Firstly, although some authors, such as Gutiérrez (2010), claim that our field is currently experiencing a ‘sociopolitical turn’ (that is, a growing awareness of the need to consider the political, power and identity issues associated with mathematics education), our field is still dominated by views that consider the relationship between the teacher, the students and the mathematical content as the main space of inquiry (Pais & Valero, 2012; Valero, 2007). Similarly, amongst practitioners there exists a limited view of the role that mathematics education can play in forming critical citizens able to live in and sustain democratic societies. Thus we believe that a literature review addressing the links between mathematics education and democracy may help to challenge and contest these perspectives, and increase awareness about the need to widen the area of inquiry that has been favoured traditionally.

Secondly, although discussion of the connections between mathematics education and democracy is not new, it has branched out into related topics such as equity and social justice, indicating that this discourse is far from complete. In fact, there are several research topics related to mathematics education and democracy that need further exploration. One contribution of this literature review is to highlight some of the theoretical and empirical research that is necessary to further develop this field.

1. The definitions of democracy that are used.

2. Identified links between mathematics education and democracy.

3. Suggested strategies to foster democratic competence in mathematics students.

4. Tensions and difficulties inherent in mathematical education for democracy.

5. The fundamental role of the teacher in the implementation of democratic education.

6. Selected criticisms of mathematical education for democracy.

The review concludes with a discussion of the literature analysed, where we indicate some of the theoretical and empirical research that is required to further develop this area of research.

This review included five journals in the ‘international’ category: Educational Studies in Mathematics, ZDM: The International Journal on Mathematics Education, For the Learning of Mathematics, International Journal of Science and Mathematics Education and International Journal of Mathematical Education in Science and Technology.

The Latin American journals included in this review were: Educación Matemática, Revista Latinoamericana de Investigación en Matemática Educativa and Bolema: Boletim de Educação Matemática.

We also included two North American journals, namely Journal for Research in Mathematics Education and The Journal of Mathematical Behavior.

The Australasian region was represented in this review by the journal Mathematics Education Research Journal.

For the European region we selected the journals Research in Mathematics Education and Philosophy of Mathematics Education Journal.

Finally, we included the journal Pythagoras to represent the African region.

Due to its importance and influence, we would have liked to include in our review the proceedings of the conferences organised by the International Group for the Psychology of Mathematics Education (PME). However, these proceedings are not available online and they were not accessible through the library of our university; hence, they could not be included in this review. This can be considered as one of our review’s limitations.

The documents selected for the review complied with the following condition: in the title, abstract, keywords or the body of the paper they used the key term ‘democracy’, or related terms such as ‘democratic’ and ‘democratisation’. We set this condition to try to ensure that the selected texts would address the relationship between mathematics education and democracy. However, we are aware that this condition may have excluded some sources that discuss political issues related to democracy, such as equity and social justice, but fail to explicitly use the term ‘democracy’. This should be considered as another limitation of our review.

We used search engines to find key terms within the documents. For example, for the articles contained in Layer 1 we used the Web-based search engines included in the Web pages of the journals. These tools allowed us to quickly locate relevant articles contained in large collections of documents. For the documents contained in Layer 2 and Layer 3, we located the key terms by using the ‘search’ function of the PDF reader program. For some documents in Layer 3 it was necessary to locate the key terms manually.

It is important to note that not all the documents containing a key term such as ‘democracy’ or ‘democratic’ were relevant to the review. Consider, for example, an article by Hanna and Sidoli (2002) where the phrase ‘mathematical education and democracy’ appears in the body of the article. Within the article, however, the phrase is used to refer to the title of an article written by Skovsmose (1990). In fact, Hanna and Sidoli (2002) do not address the relationship between democracy and mathematics education at all, but rather focus on providing a statistical profile of articles published in the journal Educational Studies in Mathematics. Another category of articles that was not considered in this review was those that mentioned a possible relationship between mathematics education and democracy, but only superficially. For example, there were texts claiming that mathematics is important for the education of citizens, but the reasons why mathematics is important were not clarified.

