Mathematics education in the English and French contexts and the implications for New Zealand of a “Europeanised” curriculum

Stephanie Ng

Abstract

Though they are geographically close, England and France's underlying philosophies regarding education and, for the focus of this paper, mathematics education, exhibit differences worth considering. The English system, influenced by the humanism school of thought, can be characterised by its desire to treat each student as an individual—and to guide the students in their social, emotional, as well as cognitive developments. In contrast, the French system places less emphasis on affective concerns, but rather focuses on the rational and functional aspects of education for all its citizens—a reflection of the encyclopaedic roots of French education. The results of these distinctive philosophical orientations can be seen in the practice of mathematics education in the two countries. For example, differences exist in their views on “setting”, the availability and use of textbooks, and in the day-to-day school culture. An examination of the strengths and weaknesses of the two European systems suggests potential changes could be made in New Zealand. These changes include: making mathematics an explicit, rather than implicit, gatekeeper; addressing the roles of the teacher; and changing the structure of the school day.

Introduction

Every country is unique—defined by its history, its values, and its people—but that is not to say it does not share similarities with other nations. England and France are two countries that share an intermingled history and geographical proximity, yet that are philosophically quite different when it comes to the principles governing education, and in this instance, mathematics education. I believe it is these differences that should be explored further in our consideration of the New Zealand curriculum and its development. Such international comparisons enable us to get a better appreciation of where New Zealand is from a global perspective, and provide an avenue for assessing what we are doing well, and what lessons can be learnt.

The initial inquiry into the similarities and differences of education in an Anglo-Saxon context, in comparison with a French one, stemmed from a personal visit to France in the summer of 2004/2005. I discovered that, despite having a poor level of French, I was generally able to understand the mathematics studied in the classroom. It soon became evident that the linguistic differences were not the problem; the challenges were adapting to the socio-mathematical norms established in the class. While the mathematics itself appeared to be much the same, there are nevertheless pedagogical differences between the French and Anglo-Saxon cultures, which I aim to address in this article.

First, some contributing influences to the philosophy and practice of education in both countries today are examined. Second, examples of differences in classroom realities within these countries, including the manner in which the mathematics is taught, the use of teaching resources like textbooks, and the implications surrounding homework activities are considered. These cultural differences, however, are simply examples of political, social, or philosophical influences which manifest themselves in each of the countries. Moreover, there have been significant political, philosophical, and pragmatic shifts in the course of each country's educational and social history—which can have profound effects on the educational practices we see in today's classrooms. Therefore, it is not intended to suggest that these differences are generalisable for the whole of England, France, and New Zealand.

In today's context, it is first and foremost interesting to analyse the French and the English approach to mathematics education, given the blurring of geographical boundaries, and the prevalence of educational comparisons between European countries, in addition to the “Europeanisation” that is allowing for much greater mobility of teachers (Broadfoot, Osborn, Planel, & Sharpe, 2000; McLean, 1990; Pepin, 1998, 1999c; Planel, 1997; Ravn, 2002; Robertson, 2000). To a larger extent, the impact of globalisation in general means we can no longer be rigid in our approach to mathematics education. Historical methods of teaching, that were once acceptable, may no longer be adequate in dealing with the demographic, and hence cultural, diversity in modern classrooms.

Although the findings from studies of these two European countries may not lead to one system of mathematics education being favoured over another, it is nevertheless insightful to study the processes and historical influences in other countries. By having an appreciation of these differences, one may better understand and build on the strengths of each culture—whilst addressing the weaknesses that are hindering progress in our own. It seems appropriate to study France, because the French tend to have a high level of attainment in mathematics. But also, of the European nations other than England, it appears culturally similar from an Anglo-Saxon point of view; it has similar issues with immigration, cultural diversity, and the problems of attainment relating to socioeconomic status (Fowler & Poetter, 2004).

Whilst much of the research literature is based around an English context, it would seem plausible to draw references to the New Zealand environment, given that the New Zealand education system has Anglo-Saxon roots. By taking into account the dilemmas of immigration, assessment, and teacher training, from both a French and English perspective, the New Zealand situation can be evaluated.

