Mathematics curriculum documentation currently presents important information and messages for New Zealand teachers. Mathematical processes are not explicitly set out but embedded in different locations and there are multiple sources of proxy official curriculum information for the primary school. This article identifies and discusses examples of curriculum tensions for teachers and suggests possible changes for any future renewal of the mathematics (and statistics) curriculum.
Searching the New Zealand curriculum landscape for clarity and coherence: Some tensions in Mathematics and Statistics
https://doi.org/10.18296/cm.0025
Abstract
Mathematics curriculum documentation currently presents important information and messages for New Zealand teachers. Mathematical processes are not explicitly set out but embedded in different locations and there are multiple sources of proxy official curriculum information for the primary school. This article identifies and discusses examples of curriculum tensions for teachers and suggests possible changes for any future renewal of the mathematics (and statistics) curriculum.
Introduction
As a national curriculum, The New Zealand Curriculum’s (NZC) “principal function is to set the direction for student learning and to provide guidance for schools as they design and review their curriculum” (Ministry of Education, 2007, p. 6) After 10 years of NZC, how do we identify conflicting or problematic aspects in national curriculum documentation? Curriculum content and structure is important as a whole, as well as within any particular learning area, due to “the contentious nature of curriculum; the nature of knowledge, what counts as valued knowledge, and how we might know or understand curriculum processes and contexts” (Abbiss, 2014, p. 5). Sources of curriculum information therefore act as carriers of meaning, meanings about the nature and value of content as well as messages about pathways or trajectories of learning.
This article investigates the Mathematics and Statistics learning area in the English version of NZC, and the associated mathematics resources from the Ministry of Education. I use mathematics as an inclusive label to describe the Mathematics and Statistics learning area; this shorthand of “maths’ reflects how in my position as a teacher educator I hear teachers continue to talk about the Mathematics and Statistics learning area of NZC. My main focus is Levels 1–5 of NZC because during the past 15 years the Ministry of Education has published more sources of curriculum information for teachers than in the later levels (Levels 6–8). In addition, my research focus in mathematics education includes the primary school and the first 2 years of the secondary school, where I work with teachers in their postgraduate studies and hear about their practice in their local school contexts. School contexts are strongly affected by curriculum information produced by central agencies and it is this next layer of curriculum detail that becomes a proxy curriculum for teachers, standing in for the missing information of the national curriculum document. A school curriculum is therefore a complex and sometimes shifting landscape populated by multiple resources (Connelly & Xu, 2004).
In this article, I focus on clarity and coherence as two perspectives for examining curriculum information. Clarity relates to ease of access to information and use of shared meanings for teachers who are the main audience of official curriculum information. Coherence is a perspective often taken when analysing cross-national studies where coherence is identified and described in terms of consistency and alignment (Schmidt & Prawat, 2006). Curriculum content is typically analysed for alignment between the formal curriculum, curriculum materials, and teacher practice (Schmidt & Prawat, 2006). Alignment can be examined within each factor, between any two factors, or between all three (Cobb & Jackson, 2011; Schmidt & Prawat, 2006). It can involve tracking “coherent learning progressions … both within and across grades” and whether mathematics ideas are appropriate which involves “values about what is worth knowing and doing mathematically” (Cobb & Jackson, 2011, p. 184). In examining the content and presentation of curriculum information, I am interested in examples where there is lack of alignment, which therefore presents conflicting or contradictory information for teachers. I firstly examine NZC in relation to mathematical processes, and then scrutinise official curricular information within the primary school. The NDP (the collection of Numeracy Development Projects), in providing another layer of official detail, acts as a proxy curriculum, and has substantially influenced teachers who look to it for their long-term, and often short-term, planning, teaching, and assessment. In conclusion, I set out some possible directions for renewal of future official curricula information in mathematics, as prompts or topics for a wider discussion in the educational community.
