- The literature related to mathematics education and democracy is extensive. This article consists of a review of that specialised literature, presenting it in a summarised and organised way. This review is aimed at readers who are unfamiliar with this research area, and would like an introductory overview of it. The review is based on the analysis of a collection of texts produced in different regions of the world. The analysis of these articles is focused on six aspects:

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

- 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:

- 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:

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

- In the previous section we emphasised the importance of having mathematically educated citizens, able to critically analyse how mathematics is applied in their societies. However, an adequate mathematical education is not sufficient to produce critical citizens. A critical citizenry also requires the promulgation of democratic values and attitudes. Values like tolerance and respect for diversity, and attitudes about truth that demand the critical analysis of information. The second link between mathematics education and democracy identified in our review is the claim made by several authors that the mathematics classroom can be any place where, alongside mathematics learning, it is possible to transmit and acquire (perhaps subconsciously) both democratic and undemocratic values and attitudes. This link is closely related to the socio-cultural dimension of democracy, which refers to the social space where democratic values are produced. Bishop (2002) refers to the transmission of values in the mathematics classroom as follows:

- 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 third link that we have identified relates to the fact that mathematics education can function as a kind of social filter. It is a social filter in the sense that it not only restricts students’ opportunities for development, but may even limit their civic participation. Several researchers acknowledge this situation (e.g. Amit & Fried, 2002; Anderson & Tate, 2008; Christiansen, 2006; Knijnik, 2002; Malloy, 2008; Skovsmose & Valero, 2008). For instance, Thomas (2010), referring to the Australian situation, states:

- 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):

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

- 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:

- 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:

- 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:

- It is difficult to design activities that are both open and empowering at the same time. For example, what do you do when a student is truly interested in an activity but it does not address any socially relevant problem? Similarly, because teachers want students to understand the functions and assumptions behind a real mathematical model, it is difficult for them to avoid proposing activities that are too structured and guided. Skovsmose (1990) sums up this problem:

- D’Ambrosio (2003) observes that it is unfortunate that many mathematics educators are not familiar with UNESCO’s World Declaration on Education for All (UNESCO, 1990), which enshrined the right to education for all human beings. Due to the fact that human rights are an intimate part of democracy’s legal dimensions, he notes that it is regrettable that there is not a widespread interest in the community of mathematics educators to know and try to implement the resolutions and mechanisms established in that document. The paradox is that, despite the vital importance of the UNESCO declaration, many mathematics educators are indifferent to this right, and to other dimensions of democracy. This paradox is similar to the issue raised by Ernest (2007) concerning the status of social justice within the mathematics education community:

- Obligations, as conceptualised by Christiansen (2008), are those qualities that teachers responsible for implementing a mathematical education for democracy should possess. Framed in a juridical sort of rights and obligations discourse that is one dimension of democracy, Christiansen also refers to the rights of teachers:

- Mathematics education for democracy has drawn its share of criticisms. Some of these criticisms are aimed at applications of this approach, whilst others refer to unwanted results that it could produce. We reviewed enough works for it to be evident to us that most of this literature consists of programmatic theoretical and rhetorical statements rather than careful empirical research. There is a clear need for empirical studies to test and expand these theoretical ideas. Vithal (1999) explicitly addresses this issue:

- Mathematics education for democracy consists of a series of mathematical activities and modes of interaction that are considered to be beneficial and empowering. They are based on the assumption that teachers with the appropriate training can tell what kinds of education will further the civic development of students. Yet entailed in this proposition is the assumption that their superior position gives them the right to modify the curriculum, and to decide what is beneficial for their students. Christiansen (2008) questions this ‘right’:

- Valero (1999) makes a criticism of the critical ideology that underlies the link between mathematics education and democracy that seems particularly relevant to us as Latin Americans. We refer to the theoretical position that holds that mathematics is ubiquitous in modern societies, and that mathematical models and applications influence many of the decisions that affect and shape modern societies. Valero (1999) analyses this ideology from a Latin American perspective:

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

- 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: