) assessment studies, as well as support on how to use this information to improve learning and teaching practice. Thus a critical challenge would be to introduce appropriate policies and systems to disseminate information to teachers. For example, teacher-support materials could be developed using test items administered in national assessments. (p. 493)

It appears that in using Annual National Assessments the South African Department of Basic Education is aiming to provide teachers with timeous information from national assessments to guide planning and monitor progress (Department of Basic Education, 2010). What is not clear is how the department is planning to support teachers on how to use this information to improve learning and teaching practice. Very little attempt has been made to involve teachers in data interpretation and not enough emphasis has been placed on the potential value of the data available from these systemic evaluations for informing teaching and learning practices. International research has engaged with the question of how to use assessment data beyond benchmarking (Earl & Fullan, 2003; Earl & Katz, 2005; Katz, Earl & Ben Jaafar, 2009). In thinking about this question, Katz, Sutherland and Earl (2005) drew an important distinction between two very different kinds of practices in benchmarking: ‘accounting’, which is the practice of gathering and organising of data, and ‘accountability’, which refers to teacher-led educational conversations about what the data means and how it can inform teaching and learning. Katz et al.’s (2005) distinction is very important and is in line with Elmore’s (2002) and Hargreaves’s (2001) important arguments. Hargreaves (2001, p. 524) argues that the future of collegiality may best be addressed by (inter alia) taking professional discussion and dialogue out of the privacy of the classroom and basing it on visible public evidence and data of teachers’ performance and practices, such as shared samples of student work or public presentations of student performance data. Elmore (2002) claims that teachers can be held accountable for their performance only if they have a deep sense of the demands made upon them. Although this may seem obvious, the challenge lies in identifying what counts as making accountability standards explicit.

Literature on professional development programmes for teachers shows that piecemeal forms of intervention are not effective (Borko, 2004; Cohen & Ball, 1999; Earl & Katz, 2005; Elmore & Burney, 1997; Katz et al., 2009). A broad consensus seems to emerge around the following claims: firstly, that teachers require continuous interactive support over a substantial period of time. Secondly, that teacher learning should be focused on specific (and few in number) educational objects and guided by an expert who is acting as a critical friend. Thirdly, that within the current emphasis on accountability, professional conversations by teachers, in support networks (broadly referred to as ‘professional learning communities’), can provide teachers with a productive opportunity to cultivate a sense of ownership of what the data means, specifically in relation to their current practices.

The positive outcomes of research done on the efficacy of professional learning communities served to inform the approach used in this project (Brodie & Shalem, 2011). The term ‘professional learning communities’ generally refers to structured professional groups, usually school-based, providing teachers with opportunities for processing the implications of new learning (Timperley & Alton-Lee, 2008). Commonly, professional learning communities are created in a school and consist of school staff members or a cross section of staff members from different schools in a specific area of specialisation. The groups in the DIPIP project were structured differently and included teachers and practitioners with different knowledge bases and role specialisations (see below). As professional learning communities, the groups worked together for a long period of time (weekly meetings during term time at the Wits Education campus for up to three years from 2007–2010), sharing ideas, learning from and exposing their practices to each other. In these close-knit communities, teachers worked collaboratively on curriculum mapping and error analysis, lesson and interview planning, test setting and reflection.

To provide the basis for a systematic analysis of learners’ errors, test items and learner achievement data of an international standardised multiple-choice test, the 2006 and 2007 International Competitions and Assessments for Schools (ICAS), was used.¹ For the curriculum mapping activity the groups were tasked with investigating the alignment of the ICAS tests items (not learner achievement data) with the curriculum at the time, that is, the NCS for Mathematics (Department of Education, 2002). This article focuses on the nature and outcome of the curriculum mapping activity, presenting findings on how the curriculum mapping activity provided groups of practitioners an opportunity to engage with and reflect on the curriculum, and discussing in what ways and to what extent this activity succeeded.

