Advertisement

Social and Cultural Contexts in the Teaching and Learning of Whole Number Arithmetic

  • Maria G. Bartolini BussiEmail author
  • Xu Hua SunEmail author
Open Access
Chapter
  • 9.3k Downloads
Part of the New ICMI Study Series book series (NISS)

Abstract

This chapter witnesses the growing importance of understanding the role of the social and cultural context in which the teaching and learning of mathematics is situated, outlining the background to the studies conducted in recent decades. The aim of this chapter is to report on the process that led the IPC to prepare a background information context form for each submitted paper, for the first time in an ICMI Study and, also, in any major international conference. A short analysis of the 66 completed context forms that were received is provided with elaboration and commentary. These data are a convenience sampling based on these submissions, rather than a representation of the population of mathematics educators as a whole. The information provides an ‘insider’ view based on the applicants’ perceptions, rather than a collection of objective data. This contextual information, however, concerns the participants attending the ICMI23 Macao Conference; hence it is important to understand the perceptions of the contributors involved in writing this volume: the data provide outlines of the pre- and primary level schooling cultures and systems within which particular kinds of findings, interventions and outcomes are achieved.

2.1 Introduction

At the first meeting of the ICME 23 IPC group, held in Berlin in January 2014, there was unanimous agreement on the relevance of cultural diversity in ICMI Studies. The Discussion Document for the study noted that:

It was decided that cultural diversity and how this diversity impinges on the early introduction of whole numbers would be one major focus. The Study will seek contributions from authors from as many countries as possible, especially those in which cultural characteristics are less known and yet they influence what is taught and learned. In order to foster the understanding of the different contexts where authors have developed their studies, each applicant for the Conference will be required to prepare background information (on a specific form) about this context. (see this volume, Appendix 2, “Introduction and Rationale for ICMI Study 23”)

This statement was based, on the one hand, on the awareness of the increasing participation of scholars from developing countries in international conferences and of the number of submissions to international journals of manuscripts from all over the world and, on the other hand, on the ICMI aim to improve the quality of mathematics teaching and learning worldwide. Most IPC members, including the first author of this chapter, have experience in reviewing papers for international conferences and journals: in many papers, there is an implicit belief that the readership knows enough about the context in which a study has been carried out (especially if it concerns European or North American countries) and that the transposition of findings from one country to another is possible and natural, if the theoretical framework and methodology are sound enough.

However, as early as the ICMI Study 8 (1992–1998) on Mathematics Education as a Research Domain: A Search for Identity (Sierpinska and Kilpatrick 1998), working group 4, led by Susan Pirie, Tommy Dreyfus and Jerry Becker, was raising questions about the issue of results and their validity. An interesting question was raised:

To what extent can research results from one environment or culture (e. g. Japan) be linked to those from another culture (e.g. the USA) and to what extent are results culture specific? (p. 27)

Although the issue was raised about 20 years ago, at the ICMI Study Conference in Washington, DC, in 1994, the acknowledgement of the issue of cultural context in major international journals and conferences remains uncommon (Bartolini Bussi and Martignone 2013). In support of this claim, it is enough to quote some excerpts from the information given to prospective authors of empirical studies by one of the major international journals, i.e. the Journal for Research in Mathematics Education (NCTM n.d.).

The Journal for Research in Mathematics Education seeks high quality manuscripts that contribute knowledge to the field of mathematics education. For an author’s work to be publishable, it needs to exhibit qualities that characterize well-conceived and well-reported research studies. The following information illustrates characteristics of strong manuscripts that have been submitted to JRME.

The following items are then elaborated:
  • appropriate purpose and rationale

  • clear research questions

  • an informative literature review

  • a coherent theoretical framework

  • clearly described research methods

  • sound research design and methods

  • claims about results and implications that are supported by data

  • contribution to the field of mathematics education

  • clearly explained and appropriately used terms

  • high quality writing

  • mathematical accuracy.

An abridged version of the same document appears in the PME 39 (2015) guidelines for research reports of empirical studies.

Observational, ethnographic, experimental, quasi-experimental, and case studies are all suitable.