It is important to be clear from the outset that this article intends only to provide a snapshot of mathematics education in various cultural contexts, and that—more specifically—these are generalised cultural contexts from a New Zealand perspective, based on research literature also written predominantly from an Anglo-Saxon point of view. A French person's interpretation of these contexts may be very different. Furthermore, the teaching environment would vary enormously within countries as well as between countries. Nevertheless, there are some interesting observations that can be made about these two countries that can potentially contribute to the educational debate in New Zealand.

Contributing philosophical and political influences

The diverse classroom realities observed in French and English education often reflect the different underlying political and philosophical influences in each country; encyclopaedism and humanism are two such philosophies. These different philosophies can impact on each culture's view on the role of the school, the role of mathematics, and how this subject is learnt.

Before examining the mathematics taught and learnt in different countries, it is often necessary to gain an insight into the particularities of la vie scolaire (the school life) of the countries in question. Even defining the word “school” may prove to be a challenge, as it varies—depending on which school, community, and city, let alone country, you are in. The meaning could vary from a place “where one is extended academically”, such as in France, to a place “where one develops academically, as well as socially and emotionally”, as in England (Pepin, 1998, 1999a, b, c; Planel, 1997; Ravn, 2002).

McLean (1990), Pepin (1998, 1999a, b, c), and Ravn (2002) noted that one of the key historical influences on the English system is the philosophy of humanism (i.e., the importance of autonomy and self-realisation). The significance of this ideology is that schooling is meant to support and prepare students in the challenges they will face as an adult in society—which encompasses not only academic training, but also training in the arts and physical education, alongside provisions for general pastoral care. The focus in an English classroom is on developing the needs and abilities of the individual child, and hence Anglo-Saxon methods of teaching are commonly described as “child-centred pedagogy” (Ravn, 2002). This ideal is strongly manifested by the “setting” (grouping according to their abilities) of students in English classrooms, where it is believed that teachers can better address the needs of gifted (or less gifted) students (Ravn, 2002).

The French vision is for education to be gratuite (free) and laíque (secular) whilst adhering to their national motto of liberté, égalité, fräternité (liberty, equality, fraternity). French society is also strongly influenced by the encyclopaedism school of thought, where universality, rationality, objectivity, and utility are values that permeate not only the mathematics classroom, but the school system in general (Broadfoot et al., 2000; Henry & Cornu, 2001; McLean, 1990; Pepin, 1999a, b, c). The universality aspect (the absence of differential treatment of students) is strongly reflected in the égalité principle, where everyone is to be treated equally and given the same education irrespective of their individual needs. Setting at school would be unacceptable in France, because in the end, the main objective for education is to educate the whole group, together.

Cultural influences strongly affect the students' exposure to mathematics, as well as how it is taught (Geary, 1996). There is a French belief that all the students will eventually come to understand the subject matter taught, hence it is the teacher's duty to guide and support the students in their “discovery” or “development” of mathematical concepts (Fowler & Poetter, 2004). That is, mathematics is not meant to be learnt “sequentially” in France. The problem then, of course, is the assumption that students will come to understand the subject matter on the same time scale as their peers, which is reflected in the homogeneous treatment of the class (Haggarty & Pepin, 2002). This assumption also fails to recognise that students bring their own preconceptions and experiences to their learning—providing, therefore, another challenge to the egalitarian approach in the French classroom.

The belief that mathematics is learnt “sequentially” was a powerful sentiment that emerged from Jennings and Dunne's (1996) study of English classrooms. Many British schools were denying students opportunities to learn other topics if it were deemed that the “basics” had not yet been mastered. The efficacy of this has been put into question in the French context, which illustrates that students are capable of understanding relatively straightforward tasks whilst attempting a more challenging one (Jennings & Dunne, 1996).

Differences in practice

In either country, the political, cultural, and economical influences in the educational practices—including the influence on textbook use, the role of the teacher, and the nature of homework tasks—cannot be escaped.