Teachers’ understanding of accountability demands, their consent and their readiness to accept change are interrelated processes (Shalem, 2003), but policymakers often assume that curriculum standards make policy requirements sufficiently clear to teachers. In practice, ‘reading’ the curriculum requires an application of teacher knowledge. Shulman (1986) refers to three categories of teacher knowledge, namely, pedagogic knowledge, content knowledge and pedagogic content knowledge. In order to properly interpret the curriculum, teachers are expected to draw on their subject matter knowledge and to contextualise curriculum standards within their learning environment, taking into account the needs of their learners. In terms of Shulman’s categories of knowledge, this means that teachers need to draw on both their content knowledge and pedagogic content knowledge in order to interpret and apply the curriculum. More specifically, Ball’s sixth domain of teacher knowledge, ‘horizon knowledge’, is useful here. It refers to teacher knowledge ‘of how mathematical topics are related over the span of mathematics included in the curriculum’ (Ball, Thames & Phelps, 2008, p. 403). Following the work by Ball et al., one can say that in order to set high expectations for their learners, in addition to their specialised mathematical knowledge which straddles six domains of mathematical knowledge for teaching, teachers need to understand the sequence and progression of the mathematics they teach. Teachers need to understand what the curriculum aims to achieve in an earlier grade and in what ways the topics they teach connect to the conceptual development of the same concept in a later grade. In this way, teachers could better understand the standards required of the curriculum.

International empirical research shows that curriculum statements about assessment standards, together with results of various standardised assessments, do not, in themselves, make standards clear (Darling-Hammond, 2004; Katz et al., 2009). Empirical research in South Africa has identified misalignment between the demands of the curriculum, teaching and assessment (Reeves & Muller, 2005). Classroom research suggests that many teachers simply ignore important aspects of the NCS and continue to teach poorly what they taught before (Brodie, Jina & Modau, 2009; Chisholm et al., 2000; Fleisch, 2007; Jansen, 1999). There are a variety of reasons for this overarching finding. Research in South Africa gives primacy to two inter-related explanations: poor teacher knowledge, in particular subject matter knowledge, and poor signalling of the (NCS) curriculum (Taylor, Muller, & Vinjevold, 2003). The argument is that the outcomes-based curriculum provided teachers with very weak signals as to what content should be made available to learners and how this should be done. Many teachers in South Africa lack strong content knowledge to ‘design down’² tasks, activities and assessments from the outcomes specified in the curriculum (South African Qualifications Authority, 2005). NCS curriculum standards were generally weak, both in content and progression, and therefore provided a weak guide for teachers (Muller, 2006; Reeves & Muller, 2005; Shalem, 2010). Reeves and McAuliffe (2012) found in their study of ‘topic sequence’ and ‘content area spread’ in mathematics lessons that ‘for most learners mathematics was not presented in a coherent and composite manner over the school year’ (p. 28). When the curriculum specifies content as a list of topics, it does not elaborate sufficiently on the topics conceptually, and does not relate the topics to one another adequately. Furthermore, lists of skills of what learners must do without any specific content attached to these skills allow for too much variation (low reliability) in the types of textbooks that are produced, in the criteria used by schools to select textbooks, in teachers’ professional judgement of what counts as an achievement, in the kind of tasks teachers design and in ‘curriculum coverage’. The main point here is that ‘lists of statements’ do not necessarily show what concepts are key to a field, what activities are worthwhile and what texts are worthwhile (Shalem, 2010, p. 91). Taken together, these explanations suggest that teachers struggle to interpret the curriculum (Brodie, Shalem, Sapire & Manson, 2010).

