Critical mathematics pedagogy

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Critical mathematics pedagogy is an approach to mathematics education that includes a practical and philosophical commitment to liberation. [1] Approaches that involve critical mathematics pedagogy give special attention to the social, political, cultural and economic contexts of oppression, as they can be understood through mathematics. [2] They also analyze the role that mathematics plays in producing and maintaining potentially oppressive social, political, cultural or economic structures. [3] Finally, critical mathematics pedagogy demands that critique is connected to action promoting more just and equitable social, political or economic reform. [3]

Contents

Critical mathematics pedagogy builds on critical theory developed in the post-Marxist Frankfurt School, as well as critical pedagogy developed out of critical theory by Brazilian educator and educational theorist Paulo Freire. Definitions of critical mathematics pedagogy and critical mathematics education differ among those who practice it and write about it in their work. The focus of critical mathematics pedagogy shifts between three core tenets, but always includes some attention to all three: (1) analysis of injustice and inequitable relations of power made possible through mathematics, (2) critiques of the ways in which mathematics is used to structure and maintain power, and (3) critiques toward plans of action for change and the use of mathematics to reveal and oppose injustices, as well as imagine proposals for more equitable and just relations.

Core concepts and foundations

Critical theory and critical mathematics

Those who build their critical mathematics pedagogy with close relations to critical theory, focus on the analysis of mathematics as having "formatting power" [3] that shapes the way we understand and organize the world. The assumption underlying critical mathematics pedagogy that comes from critical theory is the notion that mathematics is not neutral. According to critical mathematics, neither mathematics itself nor the teaching or learning of mathematics can be value-neutral, or free of interpretation. The critical mathematics group (est. 1990), [4] one of the first groups of teachers and researchers to convene around the work of critical mathematics, state that mathematics is (1) knowledge constructed by humans, (2) the set of knowledges constructed by all groups of humans, not only the Eurocentric knowledge traditionally included in academic texts and (3) a human enterprise in which understanding results from action in social, cultural, political and economic context. [4]

Marilyn Frankenstein, the first educator to coin the term critical mathematics pedagogy in the United States in her 1983 article "Critical Mathematics Pedagogy: An Application of Paulo Freire's Epistemology," [2] illustrates one way in which mathematics is not neutral using the example of the world map. She explains that in order to represent a three-dimensional object on a two dimensional surface, such as is necessary when mapping the earth, map-makers must make decisions about which types of distortions to allow. For example, the most traditionally accepted and commonly used world map is the Mercator map which enlarges the size of Europe and shrinks the size of Africa - a side-effect of the way it works (to assist navigation). This representation can be read to suggest that certain parts of the world are larger, and therefore more important or more powerful than others via the (inaccurate) size comparison presented in the map.

Ole Skovsmose's first publication on critical mathematics pedagogy in Europe coincided with Marilyn Frankenstein's in the United States. [1] It refers to "mathemacy" which would parallel critical literacy for mathematics. [3] He explains that "mathematics colonizes part of reality and reorders it." [3] Therefore, "the goal of mathematics education should be to understand the formatting power of mathematics and to empower people to examine this formatting power so they will not be controlled by it." [1] According to him, mathemacy would consist of three components (1) mathematical knowing, or the skills developed in traditional mathematics classrooms, (2) technological knowing, or the ability to build models with mathematics and (3) reflective knowing, or competency in evaluating applications of mathematics. [3] It is specifically the third component that makes this approach to mathematical literacy a critical one.