Reports of empirical studies should contain, at minimum, the following:
  • a statement regarding the focus of the submitted paper;

  • the study’s theoretical framework;

  • references to the related literature;

  • an indication of and justification for the study’s methodology; and

  • a sample of the data and the results (additional data can be presented at the conference but some data ought to accompany the proposal)

In both cases, no reference to the social and cultural context is explicitly mentioned. Hence, the limited space allowed either for manuscripts or (even more limited) for research reports is likely to inhibit the author’s intention of framing the empirical study within its context. Moreover, it implicitly conveys the idea that every relevant scientific communication must follow the above structure, where there is no reference to the social and cultural context. It seems a limiting rather than a proactive statement.

For example, open-class activities/lesson studies that view the classroom as an open or public space, which has been a major influence in the professional development of teachers in China and Japan for many years, may be contrasted with the view of the private and autonomous classroom that has been described as common in the Western tradition (see, for instance, Sztein et al. 2010).

Instead, the evidence of some ongoing changes may be found in the guidelines for reviewers in two subsequent Conferences of the European Society for Research in Mathematics Education. The CERME 8 (2013) guidelines read:
  • Reports of Studies (Empirical or Developmental)

  • Surveys, observational, ethnographic, experimental or quasi-experimental studies, case studies are all suitable. Papers should contain at least the following:

  • a statement about the focus of the paper;

  • an indication of the theoretical framework of the study reported, including references to the related literature;

  • an indication of and justification for the methodology used (including problem, goals and/or research questions; criteria for the selection of participants or sampling; data collection instruments and procedures);

  • results;

  • final remarks or conclusions

The CERME 9 (2015) guidelines added a new indicator:
  • an indication on the scientific and cultural context in which this study is embedded (explaining crucial assumptions and the possible contingency of the relevance of the study for a specific cultural context)

What happened between the CERME 8 and CERME 9 guidelines? Both co-chairs of this ICMI23 Study were present at CERME 8, and the first author of this chapter was invited by the organising committee to introduce a forum discussion about the neglected importance of the social and cultural context. The CERME board was favourably impressed and accepted the challenge to adapt the widespread tradition mentioned above. CERME 9’s scientific committee not only introduced a small change in the instruction (for authors and reviewers), but also decided to host a panel chaired by Barbara Jaworski on Cultural Contexts for European Research and Design Practices in Mathematics Education (Jaworski et al. 2015). The panel was held very successfully in Prague in February 2015. This panel represents a milestone in making explicit international awareness of the importance of the social and cultural context in the teaching and learning of mathematics.

Another milestone is represented by the explicit request for contextual detail in the ICMI Study 23. The ICMI Study IPC unanimously agreed to highlight the role of the social and cultural context and to design a specific form (see below) for collecting relevant information about this context, in order to leave the limited space of the paper (eight pages) for the scientific report according to the usual formats. The aim was twofold: not only to collect relevant information for understanding the different contexts (as explicitly written in the Discussion Document), but also to foster authors’ awareness about the relevance of their own cultural contexts.

2.2 The Context Form: Design

The form designed by the IPC tried to address some very basic issues about the situation in the country where either the empirical research study or the theoretical reflections were carried out. The IPC was aware that a complete answer to all the questions would have been very demanding, and akin to a study itself, unless the authors knew some already existing documents at the national level (e.g. ICMI 2011).

The form designed by the IPC follows (Table 2.1).
Table 2.1

The context form

Please fill in as many of the following as completely as possible so that we understand the context of your paper

General (objective data)

Give a rough idea of the numbers of:

 Students up to the age of 11 years

 Teachers for pre-primary and primary education

A short description of the National Education System (please match grades with pupils’ age)

If relevant, please explain whether the system is inherited from colonial period or is related to local traditions

Give information about what you consider an important feature in your country (e.g. the pillar of the network of monastic schools in Burma)

Inclusiveness

Is the system totally inclusive?

Are there special schools/classrooms for

sensually impaired students (blind, deaf)?

Are there special schools for students with disabilities?

National language(s)

List the national language(s) of the country

List the local languages (minorities)

Is pre-primary/primary school carried out in the local languages?

Migrant/refugee/marginalised students

Is there a significant minority of migrating students (coming from other countries), of refugee students and of marginalised students?

Are there specific rules for schools which take care of these students? Is there some help from the national/local government?

Pre-primary general

Is pre-primary education extended to the whole country?

Which percentage of students are expected to enrol in pre-primary education?

Pre-primary textbooks

Do they exist?

In what language (in the case of more local languages)?

Is there only one national textbook? Or a limited number?

Is there only one teachers’ guide? Or a limited number?