In this article we add a third explanation. We propose that even if standards are sequenced and well explicated by examples, they do not disclose to teachers what instructional practice should look like or what constitutes acceptable coverage and cognitive demand of curriculum content. Curriculum standards intend to transmit criteria to teachers of what, when and how to teach mathematical content, but transmission this through telling teachers is not enough. Teachers need to be involved, we argue, in a practice that will require them to use the curriculum standards so that they understand what they mean and how they are related to their existing practice. Criteria, says Cavell (1979), are embedded in practice. We ‘find’ them in the way we do and say things. It is in the way we speak or in the way we do things that we make relevant connections, and thereby show that we understand the way a concept is related to other concepts, or its criteria (Shalem & Slonimsky, 1999). Put differently, by doing knowledge-based professional work, teachers, we argue, are given an ‘epistemological access’ (Morrow, 1994) to the form in which the curriculum is designed, and more specifically to the content that it privileges. According to Ford and Forman (2006), this kind of professional development work requires a relational framework between three fundamental constitutive disciplinary resources: disciplinary material (working with ‘the material aspects’ of a specific intellectual field or with a set of propositional knowledge limited to the field), collectivity (using the norms of the intellectual field to produce proofs and grounds for judgement), and disciplinary procedure (following procedures to evaluate claims made about the natural or the social world) (p. 4). Taking part in curriculum mapping activities, we argue, provides such an opportunity for teachers’ professional development.

Teachers can become more familiar with the requirements of the curriculum and in this way improve the conditions for achieving curriculum alignment (Burns, 2001; Jacobs, 1997) through their involvement in curriculum mapping activities. Curriculum mapping is defined as a ‘tool for establishing congruence between what is taught in the classroom and what is expected in state or national standards and assessments’ (Burns, 2001). The idea was formulated by English in the 1980s (in Burns) and in its common form includes a type of calendar on which teachers, in grade-level groups, record time-on-task in each of the topics they teach and the order in which they teach the topics. Over time this practice developed to include teachers’ records of the ways they taught and assessed the topic. In this common form, curriculum mapping is focused on the relation between the enacted curriculum and the intended curriculum.

By working with test items (the examined curriculum) and thinking about the links between the content present in the test items in relation to the content present in the curriculum standards (the intended curriculum), the teachers in the DIPIP project were doing a different and more unusual form of curriculum mapping. The use of test items as an artefact to focus teachers’ thinking when they interpret the curriculum addresses the main challenge faced when interpreting any curriculum document, that is, to identify ‘what’ has to be covered as well as ‘the level’ at which the selected content needs to be taught. In curriculum terms this refers to curriculum coverage in a specific intellectual field at levels of cognitive demand appropriate for specific grades. By structuring professional conversations around curriculum mapping of test items, the mapping activity intended to provide the teachers with a relational framework, one in which they enact dimensions of expertise that are commonly excluded from them (curriculum mapping). Through this we hoped to enable the teachers to gain a deeper and more meaningful understanding of the curriculum (the NCS), which, as we have shown above, is a skills-based curriculum that is, in best case scenario, opaque, especially in the case of teachers with weak subject matter knowledge. It is to the design of the activity that we turn next.

The ICAS tests were not designed especially for the South African curriculum. These tests, which are used in many countries in the world, were used in South Africa in good faith that they represented an ‘international’ mathematics curriculum. The mapping activity that the groups were given to complete was not done on this test by any expert or department official. The Gauteng Department of Education treated the test as generally valid for the mathematical content of the grades tested. Our curriculum mapping confirmed this assumption. Table 1 shows our analysis of the content coverage in the ICAS 2006.³ The table lists the number of items per curriculum content area for each of the grades studied in the project (consistent with the NCS topic weighting).

A modified curriculum document was prepared for use by the groups (Scheiber, 2005). The tabulated curriculum enabled the groups to navigate and refer to the NCS document more easily, to look at and compare the content and contexts across the different grades. The tabulated curriculum has a landscape page setup and matches the assessment standards for each grade, across the page, using numbers. This makes it easy to compare the assessment standards across grades and to see at a glance how concepts are built up in each grade. Figure 1 gives an illustrative example of the mental arithmetic assessment standard strand from Grade 1 to 5. In the full tabulated document, assessment standard strands from Grade 1 to 9 are given across the page.