Bülent Avcı, through classroom-based participatory action research, in his recent book, Critical Mathematics Education: Can Democratic Education Survive under Neoliberal Regime?, [5] re-conceptualizes Critical Mathematics Education as a bottom-up response to the top-down imposed market-driven implementations and neoliberal hegemony in education. In this context, Bülent Avcı offers rich ethnographic data to redefine concepts such as dialogic pedagogy, collaborative learning, and inquiry-based mathematics education in order to promote justice-based critical citizenship and participatory democracy. In that he distinguishes these concepts from neoliberal pedagogy. Bülent Avcı simultaneously draws on the ideas of Paulo Freire and Jurgen Habermas to develop a unique approach to Critical Mathematics Education. [6]

Critical pedagogy and critical mathematics pedagogy

Those who build their critical mathematics pedagogy out of critical pedagogy focus on empowerment of the learners as experts and actors for change in their own world. Critical mathematics pedagogy demands that students and teachers use mathematics to understand "relations of power, resource inequalities between different social groups and explicit discrimination" [1] in order to take action for change. Paulo Freire (1921–1997), Brazilian educator and educational theorist, commonly regarded as the originator of critical pedagogy, suggests that most teaching happens in a "banking" model where teachers hold the information and students are assumed to be passive receptacles for that knowledge. [7] Freire's alternative to the banking method is a "problem-posing" model of education. Through this model students and teachers participate together in a mutually humanizing process of dialogue. With the support of their teacher, students examine problems from their own lives and work collaboratively to generate solutions. [1] One goal of critical pedagogy, according to Freire, is to develop critical consciousness or conscientização (Portuguese). [7] Both teachers and students are expected to challenge their own "well-established ways of thinking that frequently limit their own potential" [1] and that of others. They are especially expected to challenge those ways of thinking that might reproduce instead of challenge oppressive ways of thinking and being. This commitment to learning and critique for the purpose of action for change is also known as praxis, the intersection of theory and practice, another core tenet of the critical pedagogy of Paulo Freire.

Marilyn Frankenstien argues that "most current uses of mathematics support hegemonic ideologies." [2] In particular, she focuses on the mathematical science of statistics which supports the unquestioned acceptance of uncertain conclusions. She argues that the use of the banking model in mathematics education (memorization and procedural focus) produces "math anxiety" in many people, especially and disproportionately those in non-dominant groups (women, people of color, lower income students). This math anxiety then leads people to "not probe the mathematical mystifications" [2] that drive industrial society.

Eric (Rico) Gutstein applies Freire's notion of the inherent connection between "reading the word and the world" [7] to mathematical literacy. [8] He suggests that teaching mathematics for social justice involves both reading the world with mathematics, or more explicitly, "using mathematics to understand relations of power, resource inequalities between different social groups and explicit discrimination," [1] as well as writing the world with mathematics, or developing the tools of social agency in young people for acting in their own worlds. Mathematical literacy according to Gutstein must include both the capacity to "read the mathematical world," necessary for traditional academic and economic success, as well as the capacity to "read the world with mathematics," meaning the use of mathematics to understand and interrogate potentially problematic or unjust structures in their own lives. [8]

Critical mathematics pedagogy in action

Because critical mathematics pedagogy is designed to be responsive to the lives of the students in a given classroom and their local context, there is no set curriculum. Some educators re-use lessons or units from year to year that may apply to multiple groups of students, while other educators develop projects that respond directly to the concerns of a particular group of students, building a project together around a problem the students have posed. Precisely for this reason it is pertinent to consider a few examples of what critical mathematics pedagogy might look like in action.

William Tate, critical race theorist and promoter of culturally relevant teaching, describes the work of one teacher who brought together many of the core components of critical mathematics pedagogy. [9] This teacher elicited concerns from her students about their own neighborhood and lives, and found out that one concern was the prevalence of liquor stores in the neighborhood. Students were being harassed on their way to and from school, having to step over or walk past drunk individuals, making them feel uncomfortable and unsafe. This teacher led her students through the process of in-depth research to better understand the distribution of liquor licenses and the reasons behind the concentration in their neighborhood. The class then met with local journalists to discuss the use of different types of graphic for representing statistics to the general public. The class then considered and determined which graphics and statistical representations (decimals, fractions, percents) might be the strongest for communicating their findings. Finally, the students used their research to produce a policy solution which they presented to the local community council. The work of this group of students and their teacher succeeded in leading to the closing of two of the nearby liquor stores in the neighborhood. [9]