Primary general

Is primary education extended to the whole country?

Which percentage of students are expected to enrol in primary education?

Primary textbooks

Do they exist? In what language (in the case of more local languages)?

Is there only one national textbook? Or a limited number?

Is there only one teachers’ guide? Or a limited number?

Primary teachers’ qualification

Generalists or specialists?

Assessment

Is there a national system of assessment?

At what ages/grades are students assessed in mathematics (focus on both pre-school and primary school)?

Standards

Is there a governmental/national document for standards?

Teacher education and development

What are the national rules?

Is there some shared practice you consider relevant (e.g. Lesson Study in Japan, guānmó kè in China)?

Do you have forms of distance learning for teacher development?

Teacher education and development: pre-primary

How is organised pre-primary teacher education?

Please distinguish (if relevant) the governmental rules and what happens in practice?

Teacher education and development – primary

How is organised primary teacher education?

Please distinguish (if relevant) the governmental rules and what happens in practice?

Contents (limiting the focus to whole numbers)

Local languages

Place value: do you have tradition of system of representation in base not ten?

Problems: which kind of problems are typical of school practice? (e.g. China: problems with variation)

Problems: which kind of problem-solving strategies? (e.g. Singapore: model method)?

Any other information related to the context of your paper

 

Some applicants expressed surprise at this unexpected additional task, asking the reasons for completing such a form with information that should already be known by all mathematics educators: this was further evidence, if any were needed, that the awareness of the relevance of the social and cultural context and the need to offer information about these are far from being shared in the field.

The following story of the Macao Conference, with the visit to Chinese schools and with the discovery of the differences between Western and Eastern mathematical traditions, provided further evidence that this awareness is really needed and useful in order to understand and to start a fruitful dialogue between different cultural contexts. This aspect will be further elaborated in this chapter and in the whole volume.

2.3 The Context Form: Data

Sixty-six context forms were collected, concerning 29 countries (counting separately China and SARs Hong Kong and Macao). The distribution by country is detailed in Table 2.2.
Table 2.2

The countries

Country

Number of forms

Country

Number of forms

Algeria

1

Australia

5

Belgium

1

Brazil

1

Canada

4

China

5

China HK SAR

2

China Macao SAR

2

Cyprus

1

Czech Republic

1

Denmark

1

Dominican Rep.

1

England

1

France

4

Germany

4

Israel

3

Italy

4

Jordan

1

Netherlands

2

New Zealand

2

Serbia

1

Singapore

1

South Africa

3

Sweden

2

Switzerland

1

Taiwan

4

Thailand

1

USA

5

Vietnam

1

All Francophone countries

1

Three submitted papers concerned cross-cultural studies (Cyprus – Netherlands, Germany – Australia, England – Sweden, where the context forms for both countries were filled (and, hence, were counted twice in the above table). In one case, the submitted paper concerned a cross-cultural study where all the Francophone countries were analysed for a study commissioned by the World Bank: a single context form was filled for all the Francophone countries, with reference to the colonial influence of the French system.

The applicants were encouraged to fill the form as completely as possible, drawing on their own knowledge. Hence, rather than on objective data, in most cases, the information drew on applicants’ knowledge and perceptions of their national contexts. Moreover, the sample was a convenience sample involving the selection of the most accessible subjects (Marshall 1996), limited to the applicants in the study, hence excluding or limiting the contribution of some major areas (e.g. India, Russia, Latin America, much of Africa, Southeast Asia).

In the following, we briefly outline the main outcomes of an early analysis of the collected data.

2.3.1 The General Structure of Education Systems for Early Years Mathematics

The data reported by the applicants have been matched with Education Database (n.d.). Although in some countries (e.g. Australia, Brazil, Canada, Cyprus, Germany, Switzerland, USA) there are differences between the different states/provinces/regions/territories, the models may be summarised as follows. While primary school or elementary school is the accepted wording, in some cases pre-primary school is named in different ways. Usually pre-primary is not mandatory but attended by many students (in some cases up to 95%) at least in the last year before entering primary school.