The groups were given a template (see Figure 2), which structured their conversations and guided the process by which they arrived at a consensus, which was recorded in the template as the ‘group response’. The template was given to the groups in order to focus the conversation around what the ICAS test assessment data (the examined curriculum) means, how it aligns with the conceptual demands of the NCS (the intended curriculum), and how it fits with teachers’ professional knowledge and experience (the enacted curriculum) (Brodie et al., 2010).

For each test item the groups needed to:

• identify the mathematical concept or concepts being tested by the ICAS item
• find the relevant assessment standards relating to the concepts
• justify the choice of the assessment standard
• state when or if the content is taught and whether it is taught directly or indirectly.⁴

FIGURE 1: Exemplar assessment strands (mental arithmetic, Grade 1–5) in tabulated format.

FIGURE 2: Curriculum mapping activity template.

• Since only one group of Grade 7–9 mapped items in Round 2, comparisons cannot be made for these grades with Round 1 mapping.

• One of the groups (Grade 7) attained full matching with the expert. This may have skewed the data.

• Round 2 was a slightly abridged version of the curriculum mapping, due to time constraints, in which the teachers only mapped curriculum content and did not report on when and how they taught this content.

We first present the overall results of the curriculum mapping, in which we look at the alignment quality of the groups’ mapping. We then discuss the groups’ reporting on content ‘taught’ (directly and indirectly) and content ‘not taught’, which yields insight into the relationship between the intended and the enacted curriculum.

Round 1 groups worked with group leaders whilst in Round 2 they worked without group leaders, which may have contributed to the increased misalignment in the Round 1. Secondly, the mapping alignment of Grade 7–9 groups was found to be stronger than Grade 3–6 groups. It stayed at the same level of accuracy (around 80%) in both rounds.

This finding suggests that with more experience groups gain confidence in mapping test items against the curriculum and make better judgments in relation to curriculum alignment.

FIGURE 3: Comparison between Round 1 and Round 2 in terms of mean alignment for grade groups that mapped more items or mapped fewer items.

Quotes taken from grade groups’ recorded responses are given as examples of teachers’ reporting on:

• Direct teaching: ‘When we teach bonds’ (G4gA); ‘Taught in term 1, as mental calculations’ (G5gA); ‘Decimal fractions are taught in the first term of Grade 7’ (G7gA).

• Indirect/linked teaching: ‘Should be covered in all problem-solving activities across all grades’ (G6gA, G8gB); ‘Place value is taught in the first term. Link it with money, mass and capacity’ (G5gB); ‘Should be done specifically as the concept of symmetry but it can be done via the theme e.g. Special me (body parts-left and right sides of the body)’ (G3gB).

• Content not taught at all: ‘Number patterns – Grade 1 onwards. Not focused on in Grade 8. Knowledge is assumed’ (G8gB); ‘The concept of odd and even numbers – Assume that it has been taught in earlier grades’ (G5gB); ‘… pictorial representation of patterns is a neglected area, thus making it difficult for them to conceptualise what is required’ (G3gB); ‘Rotation is not taught in Grade 4, but is in the curriculum for Grade 5’ (G4gA, G4gB).

FIGURE 4: Grouped grades’ reporting on ‘when I teach it’ (Round 1).

FIGURE 5: Grouped grades’ reasons given for content not taught.

We further investigated the reasons given by the groups for content ‘not taught’ (see Figure 5) in their completed mapping templates. Our investigation gave rise to two categories of mapping referred to as ‘mapping downwards’ and ‘mapping upwards’. Mathematical content of an item that according to the curriculum should be covered in a lower grade than in the test was classified as ‘mapped downwards’ – reported as: ‘This [different perspectives of geometric solids] is not specifically covered in Grade 8, it is formally required to be taught first in Grade 6’ (G8gB). Or, pointing to the problem-based nature of an item, groups reported: ‘Although the number range falls within the scope of the Phase, we do not teach this, because the way in which the problem is presented is beyond the scope of the Phase’ (G3gA). Mathematical content of an item that according to the curriculum should be covered in a higher grade than in the test was classified as ‘mapped upwards – reported as: ‘We would use this task [modelling involving area] as an extension for the stronger learners’ (G8gA). Most commonly, explanations for ‘not teaching’ fell into one of these categories.