Textbooks have become the very embodiment of “accepted and authoritative” knowledge (Haggarty & Pepin, 2002). Take the French scenario: a selection of the textbooks examined by Haggarty and Pepin (2002) was written by the mathematics inspectors who evaluate a teacher's quality of teaching, and subsequently their salary levels. Not surprisingly, the French teachers were more likely to use these textbooks (with preference over other options) in class preparation, and in the actual classes themselves (Haggarty & Pepin, 2002), even though the French curriculum does not provide a list of “approved” tests (Fowler & Poetter, 2004).

French schools provide students with textbooks, however this is not always the case in English schools, especially in lower socioeconomic areas (Haggarty & Pepin, 2002; Jennings & Dunne, 1996; Malleus, 2000). This fact does not only concern the access of learning material, but it would also influence the students', teachers', and parents' expectations of what and how mathematics should be learnt. Students who have access to textbooks at home, and at school, have more opportunities to revise and re-read for themselves the explanations and examples of the related topics—before commencing the questions. In contrast, English schools tended to encourage students to purchase reference material only if they were preparing for national exams (Haggarty & Pepin, 2002). However, in both France and England, students must learn how to use and recognise that their textbooks are resources, in order for the textbooks to be beneficial.

The content of the textbooks in England and France also differs. Some general features of French textbooks include: having explicit objectives; frequent usage of technical vocabulary; and an emphasis on the necessity in reading, understanding, and communicating mathematical ideas (Haggarty & Pepin, 2002). Conversely, the English texts are generally less dense and contain fewer examples that are, arguably, less cognitively challenging and less linguistically complex in nature. In addition, Haggarty and Pepin (2002) noted that English teachers were more likely to read questions to the students, reducing the need for students to read and decipher this mathematical knowledge themselves. By reading the texts for the students, the teacher's input into the pupil's learning of mathematics appears greater in the Anglo-Saxon context. English teachers were also more likely than French teachers to base their teaching on the textbook. It is claimed that “textbooks increasingly define the boundaries of what is possible in mathematics classrooms in England”, especially in the case where inexperienced or non-specialist teachers are concerned (Haggarty & Pepin, 2002, p. 587).

This reliance on textbooks for teaching is less problematic in the French context, since the recruitment process for teachers is in its nature very academic and competitive, seemingly more so than in Britain. In France, candidates must complete a minimum of four years' tertiary study and pass rigorous written and oral exams—the CAPES (Certificat d' Aptitude au Professorat de I' Enseignement du Second Degré) or Agregation—before one would even begin training on the pragmatics of being a secondary school teacher (Bonnet, 1996; OECD, 1996). To highlight the competitive nature of becoming a teacher, 16 percent of the candidates who sat the written exams in 2006 were eventually offered a teaching position in mathematics (Ministère de l’Éducation, 2006). In contrast to England, where a shortage of mathematics teachers exists, it is not uncommon to find a surplus of mathematics teachers in France (Hoyles, 2001). However, it is important to note that, although the French teachers may be more academically skilled, it is suggested that the English teachers connect more effectively on a social and emotional level than their French counterparts (Pepin, 1998, 1999a, b, c; Ravn, 2002).

The amount of mathematics instruction and the amount of mathematics homework a student does also varies in different countries (Geary, 1996). French students believed that doing homework was important for the learning process and were found to do more of it than their peers in England-suggesting that French students are also exposed to more mathematics than students in England (Broadfoot et al., 2000). French students have their own homework exercise books—un cahier d' exercices—whereas the English students are more likely to receive photocopied worksheets on an irregular basis from their teachers (Haggarty & Pepin, 2002). In general, it is found that European children indeed do more mathematics homework and mathematics instruction when compared with their Anglo-Saxon counterparts (Geary, 1996). Furthermore, the French teachers in Haggarty and Pepin's (2002) and Jennings and Dunne's (1996) research clearly stated and reinforced the learning outcomes by going over the previous lesson's homework. This reinforcement was often achieved by asking one of the students to write their response on the blackboard, where the students would be “expected to justify reasoning and calculations”, hence creating an atmosphere for discussion (Jennings & Dunne, 1996; Schmidt et al., 1996, p. 148). The French students were free to make mistakes, with supposedly less ridicule from their peers, than if the situation were repeated in England (Jennings & Dunne, 1996)—suggesting that students in France are more empowered in their learning than their counterparts in England.