The positioning of mathematical processes
Valued ways of specialised subject thinking can be presented in different ways within the school curriculum. In the previous curriculum, Mathematics in the New Zealand Curriculum (Ministry of Education, 1992), a strand called Mathematical Processes was included to complement the five content strands (Number, Measurement, Geometry, Algebra, and Statistics). Jim Neyland, who chaired the writing group, explained that:
If the content of mathematics is the ‘what’ of mathematics, the processes are the ‘how’. Mathematical processes focus on, for example, how to solve a mathematical problem of a type you have never seen before, how to carry out an open-ended investigation of a mathematical idea, how to form a conjecture and go about justifying or refuting it, how to reason mathematically using both inductive and deductive methods, and how to discuss mathematical ideas. (Neyland, 2004, p. 148)
Mathematical processes were therefore about important ways of investigating, reasoning, and discussing in a mathematics domain. The Mathematical Processes strand was split into three sections of Problem solving, Developing logic and reasoning, and Communicating mathematical ideas, each with achievement objectives and “Suggested Learning Experiences” that clarified the scope of the processes. For example, the first Achievement Aim emphasised opportunities for students to “develop flexibility and creativity in applying mathematical ideas and techniques to unfamiliar problems arising in everyday life, and develop the ability to reflect critically on the methods they have chosen” (Ministry of Education, 1992, p. 23). Content and explanatory information for teachers included a list of problem-solving strategies (p. 25), as well as the importance of presenting ideas using language and representational tools of mathematics. In addition, the Mathematical Processes strand was the first strand presented in the document (pp. 23–29), sending a clear message that these processes were “the “basics” of mathematical knowledge. And, this strand amounted to a charter for an extremely open-ended, yet discipline-based, education in mathematics” (Neyland, 2004, p. 148). The official curriculum information therefore clearly communicated that mathematical processes were important for learning, had curriculum status at all levels, were valued for assessment, and should infuse all content strands.
In terms of curriculum alignment, there is some evidence that the Mathematical Processes strand in the official curriculum was aligned with teacher practice. The 2001 Mathematics survey of the Curriculum Stocktake found the “vast majority (89.9%) across all school levels indicated that the Mathematical Processes strand was woven” within the content strands of their mathematics programme (McGee et al., 2002, p. 30). Yet comments from a sample of 400 teachers revealed a more complex picture. There were widely varying interpretations of the mathematical processes ranging from, for example, problem solving as tasks set in everyday events, tasks that involved practical work or use of equipment, group work or discussion. The report concluded that the responses were not sufficient to determine alignment with the intent of the curriculum (p. 45). This is not surprising, as I have noticed various approaches of teachers to the inclusion of mathematical processes in their classroom practice; including problem solving within every unit, or a specific problem-solving unit usually taught at the beginning of the year, or a one-day-a-week approach often known as “problem-solving Fridays”. These last arrangements were counter to Neyland’s wish that the Mathematical Processes must be “inseparable” from content strands, “could not be taught as a separate unit, and other strands could not be taught without giving emphasis to these mathematical thinking processes” (Neyland, 2004, p. 148).
In the current NZC, there is not a separate Mathematical Processes strand. Instead, processes are incorporated within different sections of the NZC document. The one-page “Essence” statement for Mathematics and Statistics states that these “two disciplines are related but different ways of thinking and of solving problems, both equip students with effective means for investigating, interpreting, explaining, and making sense of the world in which they live” (Ministry of Education, 2007, p. 26). There is also mention of “to think creatively, critically, strategically, and logically” and that students “learn to create models and predict outcomes, to conjecture, to justify and verify, and to seek patterns and generalisations (p. 26). Although some mathematical processes are mentioned within the Essence Statement, this page is not a regular reference point for teachers. When teachers consult the content Achievement Objectives, they see that each level begins with a sentence stem of “In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to: …”, but this sentence stem is positioned more as background information for teachers when designing their local school curriculum. Other learning areas in NZC have taken a different approach to including the valued processes of their subject. For example, the Science learning area includes Nature of Science as a learning strand, stretching across all four of the content strands and for every curriculum level. The purpose of the Nature of Science strand is to “learn what science is” and “how scientists carry out investigations”. These science practices might be considered parallel to mathematical processes. Similarly, the learning area of English has an overarching strand called Processes and Strategies, again for every curriculum level.