It is also interesting to note that more content in the primary school (Grade 3–6) than in the secondary school (Grade 7–9) was classified as ‘not taught’ for reasons of being at a higher than expected level for the grade (according to the intended curriculum identified in the NCS).

Table 2 shows that most items reported as ‘not taught’ were at the grade level of the test, according to the intended curriculum. Few of the items reported as ‘not taught’ were mapped up or down, relative to the grade level according to the intended curriculum.

In the Grade 3–6 group, 44% of the content reported as ‘not taught’ was at the expected grade level. In the Grade 7–9 group, 76% of the content reported as ‘not taught’ was at the expected grade level. In both grade groups, the content reported ‘not taught’ at own grade level included mathematical content across all five of the NCS content areas. The Grade 3–6 group mapped up some data, measurement and geometry items and they mapped down some number and data items. The Grade 7–9 group did not map down any items but they mapped up some number, geometry and measurement items.

Some of the specific neglected areas reported by the teachers include (quotes are taken from grade groups’ recorded responses):

• ICAS items that included irregular shapes, rotational symmetry, tessellations, reflections, rotations and probability were reported as beyond the scope of Grade 3 (G3gA, G3gB).

• The pictorial representation of a pattern was reported as not taught at the Grade 3 level. Patterns are usually taught as a horizontal sequence of numbers: ‘… pictorial representation of patterns is a neglected area, thus making it difficult for them to conceptualise what is required’ (G3gB).

• Reasoning logic was reported as not taught in Grade 8: ‘Never! Not mathematics’ (G8gA).

• Finding fractional parts of whole numbers was reported as not taught using learning aids in Grade 5: ‘We never use manipulatives to determine fractional parts of whole numbers’ (G5gA).

Our data analysis shows a direct relationship between the teachers’ perception of the enacted curriculum – content taught ‘directly’ – and the degree of success in aligning the international test item to the curriculum. Figure 6 shows higher percentages of misalignment of item content reported as ‘not taught’ (compared to content reported as ‘ taught’) for both groups, but particularly in the lower grades. Content reported as ‘taught directly’ is, for the best part, aligned better. This difference in alignment could be an indication of teacher content knowledge. It could be that in the higher grades teachers are teaching more work with which they are not sufficiently familiar, yet they do teach it because it is required of them. It is also possible that the teachers in the lower grades may have reported more openly on content ‘not taught’. The teachers in the higher grades may leave out content with which they are not familiar but they do not report on it. Alternatively, the items may include content that the teachers expect should be taught earlier and thus do not report on it.

In conclusion, by allowing them to analyse if and when the content specifications of the intended curriculum are covered in practice, the mapping activity gave the teachers an opportunity to reflect on their practices. We argue that the mapping activity enabled them to develop their pedagogical content knowledge (Shulman, 1986). By examining curriculum coverage, cognitive demands and alignment, the teachers were involved in ascertaining the match between an international test, the South African curriculum and their professional knowledge and experience. This should have, at least to some extent, developed their understanding of the sequence and progression of the mathematics they teach and hence their grasp of Ball’s sixth mathematical knowledge domain (Ball et al., 2008).

FIGURE 6: Misalignment of content taught and content not taught.

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2.‘Design down’ was one of the imperatives of the NCS. This meant that teachers had to start with curriculum specifications and design lesson plans through which these specifications would be delivered in their classes.

4.‘Indirectly’ means through an assignment, a project or homework task, or linked to another content area.