Mathematics education for a better life ? – voices from

MES6 participants

João Filipe MatosInstitute of Education, University of

Lisbon

6th Mathematics Education and Society Conference | Berlin | 23 March 2010

dedicated to my friend Ole Skovsmose

Exames? não, obrigado!João Filipe Matos

Por alguma razão pouco clara, parece existir uma fé generalizada na bondade dos testes e dos exames escolares, um pouco em todos

os níveis. Parece acreditar-se mais na objectividade do resultado das medições das aprendizagens quando efectuadas através de um teste escrito realizado durante um tempo limitado em condições geralmente bastante formais e sob uma fiscalização

atenta, do que numa avaliação…

Newspaper PUBLICO 3 Sep 2006

(...) Ao assumir o rigor da quantificação esquece-se que se trata apenas de modelos (matemáticos) que podem ser úteis ou não e que podem traduzir melhor ou pior uma dada situação. (...)

(...) While assuming the rigour of quantification people forget that this is just (mathematical) models that may be useful or not and that can represent better or worse a certain situation. (...)

The mith of quantification

EDUCAR PARA A CIDADANIA HOJE?João Filipe Matos, CIEFCUL

ResumoNeste artigo procuro integrar elementos para o

debate do sentido e do significado que tem na escola actual a educação para a cidadania numa dimensão transversal. Com o objectivo de discutir

as relações entre a educação e a cidadania democrática visito as problemáticas (i) do uso das

tecnologias de informação e o acesso ao conhecimento, e (ii) a política de conhecimento em democracia e a sua relação com a avaliação

na escola. (...)

A educação matemática como fenómeno emergente: desafios e perspectivas possíveis

João Filipe Matos, CIEFUL

(2006)

“Segundo, o ênfase deve ser colocado na educação matemática (dos jovens) e não no ensino de

matemática. No editorial do número temático da revista Quadrante sobre Educação Matemática e

Cidadania (Matos, 2002) argumentei que a disciplina de Matemática deve ser urgentemente eliminada dos currículos do ensino básico. Em vez da disciplina de matemática proponho a criação da disciplina de educação matemática com o objectivo essencial de contribuir para o desenvolvimento de

um ponto de vista matemático sobre as coisas . Isto significa naturalmente que as crianças precisarão

de conhecer alguns factos matemáticos mas significa também que o essencial da disciplina não

será a matemática mas o seu uso como um dos recursos estruturantes do pensamento, da reflexão

e da acção (...)”

“a disciplina de Matemática deve ser urgentemente eliminada dos currículos do ensino básico”

“Mathematics should be eliminated from the curriculum in basic education”

Newspaper Expresso

What does it mean to be critical?

Do I want to take the risks involved?

Do I really want to be whom (it seems) I want to be?

interrogating critical mathematics education

Voices from MES6 participants

Maths Ed vs Critical Maths Ed

ME <.......> (author)

CME <........> (author)

ME a field of research that I'm involved in (H. Mendick)

CME the relationship between mathematics education and power and in changing mathematics education to make the world a more equitable place (H. Mendick)

ME the field concerned with the teaching and learning of mathematics (A. Pais)

CME field concerned with the social and political aspects of mathematics education (A. Pais)

ME the field of the teaching and learning of mathematics, though the field is more complex than just teaching and learning (E. Norén)

CME mathematics education as part of the society, critical mathematics education may have the possibility to improve social justice by addressing conflicts and crises in society (E. Norén)

ME The development of the ability of people to understand,and apply mathematical thinking and actions, and consequently promoting the greater frequency of such thinking and actions in society (V. Frith)

CME development of the ability of people to understand and apply mathematical thinking and actions in order to better understand and critique practices in society (V. Frith)

ME the practice of teaching and learning mathematics but it is also the practice of research on the teaching and learning of mathematics (M. Johansson)

CME a "subfield" within mathematics education dealing with issues such as equity, social justice and the social-political function of mathematics education. It offers some perspectives on what mathematics and mathematics education is or should be about (M. Johansson)

ME teaching and learning about, and through, the subject area of mathematics (K. Nolan)

CME domain of particular issues highlighted and deconstructed as one teaches and learns about (and through) the discursive practices of mathematics (e.g. inclusion/exclusion in communities of learners, what it means to know/learn/do mathematics and who decides) (K. Nolan)

ME the process of opening people's minds to the nature of our way of imposing and recognising pattern and abstraction on the natural world (P. Gates)

CME the application of mathematics education to question taken for granted assumptions about society (P. Gates)