The key competencies are a new section of NZC that links to disciplinary practices, in particular the competencies of thinking, and using language, symbols and texts (McChesney & Cowie, 2008). Yet Begg was concerned “that the competencies, like the aims, will continue to be ignored while the curriculum focus remains a subject content one” (Begg, 2006, p. 22). This is even more likely because NZC expects schools to design their own localised curriculum (Ministry of Education, 2007). The Curriculum Implementation Exploratory Studies found that a focus on key competencies afforded opportunities for teachers in early adopter schools to consider how important disciplinary practices might be incorporated into both their school curriculum and their teaching practice (Hipkins & Boyd, 2011). While a useful professional learning opportunity, this is potentially very wasteful of teachers’ time when generating the detail of key competencies for each school (Wylie, 2012). Consequently, my examination of NZC for evidence of mathematical processes has found a fragmentation of clear and aligned information for teachers, which is problematic in terms of curriculum coherence.
This lack of explicit curriculum information about mathematical processes and content is not evident in curricla from other countries. In the international literature, five strands of mathematical actions are commonly used for guiding national curricula (Kilpatrick, Swafford, & Findell, 2001). The five strands are Conceptual understanding, Procedural fluency, Strategic competence, Adaptive reasoning, and Productive disposition, and these strands “are interwoven and interdependent” (p. 116). Conceptual understanding and procedural fluency are familiar terms for teachers (Anthony & Walshaw, 2007). Strategic competence is “the ability to formulate mathematical problems, represent them, and solve them … and is similar to what had been called problem solving” (Kilpatrick et al., 2001, p. 124). Adaptive reasoning is about logical thought such as reasoning, explaining, and justifying, and a productive (mathematical) disposition includes having an inclination to see mathematics as “sensible, useful and worthwhile” (Kilpatrick et al., 2001, p. 116).
These five strands are evident in two relatively recent national curricula in English-speaking countries. For example, in the new Australian mathematics curriculum, Australian Curriculum: Mathematics (National Curriculum Board, 2011), there are seven strands, three content strands, and four proficiency strands. The content strands (Number and Algebra, Measurement and Geometry, Statistics and Probability) describe the mathematics content to be taught and learnt, and the proficiency strands (Understanding, Fluency, Problem Solving, and Reasoning) “describe how content is explored or developed, that is, the thinking and doing of mathematics” (National Curriculum Board, 2011, no page). The development of the Australian mathematics curriculum deliberately involved a discussion of practical and specialised perspectives of mathematics and aimed to set out “the scope and nature of the mathematical actions that students need to experience in their mathematical learning” (Sullivan, 2011, p. 6). Similarly, the latest mathematics curriculum in the United States includes eight Standards for Mathematical Practice which are based on the “processes and proficiencies with long standing importance in mathematics education” (Common Core State Standards Initiative, 2010, p. 6). The Mathematical Practices encapsulate the five processes of problem solving, reasoning and proof, communication, representation, and connections, as well as the five mathematical proficiencies from Kilpatrick et al. (2001). The mathematical practices are expected to connect with all mathematical content suggesting that expectations for understanding “are often especially good opportunities to connect the practices to the content” (Common Core State Standards Initiative, 2010, p. 8). Within the last decade, the Australian and the United States’ mathematics curricula have included an explicit section on mathematical practices with the expectation that these will be connected to the content. Furthermore, the official national curriculum information provides examples of content connected to practices, with clearly identified expectations of valued mathematics, and signalled as worthy of assessing for learning. This, however, can still be problematic. As Cobb and Jackson remind us, when the practice standards “are presented separately from the content”, the mathematical practices “risk being de-emphasised unless users are able to infuse them into all mathematical domains” (2011, p. 185), echoing the concern of Neyland (2004).