We considered only materials written either in Spanish, Portuguese or English; as a result, articles written in other languages were excluded, as was the case for three articles from the special issues on mathematics education and democracy in the journal ZDM: The International Journal on Mathematics Education, issues 30(6) and 31(1), which were written in German.

Table 1, Table 2 and Table 3 show an overview of the references consulted for the development of the review. Readers interested in the details of the consulted references (title, journal, volume, etc.) can refer to Appendix 1, located at the end of this review.

After selecting the texts, we posed two questions to guide our detailed analysis:

1. What are the links between mathematics education and democracy that are identified in these texts?

2. What proposals or strategies do they recommend to strengthen these linkages?

Whilst reading the materials, we also realised that it was necessary to focus on other relevant aspects of the mathematics education–democracy relationship addressed in some of the texts. For example, what tensions or difficulties are encountered in implementing mathematical education for democracy, or the centrality of the role of teachers in the implementation of democratic education. Thus, we decided to widen our focus to include the six aspects listed in the explanation of the structure of this article. In the remainder of the article we will report the results obtained by focusing our review on these six aspects. We will end this article discussing some of the topics that need further research in order to develop this area of research and acknowledge the limitations of this review.

One of the most elaborate definitions of democracy is that of Murillo and Valero (1996), cited in Valero (1999), in which democracy is interpreted as an ideal form of social organisation with four dimensions:

Democracy can be defined as an ideal way social organization establishes a series of political, juridical, economic and cultural values, norms and behaviors aiming at providing a better living for the whole population of a given state. This definition highlights a conception of democracy not as an actual reality, but as a goal to reach. … This definition also considers four different dimensions of democracy. The political dimension includes the series of procedures to form governments by means of regular, free elections as the corner stone of representative democracy. The juridical dimension sets and protects the different basic legal human rights and duties. The economic dimension deals with the material conditions of living and the organization of the economy by the state. And the socio-cultural dimension which considers the space where democratic values are embedded and embodied in people’s interactions. (p. 20, [author’s own emphasis])

In this article we use this definition of democracy as a framework that allows us to present, in an orderly manner, other explicit definitions of democracy located in the articles included in the review. We decided to use this definition because it offers an overarching characterisation of democracy covering the different dimensions of democracy that are identified in other definitions.

Skovsmose (1998) proposes an alternative interpretation of democracy, inspired by the concept of direct democracy. Here democracy is conceptualised as a form of political democracy in which citizens participate directly in the discussion of public affairs. This position may seem impractical if we think of a state, but Skovsmose conceives the application of this type of democracy in all types of institutions, such as workplaces, schools and classrooms. It is in these kinds of institutions that Skovsmose’s position seems clearly applicable and feasible. Furthermore, this conception of democracy puts the type of skills that a citizen must possess in order to fully participate in the public discourse at the centre of the discussion. This point will be addressed later in the review, when we discuss the links between mathematics education and democracy.

As the above discussion shows, the concept of democracy is multidimensional; that is, it is a concept that refers to freedoms, rights, obligations, the distribution of material and cultural goods, and respect for diversity of ideas and ways of thinking. The question now is: What are the links between mathematics education and democracy? In the following section of the article we will present the links that we have identified through the literature review.

Firstly, mathematics education can provide students with mathematical skills to critically analyse their social environment, and also to identify and evaluate the uses and misuses of mathematics in society. The second link relates to the fact that the mathematical education that students receive in a classroom can promote or inhibit values and attitudes that are essential to build and sustain democratic societies. The third link is the acknowledgment that mathematics education can function as a sort of social filter that restricts the opportunities for development and civic participation of some students.