In some cases primary school is split into different steps including also what is elsewhere called middle school. Although our convenience sample is limited to 29 countries, there is a large variety, concerning both the duration and the entry age. In Europe too different models exist. This institutional diversity has implications for this study: for instance, when the entry age is postponed, it is likely that WNA is approached at pre-school level, and when the duration is extended (up to sixth grade, as in many Eastern countries), it is likely that pre-algebraic thinking is fostered before high school level. As these institutional differences cannot be cancelled, in this study we chose to focus on the contents rather than on the grades or the students’ age (Table 2.3).
Table 2.3

Structure of primary school

4-6 age: 6–10 (12)

5 age: 6–11

5–6 age: from 6

6 age: from 5

6 age: 6–12

6 age: 7–13

5–6–7 age: from 6

7 age: 7–14

8 age: 4–12

8 age: 7–15

9 age: 6–15

9 age: 7–16

10 age: from 6–16

Germany (depending on region)

Algeria (under colonial influence)

Cyprus (Greek, 6; Turkish, 5)

UK (complex system)

Australia

Taiwan

Canada (depending on territories)

South Africa

Netherlands

Serbia

Brazil (5+4)

Denmark

Jordan

France

Belgium

Singapore

Switzerland (complex system)

Czech Rep.

Sweden

Italy

China

Dom. Rep.

Vietnam

Hong Kong (modelled after UK system)

New Zealand

USA (complex system)

Macao (under different influences)

Israel (complex system based on religions)

Thailand

The influence of colonial heritage is reported in some countries: Algeria, Australia, China HK, China Macao, New Zealand, Taiwan (from Japan and China). This influence in some cases emerges also in the choice of school language different from family language. This issue was reported and discussed also in the Conference (this volume, Chap.  3).

2.3.2 Inclusiveness in Education

The focus on inclusive education has a long story in UNESCO’s documents (e.g. UNESCO 2009a; see the historical summary on p. 9) and dates back to the Universal Declaration of Human Rights (1948), but it is still actual (see, for instance, the plenary speech by Bill Barton in ICME 131). Inclusive education was taken into account in the Millennium Developmental Goals criteria (UNESCO 2010), where Universal Primary Education (UPE) is mentioned (Millennium Developmental Goal 2). It is considered also in the most recent document (UNESCO 2017) on Education for Sustainable Development Goals, where it is included in the learning objective 4: ‘Quality Education | Ensure inclusive and equitable quality education and promote lifelong learning opportunities for all’ (UNESCO 2017, p. 18 ff.).

UNESCO (2009a) states that inclusion addresses not only students with special needs2 (e.g. disable students), but also those from diverse backgrounds (cognitive, ethnic and socio-economic). Hence, this issue is related to some other questions posed in the context form (i.e. national languages and school languages, provisions for migrant, refugee and marginalised students).

This broad approach was assumed by the IPC of the study which included in the context form three different items (see above) concerning students with special needs, students with school language different from family language and students with diverse background.

The presence of different national languages has been reported by applicants, mentioning also local languages. There are countries where home languages are different from national language (or languages), for instance, in Algeria, Arabic and Berber–Tamazight; in Australia, Australian English and aboriginal languages; in Belgium, Dutch, French and German; in Canada, English and French; in the Chinese area, Mandarin, Cantonese and minorities languages; in Cyprus, Greek and Turkish; in Israel, Hebrew and Arabic; in New Zealand, English, Te Reo Maori and New Zealand Sign Language; in Serbia, Serbian, Hungarian and Romanian; in Singapore, English, Malay, Tamil and Mandarin; in South Africa, Afrikaans, English, Zulu, Xhosa, Swati, Tswana, Southern Sotho, Northern Sotho, Tsonga, Venda and Ndebele; in Sweden, Swedish, Finnish, Meankeli, Samic, and so on; in Switzerland, French, German, Italian and Romansh; in Thailand, Thai and Esann; and in the USA, English and Spanish. In most cases, the language of teaching (or school language) is different from home languages with the well-known critical consequences (Barwell et al. 2016). There are countries with acknowledged minorities (e.g. Czech Republic, France, Italy, New Zealand) where teaching in the minority language is encouraged with special funds and programmes. For instance, in New Zealand, Maori schools are very well developed and address about 15–20% students.3

The issue of migrant, marginalised and refugee students is mentioned by some applicants, although only in a few countries (e.g. Australia, Belgium, Cyprus, Germany, Jordan, Netherlands, New Zealand) official governmental support is mentioned. In other cases (e.g. France, Italy, UK), municipal support is mentioned together with the involvement of volunteers and charities.

According to the data reported in UNESCO (2017) and confirmed by some participants, there has been significant progress towards ensuring UPE in terms of access, and the conversation has now shifted from aiming for access to goals for quality UPE.