The influences of a proxy mathematics curriculum
The content of the national curriculum is often supplemented by additional information from the Ministry of Education. For example, the NDP were trialled in the early 2000s and expanded as professional development to most schools during the resource production and professional development phases. Consequently, the NDP has dominated the teaching and learning of Number in New Zealand primary schools for the past 12 or more years. Much has been written about the NDP, and Walls (2004) provided a comprehensive curriculum and political critique of the early phases. While the NDP has been variously praised and criticised (Anthony & Walshaw, 2007), the most sustained critique relates to the use of ability grouping within mathematics lessons and the serious effects for student learning (Anthony & Hunter, 2017; Anthony & Walshaw, 2007; Walls, 2004). Due to the influence of the information presented to teachers, some aspects of the NDP have been, and continue to be, a proxy curriculum; that is, to stand in as official curriculum information for teachers. Important curriculum artefacts of the NDP are the Number Framework and the series of teacher books. The Number Framework “embodies most of the achievement aims and objectives in levels 1 to 4” (Ministry of Education, 2008, p. 1) but it plays a major role in setting out the organisation of content for the learning of number (Ministry of Education, 2008, pp. 15–22), and in naming progressions of learning as Stages. An initial content analysis of the Number Framework and the information for teachers has identified two problematic aspects of alignment.
First, the Number Framework organises the content into two distinct sections: Strategies and Knowledge. The Strategies section “describes the mental processes students use to estimate answers and solve operational problems with numbers” (Ministry of Education, 2008, p. 1) and is organised into three “Operational domains” of Addition and Subtraction, Multiplication and Division, and Proportions and Ratios (pp. 15–17). The Knowledge section “describes the key items of knowledge that students need to learn” (Ministry of Education, 2008, p. 1) and is organised into five categories (pp. 18–22). In some respects, the attention on strategies reflected 20 years of research on mental calculation processes and the learning opportunities afforded when children verbally describe their thinking during number tasks (Anthony & Walshaw, 2007; McIntosh, Reys, & Reys, 1992). This was also considered important at a time where “children may be encouraged to develop their mathematical thinking through active engagement in working things out, rather than following learned or prescribed procedures” (Walls, 2004, p. 34). The separation of strategies and knowledge into different sections is an unusual if not unique approach to mathematics curriculum design. A predictable consequence of this separation is a focus on specific strategies of the Number Framework, such as counting strategies (in Stages 1–4) and named strategies (such as rounding and compensating, reversibility, equal additions, standard place value partitioning in the so-called Additive and Multiplicative Stages (Stages 5–7) (Ministry of Education, 2008, p. 16). Walls pointed out that the NDP emphasised the “deliberate teaching of a range of predetermined strategies” (2004, p. 34), and she warned against a hierarchy of more sophisticated solution processes rather than processes related to the contextual relevance of a task.
The strategies are also heavily implicated in assessment of learning and in assigning children into specific stages. The assessment tasks provided by the Ministry of Education overwhelmingly focus on “the many story-shell examples provided” in the NDP materials (Walls, 2004, p. 35). According to the strategy observed by the teacher, a child’s thinking is assigned a specific stage of the Number Framework. The associated assessment tools of the NDP set up specific expectations of strategy use in order to “move to the next stage” with some assessment items stipulating performance criteria such as children use only mental processes without support from any materials or written recording, or that children must demonstrate at least two different strategies for a task. In addition, teachers report that the original professional development emphasised that children needed to move sequentially through each stage. Consequently, the hierarchical nature of the Number Framework when tied to grouping practices serves
to label children according to pseudo ability categorisations as evident in teacher references to children as ‘additive thinkers’ or ‘at Stage 3’ rather than being described, for example, as ‘thinking additively, she counted the dots one at a time’. (Anthony & Hunter, 2017, p. 74)
While some over-zealous implementation of NDP assessment tools and expectations may have been moderated over time, assessment of strategies is still used to assign students to stages, and then into ability groups based on these stages.