ME institutionalised pedagogic practices and the (not explicitly pedagogic) practices (e.g. learning by participation at workplaces) of teaching and learning activities that involve mathematical knowledge, as well as the research activities that describe and theorise these practices, including research that is directed towards studying the social, economic and political conditions and consequences of those practices (E. Jablonka)

CME a not yet realised form of mathematics education that aims at providing equal access to powerful mathematical discourses as well as to a discourse that aims at understanding socio-mathematical practices and their concomitant discourses (E. Jablonka)

ME learning about mathematics (M. Frankenstein)

CME math education that includes attention to how math is used in the world and discussion of whether those uses are ethical or notANDusing math to understand injustices and act to change those injustices (M. Frankenstein)

ME allows individuals access to a wide range of career opportunities ANDgives us a powerful way of viweing and interpreting the world. (T. Cotton)

CME explores the ways in which mathematics can be used to critique society and societal norms, empowers individuals to see their own position within the world and to begin to understand how individuals and communities are positioned by societal structures, supports political engagment with the world (T. Cotton)

ME the practices of teaching, studying and learning mathematics and managing and regulating the institutional context within which this takes place, in particular the mathematics curriculumANDthe field of academic study that takes these practices as its domain (C. Morgan)

CME as above but with a perspective that understands mathematics and education as practices within society and considers the practices of mathematics education as having a potentially transformative role towards a more just society. (C. Morgan)

ME a field of practice, where teachers and students are involved to the teaching and learning of mathematicsANDa field of scientific inquiry on the practice of mathematics teaching and learning at all levels in the educational system and at all areas outside the educational system in which mathematics is embedded.(D. Chassapis)

CME an approach to mathematics education aiming at spotting and analyzing the socio-political roles mathematics education play or might play in particular socio-polityical contexts. (D. Chassapis)

ME the interface of humans and mathematics, perhaps how humans apprehend mathematics, perhaps with some discussion of how activities might be facilitated for this mode of apprehension to change (T. Brown)

CME mathematics education with a ‘social conscience’ and links to conceptions of ‘critical social science’, with a link to thinkers such as Habermas and Freire (T. Brown)

ME field of research in teaching and learning, policy, ethics, sociology, etc. in relation to mathematics (S. Lerman)

CME taking a position on issues in mathematics education from a standpoint. I suppose that is general enough to include those who take a conservative position when applying a gaze on the field, though my heart tells me that I am referring to critical from a left position, as in Habermas (S. Lerman)

ME part of engagement in the processes where one has possibility to read and engage with society in an active manner (S. Ali Baber)

CME an approach that support a person to see Mathematics as a part of the society (e.g. issues related to equity, justice and democratic participation citizens in society). This could include to become critical of the cultural practices that produce mathematics education in the context of techno-science (S. Ali Baber)

ME should be part of a liberal education that combines the intellectual/aesthetic study of patterns and structures with the analysis of applications of those patterns and structures to physical and social phenomena. It should also include study of the diversity of mathematical practices, and of the sociocultural history of mathematics (B. Greer)

CME analysis of the assumptions, goals, institutions, and practices of mathematics education (B. Greer)

ME learning how to understand and use mathematics, teachers learning how to teach mathematics, and teacher educators learning how to teach mathematics education to pre- and in-service teachers (R. Gutstein)

CME reading and writing the world with mathematics.", learning to use mathematics to study social reality and the genesis of oppression, exploitation, inequality, and injustice--in order to change that reality, to understand the sociopolitical, cultural history of mathematics (R. Gutstein)

ME induction of young people into the discipline and practices of mathematics so that it can be an empowering tool for them - enabling them to transform their own ways of seeing and acting in the world, and transforming the world for the good of everyone (K. Brodie)

CME uses the tools of mathematics to interrogate social inequality and injustice and to find ways of acting to work against oppression and marginalisation and for social justice (K. Brodie)

ME means to increase participation of the individual in a very math-oriented world (H. Westphael)

CME a critique of the use of mathematics in society is brought to the center of the education (H. Westphael)

ME includes both the science and the praxis of mathematics teaching and learning AND a scholarly reflection on the epistemology and the ontology and the praxeology of mathematics both in academia and in our lives (U. Gellert)

CME connects the politics in society with the politics of ME (as a field of production of discourse) and with ME (as the reproductory field) (U. Gellert)

mathematics education is critical

(Skovsmose, 2008)

mathematics education as serving questionable socio-

political roles

• operating as a gate keeper• ensuring the social order in ‘smart’ forms

leading to acceptance of imposed order• supporting the development of an ideology

of certainty• providing an unjustified ‘trust in numbers’• ...

mathematics education as having an empowering role on

people• ...• ...• ...• ...• ...