The question of students with disabilities or special needs seems to be ill-posed or, maybe, ill-interpreted by the applicants to the Conference. In many cases, applicants answered YES (i.e. the system is inclusive) probably meaning that all the students are allowed to go to primary school, but in many cases (at least 12 out of 29), special schools for disabled students were mentioned as the only provision.

According to UNESCO (2009a):

In most countries, both developed and developing, the steps towards achieving the right to education for students with disabilities have followed a common pattern, with some local variations. Progress has tended to follow the pattern of steps outlined below:

Exclusion from school, based on negative attitudes and a denial of rights, justified by the belief that students with disabilities cannot learn or benefit from education

Segregation, reflecting the emphasis on ‘difference’, combined with a charity-based approach, where separate education centres and schools were and are still provided by local, regional and international charitable NGOs and, more recently, by development-focused NGOs

Integration, reflecting some degree of acceptance for some disabled students, depending on their degree of disability, allowing them to attend local regular national schools, as long as they can fit in to the school and the school does not have to make significant adjustments for them

Inclusion in education, acknowledging the fact that all students, including those with disabilities, have the right to education, that all schools have the responsibility to teach every child and that it is the responsibility of the school to make the adjustments that may be necessary to make sure that all students can learn (p. 51)

Following this definition, if the system of special schools is widespread in a country, it is a segregation model and not an inclusive model.

To sum up the data, most countries are reported to have special schools only; some countries (e.g. Australia, Brazil, Canada, Czech Republic, Denmark, France, Germany, Israel, Netherlands, New Zealand) have started a process of integration, and some countries have stated by law complete inclusion in mainstream classes with support teachers. A relevant case, worthwhile to be mentioned, is Italy. D’Alessio (2011) reconstructs the historical and legislative backgrounds of the integration policy in Italy, mentioning the promulgation of the Italian Constitution (Senato della Repubblica 1947), where the spirit and ethos for integration were already encapsulated.

Since the Fascist dictatorship had denied individual freedom, one of the first targets of the democratic Constitution was to put the dignity of the person and the rights of minorities at the centre of the constitutional charter. (D’Alessio 2011, p. 6)

In the following years, legislation went in this direction. According to Ferri (2008), for Italian teachers, inclusion was considered ‘a moral issue which is more important than a legal mandate’ (p. 47). A discussion about the possible distance between laws and implementation is made by Booth and Ainscow (2011) which have designed a tool to support and assist with the process of developing inclusive education.

At the international level, inclusive education is considered to be:

a key vehicle through which the right to an equal education opportunity for all can be ensured. For this to become a reality it is necessary to provide a system in which all persons, including persons with disabilities, can access education at all levels on an equal basis with others in the communities in which they live. They should not be excluded on the basis of any disability and should get the support they require. (EASPD 2012, p. 6)

It must be said, however, that the issue of exclusion-segregation-integration-inclusion is far from being agreed upon at the international level. It is not only a matter of clear definitions; it is rather a matter of ethical consensus. A recent paper by Reindal (2016) summarises different positions, reconstructing the history of the inclusion debate from the ‘World Conference on Special Needs Education’ in Salamanca in 1994. Reindal claims:
Inclusive education as presented in documents from UNESCO was indefinite from the start in relation to both the target group and those whose responsibility was to implement inclusive education for that group. Reviews of the research also support several interpretations of responsibility and elucidations of inclusive education. In a recent study based on prior reviews and a recent search of databases covering the period 2004–2012, Goransson and Nilholm (2014a) found four different interpretations of inclusion which gave rise to four qualitatively different categories of definitions. These definitions were related hierarchically to each other employing stricter criteria concerning what counts as inclusive education as one goes from A to D:
  1. (A)

    Placement definition – inclusion as the placement of pupils with disabilities in mainstream classrooms.

     
  2. (B)

    Specified individualised definition – inclusion as meeting the social/academic needs of pupils with disabilities.

     
  3. (C)

    General individualised definition – inclusion as meeting the social/academic needs of all pupils

     
  4. (D)

    Community definition – inclusion as creation of communities with specific characteristics.