The counting stages and curriculum alignment
The second example relates to Stages 1–4 of the Number Framework, known as the counting stages. Stages 1–4 incorporate counting strategies known as “counting all”, “counting from first”, “counting from larger”, and using the principle of cardinality to recognise that the final number counted represents the total number in the group (Ministry of Education, 2008). The explicit setting out of different counting stages suggests to teachers that children in the first year need to “move through each stage” (Stages 1, 2, 3, and 4) before exploring number properties. Yet tucked away in Book 3, there is a paragraph that includes the following:
part-whole thinking is seen as fundamentally more complex and useful than counting strategies … Counting strategies are an inadequate foundation for these ideas … Therefore, your major objective is to assist students to understand and use part-whole thinking as soon as possible. (Ministry of Education, 2006, p. 9)
The urgency of “as soon as possible” appears to be under-played in the first year of school because assessment items for identifying young children’s counting are aligned with these stages, and “moving” to each stage relies on particular assessment tasks. Yet the revised edition of Book 5 (Ministry of Education, 2012) devotes three chapters (pp. 10–36) to counting strategies and associated number knowledge in a book of 78 pages. The presentation of curriculum information to teachers is also contradictory. For example, the diagram of the Number Framework strategy stages (first page of Book 1) is shown as an inverted triangle where the top half (the wider part of the triangle) indicates “an expansion in knowledge and the range of strategies that students have available” (Ministry of Education, 2008, p. 1). Unfortunately, from a vertical perspective, more than half of the vertical (altitude) length of the triangle relates to Stages 0–4. Teachers could easily construe that the four counting stages are crucially significant and require much teaching effort in the early years. Furthermore, Young-Loveridge questions “whether counting should be emphasised so heavily in the early years, or whether students would benefit from having a greater variety of mathematical experiences, including subitizing and comparison of continuous quantities” (2011, p. 82) (Subitizing is illustrated by recognising the number of dots on dice or dominoes, without having to count each dot.) This illustrates not only a mis-alignment within the internal curriculum information of the NDP but also a conflict with research about children’s learning. And, worryingly, this drawn-out focus on counting strategies may substantially delay children’s progress and prevent opportunities for richer mathematical learning at a young age.
Multiple proxy curricula in the primary years
The Number Framework was designed in the early 2000s, and clearly influenced the structure and content of the Achievement Objectives of NZC (2007) because the number substrands for Levels 1–3 are called Number strategies and Number knowledge. (In Levels 4–6 of NZC, there is one substrand called Number strategies and knowledge.) The Number Framework, though, is not the only proxy curriculum. There is also the hastily imposed National Standards in mathematics (Ministry of Education, 2009) that appear to be connected with NZC but set out specific standards for each of the 2 years now assigned to each curriculum level and across the 8 years of primary school. While some of the language in the mathematics standards is familiar from NZC and NDP (counting-on, partition, additive and multiplicative strategies), there does appear to be more specific description of fraction content, where an objective of “Know simple fractions in everyday use” (Level 2, NZC) is set out as “find fractions of sets, shapes, and quantities” (National Standards, after 3 (and 4) years at school, Ministry of Education, 2009). And more recently, in an effort to shore up the implementation of National Standards by producing an online moderation resource (Progress and Consistency Tool, known as PaCT), there are now the Mathematics Learning Progressions (Ministry of Education, n.d). The PaCT mathematics learning progressions comprise “eight aspects … organised according to the strands of the maths and statistics learning area of the Curriculum” (p. 4). Each aspect, however, involves “observable and distinct learning stages” (p. 4), where, for example, the “additive thinking” aspect “is similar to the additive domain of the Number Framework” (p. 5), but the examples of student mathematics solutions “are not a direct match to the stages of the Number Framework” (p. 5).