Ole Skovsmose describes a classroom in Denmark in which students learned about the use of algorithms for distribution of welfare support to families by attempting to create their own algorithms. The class worked in groups, where each group came up with a family profile to serve under the supervision of the instructor. Groups then were given a budget for welfare distributions to families and had to come up with how to distribute the money among all the families in their "town" made up of all the created family profiles. The task led them to develop ways of categorizing people in families by age, and families type, by income amount and type, by labor and employment, by possible productivity to society, and more. Some groups distributed the money without building a distribution algorithm, using trial and error and attempting to balance the distribution by more intuitive means. Others built algorithms, working backwards, attempting to break down the distribution using percentages. Many groups were surprised to find that their algorithms did not function comprehensively, and did not fully distribute the amount they were budgeted, and that the outcomes by group were vastly different. Perhaps more importantly, students gained an awareness of the choices and decision making that goes into how policies such as welfare for families are complex and human-created, not simply existing structures. [3] This project is an example of the way in which critical mathematics pedagogy can reveal the role that humans play in mathematizing the world. It is different from Tate's example because it does not explicitly include an action component.

Shelly M. Jones teaches Mathematics Education at Central Connecticut State University. Her classes address culturally relevant mathematics, where she explains cognitively demanding mathematics skills from a relevant cultural perspective. [10]

For a collection of sample lessons that address mathematics teaching through a critical lens see the book, Rethinking Mathematics: Teaching Social Justice by the Numbers (Eds. Gutstein and Peterson, 2005). [11]

Other work in the field of mathematics education that often overlaps at least in part with critical mathematics pedagogy includes the work of ethnomathematics, culturally relevant teaching in mathematics, and work for educational equity in mathematics.

The concept of ethnomathematics was introduced by D'Ambrosio in 1978, in response to the reliance on Eurocentric models for academic mathematics teaching to the exclusion of other cultural models. The goal of work in ethnomathematics is to de-center mathematics as a European dominated discipline by contributing research and teaching that highlights the contributions of many different cultures to mathematics as a discipline, and validating a wide range of mathematical practices. Ethnomathematics work notices, recognizes, reclaims, and celebrates the ways in which non-European communities and cultures are now and have throughout their histories been creating, using, and innovating with mathematics. [1] It differs from critical mathematics pedagogy in that its focus is on cultural and social aspects of mathematics, where critical mathematics work also includes an explicit focus on politics and power structures. [1] Though differences exist, those who work in either field oftentimes publish in similar publications and both consider their work mathematics for social justice. [12]

Culturally relevant teachingin mathematics was developed initially to support the success of African-American students, frequently poorly served by the American public school system which has a long history of educational inequality. The liquor store example provided above is shared by Tate as an example of culturally relevant teaching, but might likewise be seen to embody the tenets of critical pedagogy. He cites six core practices of the teacher from the example that make her work culturally relevant: (1) communication between students, teacher, and outside entities, (2) cooperative group work, (3) investigative research throughout the learning process, (4) questioning content, people, and institutions, (5) open-ended problem solving connected to student realities, and (6) social action. [9] While the practices listed by Tate resonate profoundly with those of critical mathematics pedagogy, the difference (if there is any) is in the goals of the two approaches. The focus of culturally relevant teaching is on the empowerment and liberation of a cultural or racial group, whereas the goals of critical pedagogy include empowerment and liberation of individuals as well as groups, in the face of any form of oppression, not only cultural or racial oppression. [1]

The notion of educational equity in mathematics education promotes the provision of high quality mathematics education to all groups and individuals in an attempt to narrow achievement gaps, for example gaps related to race and gender. This approach does not include a critical approach to mathematics itself, or the notion that mathematics education should include the learning of mathematics for the purpose of being able to analyze and change structures of power and injustice in the world. The National Council of Teachers of Mathematics, the world's largest mathematics education organization, [13] has placed equity as one of its top priorities. [14] However, critical mathematics educators suggest that the NCTM standards "fail to define equity in applicable terms for classroom teachers, and it overemphasized the economic aspects of equity." [1] [8]

Challenges and critiques

Logistically, implementation of critical pedagogy is a challenge because there is and can be no "how-to recipe." If the curriculum must be built out of students’ lives then it will necessarily change each year and with each group of students.