Alongside the cahier d' exercices there are also cahier de cours (notebooks), which, in a French classroom, serve as an effective means for communication between a student and their teacher—as the books are often marked and returned on the same day (Fowler & Poetter, 2004; Haggarty & Pepin, 2002). These notebooks allow not only the teachers and the students to effectively communicate, but parents, too, can use these “living documents” to assist with the learning of mathematics at home (Fowler & Poetter, 2004, p. 305).

A perhaps more striking difference is the prevalence in France of the livret scolaire, a record of learning that tracks student achievement—not in terms of grades, but with comments from teachers—throughout their early school experience (Fowler & Poetter, 2004). With the cahier d' exercices, cahier de cours, and livret scolaire, it would seem the French treatment of assessment—in particular, formative assessment—sharply contrasts with the English system, where “high stake”, summative assessments, such as exams that reward or punish schools and teachers, appear much earlier in a student's school life. In France, however, the first “high stakes” exam a French student encounters is that of le baccalauréat, in their final year of high school (Fowler & Poetter, 2004).

Bearing in mind the French and English philosophies to education, it would be relevant to consider how students approach mathematics, and what it is that motivates them to achieve—abroad—as well as here in New Zealand. French students are thought to be intensely motivated by their fears of failure or redoublement (repeating a year) (Broadfoot et al., 2000; Fowler & Poetter, 2004). Whether or not a student must repeat a year is based on the recommendations from their parents and all their teachers, but the French language teacher and the mathematics teacher have the most influence. This point outlines the power held by the mathematics teachers in France, and the influence they have outside the mathematics classroom. The fact that the mathematics teacher can influence whether or not a student progresses is further testimony to mathematics being a “gatekeeper”.

Applications to the New Zealand context

Having now examined some of England's and France's social, political, and philosophical developments, as well as some of the strengths and weaknesses in their education systems, it would be interesting to examine the contributions of these insights to the pedagogical debate in New Zealand.

Given that many schools in New Zealand take on the Anglo-Saxon tradition of ability grouping (setting or streaming), it would appear that we, too, value individualism (by addressing the needs of the individual students). The problem with individualism is that we risk stereotyping students, which may be detrimental—rather than beneficial—to the learners. For example, students in lower sets (or belonging to a lower socioeconomic status) end up having lower expectations of them, thus reinforcing the self-fulfilling prophecy that lower-set students achieve less (Osborn, Broadfoot, Planel, & Pollard, 1997). As a result, setting is in fact reducing the number of learning opportunities for some students, when in reality, we should be asking how we can increase and improve on the current opportunities that are available (Haggarty & Pepin, 2002).

Another interesting point of difference is the presentation of new mathematical concepts in the different countries. In a French classroom, mathematical ideas are more likely to be “developed”, rather than “stated” as in the English context (Fowler & Poetter, 2004; Haggarty & Pepin, 2002, p. 586). Students in France work on exercises individually, but the discussion and development of concepts, guided by the teacher, takes place as a whole class (Pepin, 1997, cited in Pepin, 1999c). Given the apparent academic success in the French environment, perhaps an appropriate question to ask is: Are New Zealand educators effectively developing mathematical ideas through class discussion and investigations, in order to increase student understanding?

In England, group work appears more common than in France (Ravn, 2002) and, at first, appears to diverge from the principles of treating the individual needs of the pupil. However, the use of discussions nevertheless remains true to the humanism school of thought, because arguably class discussions are beneficial for developing social skills, such as listening and effective communication. That is, values of citizenship can be learnt simultaneously with mathematics problems.