Mathematics is applied in economics, politics, marketing, administration, education, et cetera. Mathematics is an integral component of society. In fact, society is largely shaped by mathematics. Thus many decisions that are socially relevant may be strongly influenced by mathematical models and applications, for example which municipalities in a country are considered poor enough to receive additional financial aid from the state, how much an employee should produce in order to maintain their position within a company, or what level of pollution levels in a city should lead to a recommendation that the inhabitants avoid exercising outdoors. The important point here is that it would be difficult for citizens to assess whether these decisions are fair or appropriate if they have not received a proper mathematical education. In sum, a mathematical education helps citizens to identify how mathematics is being applied to support such decisions, and to reflect on the consequences, positive and negative, that this application can produce. In order to maintain a democratic society, it is important that citizens are capable of critically analysing such questions and their answers because if they are to understand the economic and juridical dimensions of democracy, for example how the economic resources are distributed in a country or the defence of labour and environmental rights, it is vital that they understand the mathematics underlying those decisions.

When we refer to the particular case of the application of mathematics in politics, we are addressing the connection between mathematics education and the political dimension of democracy. For example, Almeida (2010) remarks:

One of the ways that the government or elected representatives convince the citizens that their policies are the correct ones is by producing reports which include a mass of numerical and statistical data. There are many instances where this data is misleadingly summarised. (p. 13)

Along the same lines, Wagner and Davis (2010) assert:

As politicians and bureaucrats use numbers to claim objectivity, to mask their biases, and to legitimize their decisions, it could be said that the citizens, who have been enculturated in schools to put their trust in number, are being duped by number, not empowered to make informed decisions, and, of course, claims of objectivity are made by more people than politicians and bureaucrats. Children and adults need their number sense to be part of their critical sense. (p. 49)

These quotes illustrate the importance of having mathematically literate citizens, able to critically analyse the reports and statements issued by the politicians who govern them. A democracy without this kind of citizenry is a fragile democracy.

Underpinning any discussion about social justice and democratisation in mathematics education lies the issue of ‘values’. This is problematic at the present time because we neither know what currently happens with values teaching in mathematics classrooms, or why, nor do we have any idea how potentially controllable such values teaching is by teachers. In addition, many mathematics teachers are not even aware that they are teaching any values when they teach mathematics. Changing that perception may prove to be one of the biggest hurdles to be overcome if we are to move to a more just mathematics education. (p. 1)

A key concept for understanding the process of transmission of values and attitudes is that of classroom absolutism. Skovsmose (1998) uses this concept and explains it as follows:

The phenomenon that communication between students and teacher is structured by the assumptions that mathematics (school mathematics) can be organised around exercises and questions which have one and only one correct answer, and that, ultimately, it is the teacher’s job to make sure that mistakes are eliminated from the classroom. (p. 200)

Authors such as Valero (1999) and Almeida (2010) affirm that this type of classroom interaction creates authoritarian relations between teachers and students: relationships in which students learn to uncritically accept the claims and dictates of the authority.

Skovsmose (1990) argues that the nature of mathematics classroom interactions can teach the students to follow explicitly stated prescriptions. This process takes place through instructions such as ‘Solve the equation …’, ‘Find the length of …’, ‘Calculate the value of …’ Skovsmose argues that these kinds of instructions have little to do with the actual processes of investigations, being more closely related to the instructions that characterise the routine work processes. Hence, Skovsmose suggests that this sort of mathematical education, more than producing critical citizens, prepares students to perform routine work and become part of the workforce.

In turn, Hannaford (1998) suggests that the teaching of mathematics in which students are taught that there is no room for mistakes and there is only one correct answer does not promote plurality and respect for the diversity of ideas.

Australia and some other nations risk becoming societies divided by access to mathematical knowledge. A minority will have access to high levels of mathematics and will be the highly paid professionals and leaders. The majority will have ‘benchmark’ levels of mathematics and will be poorly paid, often unemployed or underemployed, and in ‘service’ industries. This is not the basis for either a clever country or a democracy but it is the basis for a divided society. (p. 137)

Indeed, by preventing students’ access to higher education, lack of a mathematics education limits students’ opportunities for a professional career or finding a decent and well-paid job. In short, it decreases their chances of economic and social success. Skovsmose (1998) has even suggested that lack of a mathematics education may contribute to the growth in modern societies of a new lower class.