Critiques are widespread, suggesting that mathematics is unbiased and not bound to culture, society or politics and therefore should not be wrongly politicized in the classroom. It is argued that this politicization is a distraction from achievement and risks holding students back, most specifically those it purports to support. [15]

Related Research Articles

In mathematics education, ethnomathematics is the study of the relationship between mathematics and culture. Often associated with "cultures without written expression", it may also be defined as "the mathematics which is practised among identifiable cultural groups". It refers to a broad cluster of ideas ranging from distinct numerical and mathematical systems to multicultural mathematics education. The goal of ethnomathematics is to contribute both to the understanding of culture and the understanding of mathematics, and mainly to lead to an appreciation of the connections between the two.

<span class="mw-page-title-main">Pedagogy</span> Theory and practice of education

Pedagogy, most commonly understood as the approach to teaching, is the theory and practice of learning, and how this process influences, and is influenced by, the social, political, and psychological development of learners. Pedagogy, taken as an academic discipline, is the study of how knowledge and skills are imparted in an educational context, and it considers the interactions that take place during learning. Both the theory and practice of pedagogy vary greatly as they reflect different social, political, and cultural contexts.

<span class="mw-page-title-main">Paulo Freire</span> Brazilian educator (1921–1997)

Paulo Reglus Neves Freire was a Brazilian educator and philosopher who was a leading advocate of critical pedagogy. His influential work Pedagogy of the Oppressed is generally considered one of the foundational texts of the critical pedagogy movement, and was the third most cited book in the social sciences as of 2016 according to Google Scholar.

Critical pedagogy is a philosophy of education and social movement that developed and applied concepts from critical theory and related traditions to the field of education and the study of culture.

The anti-bias curriculum is a curriculum which attempts to challenge prejudices such as racism, sexism, ableism, ageism, weightism, homophobia, classism, colorism, heightism, handism, religious discrimination and other forms of kyriarchy. The approach is favoured by civil rights organisations such as the Anti-Defamation League.

<span class="mw-page-title-main">Peter McLaren</span> Canadian scholar (born 1948)

Peter McLaren is a Canadian-American scholar and Emeritus Professor of Urban Education at the University of California, Los Angeles, having taught at UCLA from 1993 until 2013. Prior to that, he taught at Miami University of Ohio (1985-1993). Most recently, he served as a Distinguished Professor in Critical Studies at Attallah College of Educational Studies, Chapman University (2013-2023) until his retirement, where he was Co-Director of the Paulo Freire Democratic Project and International Ambassador for Global Ethics and Social Justice. He is the Honorary Director of the Center for Critical Studies in Education at Northeast Normal University, Changchun, China. According to Stanford University's database, McLaren belongs to the top 2% of the world’s most influential scientists.

Critical literacy is the ability to find embedded discrimination in media. This is done by analyzing the messages promoting prejudiced power relationships found naturally in media and written material that go unnoticed otherwise by reading beyond the author's words and examining the manner in which the author has conveyed their ideas about society's norms to determine whether these ideas contain racial or gender inequality.

Understandings of culturally relevant teaching has developed over time. Key characteristics and principles help define it, and research has allowed for the development and sharing of guidelines and associated teaching practices. Although examples of culturally relevant teaching programs exist, implementing it can be challenging.

Critical consciousness, conscientization, or conscientização in Portuguese, is a popular education and social concept developed by Brazilian pedagogue and educational theorist Paulo Freire, grounded in neo-Marxist critical theory. Critical consciousness focuses on achieving an in-depth understanding of the world, allowing for the perception and exposure of social and political contradictions. Critical consciousness also includes taking action against the oppressive elements in one's life that are illuminated by that understanding.