     
Reindal (2016) suggests to tackle this issue from the perspective of a capability approach (Walker and Unterhalter 2007), as that:

has the potential to emphasise the ethical aspects of inclusion because it builds on an understanding of difference as a specific variable of human diversity, and because it understands human dignity as the development of capabilities. The capability approach defends an understanding of difference as a specific variable of human diversity with an objective reality. […] If the central purpose of special education and inclusion is to treat all students as the same while at the same time aiming to treat them differently then one must deal with the problem of difference in a way that comes to grips with the attendant challenges – as well as those faced particularly by developing countries. (Reindal 2016, p. 6)

The issue of the diversity of school language and family language was discussed during the Conference and finds place in this Volume (e.g. Chap.  3,  4 and  9). The issue of students with special needs was discussed during the Conference and reported in some chapters (e.g. Chaps.  7,  8,  9,  16 and  20).

The capability approach, one that is very interesting, was not picked up in the Study and may suggest future developments in mathematics education.

2.3.3 Textbooks

Most applicants reported that no textbook for pre-primary exists: rather, some available collections of learning resources, working sheets and teachers’ guides are mentioned.

As far as primary school is concerned, textbooks exist everywhere, although in some cases (e.g. Australia) the adoption of a textbook is not mandatory. In most countries there is a free-market system with no official overlooking agency. In some countries only one or a limited number of approved textbooks is available (e.g. Chinese area, Algeria, Germany, Singapore and Thailand). In Vietnam, textbooks are written by specialists of the Ministry of Education. In South Africa, there are textbooks in all the national languages, though harder to access in the smaller language groups. In China too, there are textbooks in all the minority languages.

In this Study, the issue of textbooks was just skimmed in the Chaps.  9 and  11 but would deserve a study in its own.

2.3.4 National Curriculum Standards and Assessment

In nearly all the countries of this convenience sample, there are national standards. They do not exist in Algeria and are identified with the sole national textbook in Jordan. An interesting case is represented by the USA. There is no national curriculum in the USA, but National Council of Teachers of Mathematics (NCTM) Standards are widespread. Yet, locally, states, school districts and national associations recommend some curriculum standards be used to guide school instruction. The Common Core Standard initiative4 is in progress. In nearly all the countries, there is a national system of assessment (in progress in New Zealand) consistent with curriculum standards. However, the grades in which assessment takes place are not the same. Usually they are every second or third year and depend also on the structure of the education system (see Sect. 2.3.1).

2.3.5 Teachers’ Qualification and Teacher Education and Development

All the applicants reported a generalist trend for primary teacher education in their countries, with some limited exceptions: Germany, with the encouragement to get further qualification in German or Mathematics, and Italy, with testing of specialist mathematics teachers in some schools, according to autonomous choices of the school council. Only in Denmark and in the Chinese area a trend towards specialist mathematics teachers is reported. In China, this choice is common in big cities but not in rural areas. Where there are specialist mathematics teachers, it is common to form a Mathematics Teaching Research Group in the school, for in-service development according to the model of ‘open classes’, called in Chinese guānmó kè (观摩课), which means ‘to observe for imitating a lesson’ and has some similarities to the Japanese lesson study (Sun et al. 2015).

In our convenience sample, pre-service teacher education at universities (or, in some cases, teachers’ colleges) seems well established. In most cases for pre-primary and primary school, the length of the programme (bachelor) is the same:
  • 3-year bachelor in Belgium and New Zealand

  • 4-year bachelor in Australia, Canada, Chinese area, South Africa, Switzerland

  • 5-year master in Italy

  • 6-year master in Thailand

  • In other countries, the length is different for pre-primary and primary school teachers:

  • 2–3 years in Singapore (at the National Institute of Education)

  • 3–4 years in Denmark, Serbia

  • 3 1/2–4 years in Sweden

  • In some cases the length of the bachelor degree is not reported.

  • In Germany no university programme for pre-primary teachers is reported, while the programme for primary teachers is at masters level (5 years).

  • In France there is no information provided for pre-primary, while the programme for primary teachers is at masters level (5 years).

  • In the USA the rules are different in different states. For primary teachers, bachelor degrees are mentioned.

  • In the UK, different agencies are involved with programmes of different lengths (e.g. school-led teacher training, university programmes).

Practicum (internship) is mentioned with very different organisations and durations, for instance, a 600 hours practicum is required in Italy alongside the 5-year master programme, while in Israel, the practicum is at the end of the university programme. A year of practicum is required in Macao alongside the 4-year bachelor degree. In Australia 80 hours of mandatory practicum is prescribed for bachelor programmes.