The lack of mathematics education can even limit people’s participation in civic society. For example, when mathematics is used in political discussions of social problems, only those who understand the mathematics being used can criticise its use and participate in the discussion, effectively leaving citizens who lack such knowledge out of any deliberations. As noted by Christiansen (2008), ‘the use of mathematics [in political discussions] may exclude someone from (feeling confident) taking part in the discussion’ (p. 72). Johansen (2002) points out that even some politicians acknowledge that the lack of mathematical skills can be an impediment for citizens’ participation in public debates and democratic processes.

Orrill (2001) and Skovsmose (1994, 1998) go so far as to argue that the lack of such knowledge is a threat to democracy because people who are not mathematically literate cannot fully participate in civic life. Unless a population has such mathematical knowledge the potential criticism that may exercise social controls over society’s leaders is threatened. In the words of Skovsmose (1994):

Democracy may be destroyed by a dictatorship which obstructs formal democratic procedures. … Democracy can be undermined in ways other than by just neglecting rules of election. Democracy refers not only to formal, but also to material and ethical conditions and to possibilities for participation and reaction. In particular, democracy can be destroyed if a critical citizenship cannot brought into life. (p. 38)

One suggestion made by Almeida (2010), Christiansen (2008) and Moreira (2000) is that mathematics teaching should include activities that will encourage students to use mathematics as a ‘thinking tool’. These activities can be used both to assist students in developing an understanding of mathematical tools and ideas, and to analyse social problems. For example, Christiansen (2008) asked pre-service teachers to represent in different ways the share of land that Black people and White people in South Africa owned in 1981, and then to reflect on the impression given by each representation. Besides promoting a reflection on the different ways quantitative information may be represented, this activity also made these future teachers aware of the racial problems in South Africa. Moreira (2000) used similar methods to introduce students to mathematical applications that allow them to analyse various economic, political and social problems, such as trends in the number of people with AIDS, the impact of fishing policies on endangered species, and the advantages and disadvantages of adopting nuclear power as a source of energy.

Malloy (2008) in turn suggests that students should be confronted with moral issues that surround the uses mathematics:

We must present them with problems that not only tackle issues that affect their communities, but also reveal the motivations and the hidden agenda (curriculum) in their world. When students use and apply mathematical knowledge in such situations, they are learning to think critically about world issues and their environment through mathematics. Through this process students will have an understanding of inequities in society, and will be able to critique the mathematical foundations of social situations. (p. 28)

Another suggestion, offered by Skovsmose (1990), is to promote critical mathematical skills through teaching mathematical modelling and applications in order to prepare students to identify and evaluate the applications of mathematics in society. However, as Skovsmose also points out:

It is not possible to develop a critical attitude towards the application of mathematics solely by improving the modelling capability of students. … To develop a more critical attitude towards this model building we have not only to understand the mathematical construction of the model; we have also to know about its assumptions. We must be able to point out which economical ideas are hiding behind the curtain of mathematical formulas. (p. 112)

Thus Skovsmose suggests the use of empowering teaching-learning materials (that is, didactical activities) as a means for students to develop critical mathematical skills through the use of open teaching-learning materials whose main characteristics are that (1) the material has to do with a topic of subjective relevance for the students, (2) the material initiates a variety of activities, not pre-structured and fully fixed, and (3) several decisions have to be taken when involved in the teaching-learning process, which normally necessitate a discussion between teacher and students (Skovsmose, 1990, pp. 118–119).

Orrill (2001) goes even further and argues that we should avoid the compartmentalisation of the mathematical knowledge in the school curriculum. In other words, he argues that the teaching of mathematics should be spread across the curriculum. The logic behind this idea is that in real life mathematics is everywhere; it should not be isolated into a single subject. Skovsmose and Valero (2001) express the same idea this way:

There is also a need to consider that mathematical competencies do not operate in isolation outside school but as part of integrated units assembled in schooling. This implies interdisciplinarity among the school subjects as an important research issue. Competencies in one discipline interact − or counteract − with competencies developed in other disciplines. Even more, competencies development in a school setting interact − or counteract − with competencies formed and used outside the school. (p. 49)