<i>Pedagogy of the Oppressed</i> Book by Paulo Freire

Pedagogy of the Oppressed is a book by Brazilian educator Paulo Freire, written in Portuguese between 1967 and 1968, but published first in Spanish in 1968. An English translation was published in 1970, with the Portuguese original being published in 1972 in Portugal, and then again in Brazil in 1974. The book is considered one of the foundational texts of critical pedagogy, and proposes a pedagogy with a new relationship between teacher, student, and society.

Anti-oppressive education encompasses multiple approaches to learning that actively challenge forms of oppression.

Rethinking Mathematics: Teaching Social Justice by the Numbers is a 2005 book edited by Eric Gutstein and Bob Peterson, advocating a mathematics education curriculum that intertwines mathematics with social justice. The various essays in the book, including "Home Buying While Brown or Black" and "Sweatshop Accounting", advocate using social-justice issues to motivate the teaching of rigorous mathematical concepts, and the use of mathematics education as a way of promoting ideas of social justice.

The ecopedagogy movement is an outgrowth of the theory and practice of critical pedagogy, a body of educational praxis influenced by the philosopher and educator Paulo Freire. Ecopedagogy's mission is to develop a robust appreciation for the collective potentials of humanity and to foster social justice throughout the world. It does so as part of a future-oriented, ecological and political vision that radically opposes the globalization of ideologies such as neoliberalism and imperialism, while also attempting to foment forms of critical ecoliteracy. Recently, there have been attempts to integrate critical eco-pedagogy, as defined by Greg Misiaszek with Modern Stoic philosophy to create Stoic eco-pedagogy.

Banking model of education is a term coined by Paulo Freire to describe and critique the established education system in his book Pedagogy of the Oppressed. The name refers to the metaphor of students as containers into which educators must put knowledge. Freire argued that this model reinforces a lack of critical thinking and knowledge ownership in students, which in turn reinforces oppression, in contrast to Freire's understanding of knowledge as the result of a human, creative process.

Problem-posing education, coined by the Brazilian educator Paulo Freire in his 1970 book Pedagogy of the Oppressed, is a method of teaching that emphasizes critical thinking for the purpose of liberation. Freire used problem posing as an alternative to the banking model of education.

Feminist pedagogy is a pedagogical framework grounded in feminist theory. It embraces a set of epistemological theories, teaching strategies, approaches to content, classroom practices, and teacher-student relationships. Feminist pedagogy, along with other kinds of progressive and critical pedagogy, considers knowledge to be socially constructed.

Christine E. Sleeter is an American professor and educational reformer. She is known as the Professor Emerita in the School of Professional Studies, California State University, Monterey Bay. She has also served as the Vice President of Division K of the American Educational Research Association, and as president of the National Association for Multicultural Education. Her work primarily focuses on multicultural education, preparation of teachers for culturally diverse schools, and anti-racism. She has been honored for her work as the recipient of the American Educational Research Association Social Justice Award, the Division K Teaching and Teacher Education Legacy Award, the CSU Monterey Bay President's Medal, the Chapman University Paulo Freire Education Project Social Justice Award, and the American Educational Research Association Special Interest Group Multicultural and Multiethnic Education Lifetime Achievement Award.

<i>Critical Pedagogy Primer</i> 2008 book by Joe L. Kincheloe

Critical Pedagogy Primer is a book by Joe L. Kincheloe published by Peter Lang. Like other "primers" published by Peter Lang, it is an introductory text on the topic of critical pedagogy aimed at a wider audience with its use of more accessible language. The book has wide margins suitable for reader annotations, and many terms and their definitions are included in these margins for accessibility.

Abolitionist teaching, also known as abolitionist pedagogy, is a set of practices and approaches to teaching that emphasize abolishing educational practices considered by its proponents to be inherently problematic and oppressive. The term was coined by education professor and critical theorist Bettina Love.

Mathematics for social justice is a pedagogical approach to mathematics education that seeks to incorporate lessons from critical mathematics pedagogy and similar educational philosophies into the teaching of mathematics at schools and colleges. The approach tries to empower students on their way to developing a positive mathematics identity and becoming active, numerically literate citizens who can navigate and participate in society. Mathematics for social justice puts particular emphasis on overcoming social inequalities. Its proponents, for example, Bob Moses, may understand numerical literacy as a civil right. Many of the founders of the movement, e.g. Eric Gutstein, were initially mathematics teachers, but the movement has since expanded to include the teaching of mathematics at colleges and universities. Their educational approach is influenced by earlier critical pedagogy advocates such as Paulo Freire and others. Mathematics for social justice has been criticised, however, its proponents argue that it both fits into existing teaching frameworks and promotes students' success in mathematics.

References

  1. 1 2 3 4 5 6 7 8 9 10 11 Tutak, Fatma Aslan; Bondy, Elizabeth; Adams, Thomasenia L. (2011-01-15). "Critical pedagogy for critical mathematics education". International Journal of Mathematical Education in Science and Technology. 42 (1): 65–74. Bibcode:2011IJMES..42...65A. doi:10.1080/0020739X.2010.510221. ISSN   0020-739X. S2CID   119789553.
  2. 1 2 3 4 Frankenstein, Marilyn (1983-01-01). "Critical Mathematics Education: An Application of Paulo Freire's Epistemology". The Journal of Education. 165 (4): 315–339. doi:10.1177/002205748316500403. JSTOR   42772808. S2CID   141869416.
  3. 1 2 3 4 5 6 7 Skovsmose, Ole (1994). "Towards a critical mathematics education". Educational Studies in Mathematics. 27 (1): 35–57. doi:10.1007/BF01284527. ISSN   0013-1954. S2CID   123012643.
  4. 1 2 Powell, Arthur (2012). Teaching mathematics for social justice: Conversations with educators. National Council of Teachers of Mathematics.
  5. ↑ Avcı, B. (2019). Critical Mathematics Education: Can Democratic Mathematics Education Survive under Neoliberal Regime? Boston, USA: Brill-Sense.
  6. ↑ Avci, Bulent (2021). "Research methodology in critical mathematics education". International Journal of Research & Method in Education. 44 (2): 135–150. doi:10.1080/1743727X.2020.1728527. S2CID   214132580.
  7. 1 2 3 Freire, Paulo (1996). Pedagogy of the Oppressed . ISBN   9780140254037.
  8. 1 2 3 Gutstein, Eric (Rico) (2006). Reading and Writing the World with Mathematics: Toward a Pedagogy of Social Justice . New York and London: Routledge.
  9. 1 2 3 Tate, William (1995). "Returning to the Root: A Culturally Relevant Approach to Mathematics Pedagogy". Theory into Practice. 34 (3): 166–173. doi:10.1080/00405849509543676.
  10. ↑ "Black History Month Honoree 2019: Shelly M. Jones". Mathematically Gifted & Black. 25 February 2019. Retrieved 4 June 2020.
  11. ↑ Gutstein and Peterson (Eds.) (2005). Rethinking Mathematics: Teaching Social Justice by the Numbers. Rethinking Schools.
  12. ↑ Teaching Mathematics for Social Justice.
  13. ↑ "National Council of Teachers of Mathematics : Overview". Nctm.org. Retrieved 2017-03-02.
  14. ↑ "National Council of Teachers of Mathematics : Log In". Nctm.org. Retrieved 2017-03-02.(registration required)
  15. ↑ Joseph, George Gheverghese (1994-04-01). "The Politics of Anti-Racist Mathematics". European Education. 26 (1): 67–74. doi:10.2753/EUE1056-4934260167. ISSN   1056-4934.

Bibliography

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