Distance learning is mentioned especially for in-service teacher development. However, for in-service development, different models are described from inspector-led programmes, to mandatory programmes (60 hours per year in Israel, 5 days per year in Switzerland). In Australia, there is a programme for accreditation according to well-described professional standards. In some cases in-service development is appointed to municipalities (Sweden). In many cases in-service development is reported as not effective. It seems that, in general, there are not well-organised models. A relevant exception is the model of ‘open classes’ in China (see Sect. 2.3.3).

For teacher education and development, besides the panel on teacher education (this volume, Chap.  17), it is worthwhile to mention the ICMI Study 15 (Even and Ball 2009).

2.4 Conclusion

In this chapter we have briefly explored mainly structural features of the instruction systems including inclusiveness, curricula, standards and assessment and teacher education and development. We had just a glance to the many different choices existing in the countries of our convenience sample.

Our limited analysis shows that even in Europe, a small continent, many different organisations of the education systems exist. Education systems are cultural artefacts that could be studied, on the one hand, as products of socio-cultural contexts and, on the other hand, as sources of information about the society that constructed or adopted them. We do hope that, in the future, a sensitive attitude for cultural contexts will become more and more shared, in international journals and conferences. As stated by Bartolini Bussi and Martignone (2013):

The question of cultural background applies to every study in mathematics education […] It is necessary to explain in more depth how the research design and implementation is related to the cultural background: the results and success (if any) of the project may depend on implicit values which are not likely to be found in other contexts. (p. 2)

In this spirit, the investigation of the different social and cultural contexts continued throughout the whole study and is mirrored in the Study Volume.

Footnotes

  1. 1.
  2. 2.

    We are aware that there is a growing trend towards abandoning the wording ‘special needs’ and using ‘special rights’ or ‘educational rights’. For instance, Runswick-Cole and Hodge (2009) have argued for abandoning the language of ‘special education needs’ in the UK, based on the claim that it has led to exclusionary practices, mentioning an Italian rights-based approach developed in Reggio Emilia that refers to ‘children with special rights’ drawing on the United Nations Convention of the rights of the child (UNICEF 1989). Yet we decided to maintain the most common wording ‘special needs’ as it is shared in literature and better known by mathematics educators.

  3. 3.
  4. 4.