A basic idea behind the promotion of democratic values and attitudes in students is the one proposed by Vithal (1999): that within the mathematics classroom it is possible for students to experience democratic life. In the mathematics classroom students can learn, amongst other things, to listen to others’ ideas, to argue, to take decisions and to critically analyse arguments made by authorities (the mathematics teacher for example). Ernest (2002) also makes this point:

Teaching approaches should include discussions, permit conflict of opinions and views but with justifications offered, the challenging of the teacher as an ultimate source of knowledge (not in their role as classroom authority), the questioning of content and the negotiation of shared goals. (p. 6)

Skovsmose (1990) claims that it is essential to change the fixed and pre-structured mathematical activities within the classroom that characterise traditional mathematics teaching. He argues that the use of open materials (see description above) is compatible with the kind of investigative activities known as project work. He further posits that these kinds of mathematical activities give students more power to make decisions about what to study and how to study it. It also covers the mathematics lessons with uncertainty because it is difficult to predict how students’ projects will evolve. In other words, this approach fundamentally changes the roles and the power relations between teachers and students.

Hannaford (1998) makes another important proposal to promote dialogue and negotiation in the mathematics classroom. He argues that students should be taught to listen, to think, to argue effectively, and to respect others because democracy depends on those values. In a similar vein, Almeida (2010) recommends the use of (informal) mathematical proof as a means to introduce students to a culture of interrogating explanations. Students should be invited to consider the explanations provided to them, and to question their level of plausibility. It is especially important for them to learn to look critically at the information and explanations provided by the teacher. According to Almeida (2010), if students uncritically accept the information that teachers provide simply because they are authority figures, then it is likely that as citizens they will tend to accept uncritically the information and proposals politicians provide. Vithal (1999) similarly envisages the mathematics classroom as a democratic microsociety where the students can learn to both live together with and talk back to authority figures.

Open material could result in open and democratic educational situations – but no empowerment is guaranteed; and empowering material could result in critical understanding – but no openness is guaranteed. (p. 120)

Why do some individuals believe in social justice? There is great divergence in interest and commitment to social justice among mathematics educators. Some view it as central to their professional concerns, whereas others take no personal or professional interest in pursuing social justice issues. Why this divergence? (p. 3)

D’Ambrosio (2003) also stresses the importance of being conscious of the dual role that mathematics plays in society. Mathematics can be used either as a tool to improve the welfare of humanity, or applied to increase inequality and injustice. Awareness of its dual role is especially important when teaching students to identify the uses and abuses of mathematical applications in society.

A mathematics classroom that aims to promote democratic values and attitudes should model deliberative interaction, argumentation, critical analysis of the information, and respect for the ideas of others. These features require that teachers possess the pedagogical skills to manage and promote such dynamics in the classroom. As Almeida (2010) points out, this requires that teachers use effective questioning techniques and appropriately manage class discussions. Christiansen (2008) argues that teachers should be aware of the pedagogical potential of activities both for the individual student and for the class as a whole. This requires, amongst other things, specific pedagogical knowledge about how students learn mathematics, and about concept development.

Christiansen (2008) stresses the importance of having critical teachers who are willing to speak up when they detect that a potentially empowering curriculum is being blocked or mathematical creativity is being hindered by limited assessment criteria representing traditional values or by recipe-like instructions about how to teach.

Another necessary attitude that Almeida (2010) highlights is the egalitarian treatment of students in the classroom. He claims that it is the responsibility of teachers to treat students as equal partners in the teaching–learning process. For example, students’ misconceptions and mistakes should not be considered as failures of an intellectual inferior, but rather should be analysed to try to understand the students’ reasoning processes and conceptions that led them to these results.

Along similar lines, Vithal (1999) suggests that teachers can be useful models of authority for students not only to learn about their individual limits, but also to learn that it is possible to raise their voice against authorities. But for this to happen, teachers must be willing to give up part of the authority they traditionally have enjoyed in the classroom and understand that challenges to their authority are part of what constitutes a democratic education for their students.