Similarly, class discussions like those in France can also build students' social skills, such as effective communication. While having class discussions alone is insufficient in building these social skills, how these discussions are conducted, and what their underlying purposes are, must also be addressed. Despite frequent class discussions, there are few indications of success in the affective development of French students, whilst they are still considered as being “technically adept” in their mathematics (McLean, 1990). More recent trends suggest that France is now, too, addressing the emotional dimension of formal education (Ravn, 2002).

In an Anglo-Saxon environment, achievement in mathematics is treated as something exceptional. In Europe, however, it seems achievement is expected. The emphasis on producing “technical” mathematics students, as well as on the utility and rationality of mathematics, continues to present mathematics as a strong gatekeeper in France. Although mathematics is a gatekeeper in many cultures, including in New Zealand, the contrast is that everyone in France recognises that mathematics is a gatekeeper. The gatekeeping is explicit because, for example, people are aware that the mathematics teacher has the ability to recommend whether a student repeats a year. In New Zealand, however, mathematics remains an implicit gatekeeper.

Other aspects of classroom norms also manifest these implicit and explicit expectations for mathematics achievement. The role of textbooks is one such example. Although schools in New Zealand supply students with textbooks, one still needs to assess whether the students are investing adequate time in reading and deciphering mathematics problems in the classroom or at home. That is, are students being offered, and taking advantage of, the opportunities to “get used to” mathematical language? Moreover, are students being encouraged and shown how to use their textbooks as a learning resource, as they are in France (Haggarty & Pepin, 2002)?

In France, the formality of the textbooks—and of the structure of schools in general—runs the danger of alienating and disengaging students (Osborn et al., 1997). Furthermore, the problem of disengagement is thought to equally affect the teachers, because of the comprehensive syllabus developed by the French authorities that outlines the topics and learning objectives for all French children (Haggarty & Pepin, 2002; Jennings & Dunne, 1996). There is a myth that the French state-controlled education conforms education to the extent that lessons are synchronised, ensuring that every child is on page 54 of a certain textbook at 10 am on a certain day. Similar arguments have been presented by Snook (2005): that New Zealand teachers are also seen too often as “technicians” delivering a standardised curriculum, where in the past they were able to help design it. Not only would teachers seem to have fewer opportunities to think for themselves, but they are also subjected to frequent surveillance and supervision by the authorities (the Education Review Office).

Though the French myth of “synchronised education” may be a bit extreme, this structure is also arguably an effective method for offering teachers, especially new ones, guidance in the classroom. Fowler and Poetter (2004) have called this influence from the state the “top-down control strategy”, which, at first, often appears too strict to be implemented in any classroom because it would be unrealistic to treat students in such a homogeneous fashion.

To balance the top-down control strategy found in France (where the state controls the curriculum), a bottom-up empowerment strategy can be found that allows the teacher to determine how the curriculum is to be delivered, and the assessment methods employed, as well as ensuring that teachers sit alongside parents and senior management at the school council (Fowler & Poetter, 2004). To avoid the risk of disengaging teachers from their role as educators, it may be plausible to develop similar “empowerment strategies” for enabling New Zealand teachers to have a sense of fulfilment, control, and purpose in what they do. Teaching being acknowledged as a career of “professional” status, such as in France (where teachers are classified as civil servants, and subsequently become eligible to receive government benefits associated with this status), may result in an improvement to future teacher recruitment. However, French teachers, unlike New Zealand or English teachers, have no choice over in what region of the country they will be employed once they qualify. It is not uncommon for new teachers in France to be placed in inner-city schools and later move to more affluent schools when they have gained more experience (Osborn et al., 1997).