References

  1. Bartolini Bussi, M. G., & Martignone, F. (2013). Cultural issues in the communication of research on mathematics education. For the Learning of Mathematics, 33(1), 32–38.Google Scholar
  2. Barwell, R., Clarkson, P., Halai, A., Kazima, M., Moschkovich, J., Planas, N., Phakeng, M., Valero, P., & Villavicencio Ubillús, M. (2016). Mathematics education and language diversity: The ICMI study 21st. Cham: Springer.CrossRefGoogle Scholar
  3. Booth, T., & Ainscow, M. (2011). Index for Inclusion: Developing learning and participation in schools (3rd revised ed.). Canterbury: Centre for Studies on Inclusive Education.Google Scholar
  4. CERME 8. (2013). http://cerme8.metu.edu.tr/#. Retrieved January 24, 2016.
  5. CERME 9. (2015). http://www.cerme9.org/guidelines/. Retrieved January 24, 2016.
  6. D’Alessio, S. (2011). Inclusive education in Italy. A critical analysis of the policy of “integrazione scolastica”. Rotterdam: Sense Publishers.CrossRefGoogle Scholar
  7. EASPD. (2012). Analysis of the use and value of the Index for Inclusion (Booth and Ainscow 2011) and other instruments to assess and develop inclusive education practice in P2i partner countries. Brussels/Tilburg, Fontys OSO. http://www.icevi-europe.org/enletter/issue51-09EASPD3.pdf. Retrieved December 27, 2016.
  8. Education database. (n.d.). http://www.classbase.com/Countries. Retrieved January 24, 2016.
  9. Even, R., & Ball, D. L. (2009). The professional education and development of teachers of mathematics: The 15th ICMI study. New York: Springer.CrossRefGoogle Scholar
  10. Ferri, B. (2008). Inclusion in Italy: What happens when everyone belongs. In S. L. Gabel & S. Danforth (Eds.), Disability and the politics of education: An international reader (pp. 41–52). New York: Peter Lang Publishers.Google Scholar
  11. Göransson, K., & Nilholm, C. (2014). Conceptual diversities and empirical shortcomings: A critical analysis of research on inclusive education. European Journal of Special Needs Education, 29(3), 265–280.  https://doi.org/10.1080/08856257.2014.933545.CrossRefGoogle Scholar
  12. ICMI (2011). The ICMI database project. Http://Www.Mathunion.Org/Icmi/Activities/Database-Project/Introduction/. Retrieved January 24, 2016.
  13. Jaworski, B., Bartolini Bussi, M. G., Prediger, S., & Nowinska, E. (2015). Cultural contexts for European research and design practices in mathematics education. In K. Kreiner & N. Vondrova (Eds.), CERME9. Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education (pp. 7–33). Prague: Charles University in Prague, Faculty of Education and ERME.Google Scholar
  14. Jones, K., Bokhove, C., Howson, G., & Fan, L. (2014). Proceedings of the International Conference on Mathematics Textbook Research and Development. Southampton: University of Southampton. Retrieved June 2, 2016 from http://eprints.soton.ac.uk/374809/
  15. Marshall M. N. (1996) Sampling for qualitative research. Family Practice, 13(6), 522–525.CrossRefGoogle Scholar
  16. NCTM. (n.d.). Characteristic of a high quality JRME manuscript. http://www.nctm.org/publications/write-review-referee/journals/Characteristics-of-a-High-Quality-JRME-Manuscript/. Retrieved January 24, 2016.
  17. PME 39. (2015). Submissions: Research reports. http://www.pme39.com/submissions/. Retrieved January 24, 2016.
  18. Reindal, S. M. (2016). Discussing inclusive education: An inquiry into different interpretations and a search for ethical aspects of inclusion using the capabilities approach. European Journal of Special Needs Education, 31(1), 1–12.CrossRefGoogle Scholar
  19. Runswick-Cole, K., & Hodge, N. (2009). Needs or rights? A challenge to the discourse of special education. British Journal of Special Education, 36(4), 198–203.CrossRefGoogle Scholar
  20. Senato della Repubblica. (1947). Constitution of the Italian Republic. https://www.senato.it/documenti/repository/istituzione/costituzione_inglese.pdf. Retrieved 10 December 2016.
  21. Sierpinska, A., & Kilpatrick, J. (1998). Mathematics education as a research domain: A search for identity, An ICMI study. Dordrecht: Springer.Google Scholar
  22. Sun, X.H., Teo, T., & Chan, T.C. (2015). Application of the open-class approach to pre-service teacher training in Macao: A qualitative assessment. Research Papers in Education, 30(5), 567–584.CrossRefGoogle Scholar
  23. Sztein, E., Olson, S., & Ferreras, A. (Eds.). (2010). The teacher development continuum in the United States and China: Summary of a workshop. Washington, DC: The National Academies Press.Google Scholar
  24. UNESCO. (2009a). Towards inclusive education for students with disabilities: A guideline. Bangkok: UNESCO Asia and Pacific Regional Bureau for Education. http://unesdoc.unesco.org/images/0019/001924/192480e.pdf. Retrieved October 25, 2017.
  25. UNESCO. (2009b). Policy guidelines on inclusion in education. Paris: United Nations Educational, Scientific and Cultural Organization. unesdoc.unesco.org/images/0017/001778/177849e.pdf. Retrieved April 24, 2017.
  26. UNESCO. (2010). Resolution adopted by the General Assembly. 65/1. Keeping the promise: United to achieve the Millennium Developmental Goals. www.un.org/en/mdg/summit2010/pdf/outcome_documentN1051260.pdf. Retrieved April 24, 2017.
  27. UNESCO. (2017). Education for sustainable development goals. Learning objectives. http://unesdoc.unesco.org/images/0024/002474/247444e.pdf. Retrieved April 24, 2017.
  28. UNICEF. (1989). Convention on the rights of the child. www.unicef-irc.org/portfolios/crc.html. Retrieved April 25, 2017.
  29. Walker, M., & Unterhalter, E. (2007). The capability approach: Its potential for work in education. In M. Walker & E. Unterhalter (Eds.), Amartya Sen’s capability approach and social justice in education (pp. 1–18). London/New York: Palgrave Macmillan.CrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of Education and HumanitiesUniversity of Modena and Reggio EmiliaModenaItaly
  2. 2.Faculty of EducationUniversity of MacauMacaoChina

Personalised recommendations