For primary teachers, the mathematics curriculum landscape was already complex. This latest tool has simply added to the multiple sources of official curriculum information for mathematics. Experienced and prospective teachers are understandably confused that there are so many sources of information with conflicting terms such as Levels, Stages, Standards, let alone “aspects” and “learning stages”. In addition, there appear to be cumulative effects of curriculum mismatch that may be problematic. In 2013, when the National Monitoring Study of Student Achievement (NMSSA, 2015) surveyed mathematics at Years 4 and 8, they found “a mismatch at Year 8 between student achievement levels and curriculum expectations. The curriculum expectation at Year 8 is that students will be working solidly at level 4” (p. 7). The results identified a curriculum disconnect around Level 4, indicated by results from NMSSA, that points to a possible mis-alignment of curriculum content at Level 4. This could be further complicated by the National Standards requiring Year 7 students to be achieving at early Level 4, while Year 8 students will be achieving at Level 4 of NZC.
Conclusions and implications
In this article I have examined various sources of official curriculum information for teachers, recognising that “curriculum development has the two faces of Janus: one looking to the past and one looking to the future” (Atweh & Goos, 2011, p. 215). I have identified examples of mis-aligned information and inconsistent messages for teachers that are consequently problematic for curriculum coherency.
When a national curriculum document has one page of explanatory detail and four pages of Achievement Objectives for each learning area, then what is omitted is likely to be as important as what is included. Valued curriculum content removed for brevity or for the sake of introducing and strengthening the Key Competencies has left mathematics depleted. The main casualty of this process has been Mathematical Processes which are now an invisible part of the mathematics curriculum, devalued by omission, and potentially neglected within classroom practices. This is concerning, particularly at a time when other national curricula are expanding and strengthening these important mathematical processes (practices or proficiencies). Paradoxically, providing additional information does not necessarily result in clarity and coherence for teachers. For New Zealand primary teachers, there has been supplementary official curriculum information positioned as proxy mathematics curricula. It is therefore crucial that the structure and detail in any proxy curricula, whether as resource materials, National Standards, or moderation information for teachers, needs to be carefully checked for curriculum coherence. Any curriculum information conveys explicit and implicit messages about values and priorities for mathematics learning, and care therefore needs to be taken to prevent implicit messages to teachers that might be unhelpful, contradictory, and result in constricting teacher practices, particularly related to assessment.
We can look to research and practice for setting out future paths in the New Zealand mathematics curriculum landscape. There are always teachers who have “explored and tried new alternatives, and when their explorations seem to be successful other teachers have followed (and finally the ideas are often accepted at the official level)” (Begg, 2008, p. 2) The current primary school focus on worthwhile mathematical tasks brings mathematical processes to the foreground of practice and changes the local school mathematics curriculum (Anthony & Walshaw, 2009). By attending to important mathematical processes, such as the complexities of argumentation, strongly researched localised practices are transforming student experiences in mathematics (Anthony & Hunter, 2017; Hunter & Anthony, 2011). These transformations
include changes in task format, an increased focus on mathematical argumentation, changes in expectations/norms for student engagement, increased cultural awareness/responsiveness, revised teacher expectations, and changes in the teacher role. (Anthony & Hunter, 2017, p. 87)
These carefully designed tasks are changing the mathematical experiences of students, both individually and collectively, involving them in reasoning and justifying practices of mathematics; that is, in opportunities to be mathematicians (Dent & McChesney, 2016). When school curricula are reflecting these processes, what then might need to be changed in official curriculum information so that these rich opportunities for mathematical learning can continue to thrive?