Finally, another of the necessary attitudes that some texts address is a willingness of teachers to work in academic environments that are full of uncertainty. This is because, as Skovsmose (1990) observes, the evolution of a lesson based on open activities may be unpredictable, so the control that teachers usually have over the mathematical knowledge that is assigned and discussed in the classroom can be diluted and replaced with uncertainty.

In extension of these obligations, it must also be a democratic right for teachers to have a say in how curricula, guidelines and recommended teaching materials are put together; a right to have the many years of experience from the teaching profession being put to use. A right to be taken serious if they choose to criticise curricula and required teaching methods for being too idealistic and too demanding to realise in practice. Do we secure these rights? (pp. 81–82)

We think that this conceptualisation is very important as it highlights not only the qualities that the teachers should possess, but also the rights that they should enjoy.

There is now a considerable literature exploring the connections between mathematics education and democratic society, much of it theoretical about what could or should occur. The question is what happens when an attempt is made to deliberately realise such a link in a mathematics classroom. (p. 27)

Who has, when it comes down to it, the right to influence the purpose and content of education? Does our insistence on these ‘critical examples’ end up being ‘imposition of emancipation’? How would the historically advantaged feel if the educational system really came to function on the premises of the historically disadvantaged? If our cultural capital … was depreciated overnight? Would we not object to the purpose and content forced upon us − even if claimed to be emancipatory? (p. 76)

Christiansen’s criticism is similar to Ernest’s (2010) critique of Critical Theory, namely that its judgements also require an epistemologically and ethically privileged standpoint.

Critical ideology overemphasizes the role of mathematics in society. In Latin America, the power structure has lead to a clientelist political system where decisions are made based on personal loyalty of clients to patrons, political convenience, power of conviction through the use of language or violent and physical imposition. In this ‘rationality’, mathematics does not necessarily constitute a formatting power that greatly influences decision-making. (p. 22)

Harris (1998) makes a similar criticism that is also relevant in the Latin American context:

There is a peculiar pointlessness in advocating schooling for democracy and authority within broader social contexts where schooling itself undemocratically favours some individuals and groups and disadvantages others, or where the potential for individual autonomous development is otherwise fundamentally stifled. Under those circumstances ‘schooling for democracy’ and ‘education for autonomy’ are either slogans, fashionable ideals or hypocritical rhetoric. (p. 176)

The second key idea we encountered is that there is a generalised interest in the research community to promote equality, democratic values and democratic competencies in mathematics students and teachers. This is a task that is far from trivial. The relationship between mathematics education and democracy is a relationship fraught with tension, and theoretical and practical difficulties.

The third idea that became clear to us is that the majority of research on mathematics education and democracy has been developed at a theoretical level. More empirical research is necessary in order to test and expand these theoretical ideas. As noted by Vithal (2000, p. 1), ‘hard evidence to support (or refute) theoretical propositions about empowerment, emancipation, democracy, social justice, equity and so on through mathematics education are still rather thin.’

Firstly we learned that power is a concept underlying the discussion about mathematics education and democracy, especially when we refer to Link 1 mentioned in this review, where it is assumed that students are empowered through the acquisition of certain mathematical skills. Valero (2007) discusses and explains how this conception of empowerment, which presupposes power transference, is problematic and leads to contradictions.

On the other hand, when we read the concept of epistemological empowerment as presented in Ernest (2002) we found some similarities with the concept of democratic competence. This is because to achieve epistemological empowerment it is necessary not only to gain mastery over some mathematical knowledge, but also to possess certain values and attitudes such as personal engagement with mathematics and confidence. As Ernest (2002) put it:

Only when all of these powers are developed will they [the students] feel they are entitled to be confident in applying mathematical reasoning, judging the correctness of such applications themselves, and critically appreciating (including rejecting, in some cases) the applications and uses of mathematics by others, across all types of contexts, in school and society. (p. 11)

Our point here is that it is necessary to further discuss if and how the theoretical concepts related to power complement or contradict the concepts that have been used in the discussion of mathematics education and democracy. Perhaps concepts such as empowerment and democratic competence need to be revisited and even reformulated.

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