With regards to student assessment, the notebooks used in France are said to connect “the students, the curriculum, the teacher, the pedagogy, and the home in a way that brings the student's achievement into focus, making it easy for all to see what has and has not been learned” (Fowler & Poetter, 2004, p. 306). This philosophy does not appear to be far removed from that of the New Zealand goals for education, in light of the recent implementation of the National Certificate of Educational Achievement (NCEA) system, which also hopes to better report student achievement and their acquired skills. Unfortunately, the NCEA system is too frequently viewed as another way of “testing [which] has squeezed out teaching” (Snook, 2005, p. 13). Even though the aim of better reporting student achievement is similarly aligned, notebooks in France serve ultimately as a mechanism for feedback, whereas what the NCEA system offers has some intrinsic status associated with it because results are still recorded on the student's permanent transcript.

The use of the notebooks also has limitations imposed by each culture's norms. For example, French students put substantial effort into their notebooks, and would similarly expect the teacher to invest substantial effort in reading them (Fowler & Poetter, 2004). The notebooks are commonly marked and returned to the students on the same day—achievable because a school day in France, unlike in England or New Zealand, includes a two-hour lunch break. The long lunch breaks, alongside a French teacher's clearly defined non-contact time, allow not only for efficient feedback for the students, but also satisfactory time for lesson planning—a necessity (or perhaps luxury) it would seem, that New Zealand and English teachers have become deprived of in recent times (Snook, 2005).

This again leads to an examination of the type of education available to the students of modern Western society: poor lessons from exhausted teachers; or inspiring lessons from empowered teachers—using their creativity and professional expertise to teach, because they have the time to prepare lessons. New Zealand is not alone in facing a predicament so unfortunate (where teachers are inundated with paperwork, formal assessments, and, ultimately, stress) that teachers would, especially those who are non-specialist mathematics teachers, resort to relying on textbooks for lesson plans (Haggarty & Pepin, 2002). Undoubtedly, in any culture, preparation time for teachers is equally as important as the time the teacher spends with their class—a fact often overlooked by education administrators (Fowler & Poetter, 2004; Pepin, 1999a, c; Snook, 2005).

The teachers' general work environment and conditions are also points of variance not largely developed in this article. For example, there is an expectation that teachers in England are available at school outside their scheduled class time, but this is not so in France. These expectations are also likely to affect the students' interactions with their teachers. For example, students who may wish for extra assistance during their lunch hour may find this more difficult in France than in England or New Zealand.

As with England, teachers in New Zealand appear more accessible and have a closer, more social, rapport with their students (Broadfoot et al., 2000). This is supported by the fact that school life in an Anglo-Saxon context encompasses extra-curricular activities such as music and sport, in which teachers are often involved.

Perhaps one solution, then, is to address the structure of the school day. In having an extended lunch break of two hours, teachers are able to use this valuable time for lesson planning and marking students' notebooks. This extra time in the middle of the day may also be beneficial for those non-specialist mathematics teachers who may then contact their more experienced peers for support—a potential solution for reducing teacher stress. However, a school day of this nature would be difficult to implement in an Anglo-Saxon context, because of the value that is placed on participating in extra-curricular activities at school. The French, on the other hand, have an extensive range of clubs and outside organisations that offer activities the New Zealand community would expect from schools. That is, to change the culture of the school is to also change the culture of the community. Moreover, any deliberate changes to a school system requires significant consideration at all levels of the education debate, including the local school level and the national policy level. The analysis and implementation of change at these various levels must also navigate between political pressures and philosophical allegiances, as well as simultaneously merging idealist goals within realistic constraints.

Interestingly, students who had experienced both school systems tended to prefer the system they had grown up with, thus raising the issue of whether the effectiveness of a school system is more susceptible to subjective interpretation than first thought (Broadfoot et al., 2000).

The education debate is ultimately centred on values. Perhaps society values individuality and differential treatment, as in the English context, or all students should be given the supposedly same opportunities and be treated in the same way, as in France. If individualism and égalité were on a spectrum, one could speculate that the goals of New Zealand mathematics education lie somewhere in between. Being a former British colony, the New Zealand system, not surprisingly, more closely resembles the English than the French system. However, with the prevalence of immigration, it is paramount to highlight and address the forever changing needs of the students, and by examining the progress in other countries, like France, we are better able to reflect on areas in our own school system that may be improved.