The NDP has been the most substantial and highly resourced mathematics professional development project in the past 20 years. Research has shown positive outcomes related to teacher professional development, changes to classroom mathematics programmes, and student achievement (Anthony & Walshaw, 2007). Nevertheless, there are curriculum aspects of the NDP that continue to influence the intended and enacted primary mathematics curriculum long after the NDP has officially ended.
As a proxy curriculum, the Number Framework continues to have a powerful role in providing curriculum detail for teachers, including pedagogical expectations. However, some immediate changes would provide greater alignment between the various curricular resources. For example, the hierarchy of separate stages for counting in the Number Framework could be combined and clarified for teachers. The teaching of sequential counting strategies may have delayed children’s access to more powerful tools of the number system, and prevented access to more challenging mathematics in the first 2 years of school. This can lead to unintended, yet predictable, consequences of delaying rich learning for many children. Next there needs to be a clarification and alignment of the learning content with respect to stages (NDP), year levels (National Standards), aspects (PaCT), or levels (NZC). If there must be “levels”, and this is contestable (Neyland, 2004; Walls, 2004), then pragmatically this is best left at the most global level, such as the levels of NZC. More broadly defined levels of NZC would also enable a better sense of learning trajectories, particularly through the primary school and into the first 2 years of secondary school. Greater detail at the national level would strengthen curriculum information, including mathematical processes (practices or proficiencies). This should be the aim of the next iteration of the mathematics curriculum in New Zealand, and there are other international examples to guide us (see Australia and the United States).
It appears, then, that it is time for curriculum renewal to achieve greater curriculum coherence. Any curriculum renewal would need to address the current situation where there are achievement objectives of NZC, content set out in the Number Framework, plus the National Standards for mathematics for each year of the primary school, and recently the Learning Progressions that are implemented through the PaCT tool. By any stretch of the imagination, this landscape of multiple proxy curriculum guides is very messy. A renewal of the curriculum content for Number is a means to quietly retire the Number Framework and cease the separation of strategies and knowledge in any further documentation. There is no separation of strategies and knowledge in the Algebra, Geometry and measurement, and Statistics strands, so there is no logical rationale for including this for Number. In addition, it would preserve the term “strategy” to be more aligned with Strategic proficiency which is a mathematical practice connected to problem solving.
It is also time to consider how, at a system level, there can be changes to the details of a national curriculum without having to wait for at least 10 years. How, though, can we commit to a process of designing, improving, and resourcing a national curriculum in transparent and sustainable ways (Cobb & Jackson, 2011; Sullivan, 2011)? The Ministry of Education has not had a dedicated curriculum unit since 1989, resulting in a loss of institutional knowledge (Wylie, 2012). Wylie noted that separating “policy and operations in the Ministry, and chopping its curriculum functions right back, has hindered the circulation of knowledge” through the education system in New Zealand (p. 249). Curriculum re-generation needs to be founded on joint work, such as national networks of teachers, subject experts, researchers, and officials in relation to the design and implementation of educational policy. This is possibly the most urgent focus for national curriculum infrastructure because
Without such ongoing joint work, based on existing relationships, trust, and shared knowledge, new resources or standards are unlikely to be as well-grounded as they need to be to really make a difference in teaching and learning. (Wylie, 2012, p. 248)
Any new mathematics curriculum resources need to be based on clarity, coherence, and subject credibility, as well as ensuring that when proxy curricular resources are designed, predictable consequences are identified and considered more carefully before implementation. A concerted and transparent process could ensure that we can make “bigger and more challenging changes” (Begg, 2006, p. 22), leading to a clearly aligned coherent curriculum for mathematics.
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The author
Jane McChesney is a senior lecturer in mathematics education at the College of Education, University of Canterbury. She teaches in primary and secondary mathematics initial teacher education and in postgraduate courses in mathematics education and research methods. Her research interests include mathematical practices in early years and school contexts, mathematical tools and representations, and initial teacher education.