Conclusion

It is important to note that the literature reviewed has addressed only a few facets of mathematics education in France and England. This article does not discuss, for example, the direct involvement of the parents and the community in a child's vie scolaire, nor the fundamental beliefs, and consequently the identity, that a student adopts in their school life. Furthermore, the differences within a particular culture itself also warrant further examination, for these must be addressed if one wishes to understand and improve mathematics education in a culturally relevant context.

When considering variations in mathematics education in England, France, and subsequently New Zealand, the linguistic differences appear relatively insignificant when compared with the profound social and cultural influences that impact on the philosophies, expectations, and goals of students, teachers, and the governing bodies in each country. These implications are reflected in the humanism perspective of education in England, in comparison to the encyclopaedism concept, which favours universality and functionality, in French education. These philosophical differences may mean that teachers take on a purely academic role, in contrast to a perhaps more pastoral or affective role alongside their scholarly duties. Not only is there a difference in the type of mathematics that is made available to students in England and France, but the opportunities to learn mathematics in general also differ as a result of the various factors that infiltrate all aspects of la vie scolaire (Haggarty & Pepin, 2002). These influences, confounded with the somewhat political and economic influences on the production and use of textbooks, are seen to have an effect on the prevalence of homework tasks and group discussions in culturally different classrooms.

One benefit of international and comparative research is the opportunity for a country like New Zealand (whose educational needs are often an amalgamation of those of other countries) to draw on the similarities and differences, to better enhance education at home. For example, the use of class discussions, if used appropriately, can appeal to the humanism school of thought, teaching aspects of citizenship, whilst encouraging the “development” of mathematics, as illustrated in the French classroom.

It is encouraging to also note that the French philosophy of providing students with feedback on their acquired skills is similarly aligned to the New Zealand philosophy behind NCEA. However, New Zealand educators should also address the fact that student feedback is achievable without having to subject the students to high pressure assessments, which become the preoccupation in the classroom, rather than the learning.

Although a notebook system may at first be appealing, its implementation is largely affected by the structure of the school day. The school day enables the notebooks to be effective in France, but the French school day is quite different to New Zealand's. In addition, teachers' responsibilities, and expectations of what they can achieve, differ across countries. To simply transplant one country's school system into another is unwise, because the educational needs of the students are equally imbedded with other cognitive, psychological, social, and even recreational needs and goals of the individual, as well as those of the society at large.

Ultimately, from a New Zealand perspective, we may find the French system to be too academic for the needs of the individual. However, the English system may be too individualistic and humanistic in its teaching of mathematics to effectively address some of the needs specific to the teaching and learning of mathematics in the New Zealand culture: an amalgamation of the traditional Anglo-Saxon roots and the relatively more recent immigration trends from Asia and the South Pacific. In addition, the changing demographics of the urban and rural populations that have seen rapid growth in the main city centres must also be kept in mind. Nevertheless, it is refreshing to note that the abilities and the qualities of teachers are also changing in the face of modern society, and in doing so, perhaps students everywhere can be provided with the best mathematics education possible: a combination of high attainment, utility, understanding, enjoyment, and social development.

While this paper has considered some of the differences between the French and English approaches to the mathematics curriculum, it suggests much more. It implies for me that curriculum developers may be wise to look beyond the Anglo-Saxon traditions when considering change. There is much to consider from many countries other than France and England, and it seems unfortunate that comparative curriculum research is not given a higher priority.

Acknowledgements

The author thanks Dr Maxine Pfannkuch, Dr Caroline Poisard, and, especially, Dr Andy Begg for their guidance in the development of this article.

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Note

An earlier version of this paper was submitted in 2005 as part of the requirements for a graduate course in Mathematics Education at the University of Auckland.

The author

Stephanie Ng is currently completing a BSc(Hons) in Mathematics at the University of Auckland, after having completed undergraduate studies in French, mathematics, and psychology.

Email: stephanie.ng.nz@gmail.com