No optimistic position claiming the existence of an intrinsic connection between mathematics education and a better life, economic growing, democratic values, …

critical mathematics education is produced by our concerns

emerging from thecritical nature of mathematics

education

• the critical nature of mathematics education represents a great uncertainty (therefore producing risks)

A key issue:

the design and the emergent

• we can design for situated action but we must expect the emergent not as a consequence but as a reaction to the design according to the context and activity in place

On critique, critical and being critical

Critical issues in mathematics education

Voices of MES6 participants

with a strong focus on mathematics

Critical issues in mathematics education

1. algebraic comprehension2. use of grafic calculators3. geomety-proofs (L. Spijkerboer)

1. A reform initiative of mathematics education driven by retrospective market-driven ideology2. Too few qualified and critical teachers3. The problem of naturalisation of mathematical understanding on the side of many people involved in research in mathematics education (E. Jablonka)

with a strong focus on education

Critical issues in mathematics education

with a strong focus on education

Critical issues in mathematics education

1. teacher development2. class size too big for adequate attention3. for the most part it is divorced from the world and taught as a series of algorithms to memorize (M. Frankenstein)

with a strong focus on education

Critical issues in mathematics education

1. Unequal access to mathematics qualifications2. Inequitable resourcing of mathematics teaching and learning across groups3. A belief that 'setting' or 'streaming' leads to effective teaching and learning of mathematics. (T. Cotton)

1. Low pedagogic training of teachers.2. Low sensibility of teachers about mathematics education3. Low infra-strutural and material resources (R. Guambe)

with a strong focus on education

Critical issues in mathematics education

1. Mathematics as discipline has a powerful position in the context of Pakistan. This legitimizes the idea that Mathematics has a essence. (...) How to shake this idea of mathematics-has-a-essence and support the thinking that mathematics is a part of human creation and as human creation it is created through different cultural practices and historical traditions and these cultural practices could be questioned?2. How can we support efforts that Critical Mathematics Education becomes more accessible to people?2. Relating concern for Critical mathematics education with the critical citizenship? (S. Ali Baber)

with a focus on educationaddressing the social

Critical issues in mathematics education

with a focus on educationaddressing the social

Critical issues in mathematics education

1. Multilingualism.2. Assessment (as a broad notion)3. Who decides what counts as mathematics knowing and why

with a focus on educationaddressing the social

Critical issues in mathematics education

1. Centralized pressure to succumb to mathematics that is devoid of people's history and politics.2. Pressure to testing and hence teaching to testing. Reward system defined and measured by test results.3. Denial (except for occasional lip service) of serious linguistic consequences of mathematics learning. (S. Mukhopadhyay)

with a focus on educationaddressing the social

Critical issues in mathematics education

1. A crisis - the vast majority of learners do not learn even the basics of arithmetic and never gain access to the power of mathematics2. Teacher development - many teachers do not have the kinds of mathematical knowledge required to support learners' access to the power of mathematics3. Curriculum - the government seems to be moving towards prescribed curricula, even scripted lessons. (K. Brodie)

1. Mathematics (education) is implicated in neoliberal economic systems.2. Mathematics (education) is implicated in militarism (and thus in our current military engagements).3. Mathematics education is part of the way in which inequalities of social class, race and gender are reproduced.(H. Mendick)

with a strong focus on the social

Critical issues in mathematics education

with a strong focus on the social

Critical issues in mathematics education

1) Excessive governmental interference in education.2) Excessive governmental interference in education.3) Excessive governmental interference in education.(T. Brown)

with a strong focus on the social

Critical issues in mathematics education

1. The continuing strong association of disadvantage and underachievement in school mathematics.2. The very strong regulation by Government on teaching and learning in UK schools.3. The national acceptance of the need for placing children in ability sets from a very young age. (S. Lerman)

coming into closing...

I wrote in the Abstract...

“(…) a powerful exercise to start establishing a redefined form of conceptual harmony where minor and major tones frame mathematics education priorities for a better life.”

weight price

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501g to 2000g €4.00

Tabela CTT – Correio Azul (preços de Setembro 2008)

How much shoud I pay to send a letter that weights 30g?

Portuguese mail prices (Dec 2009)

outlining

• the relevance of critique• the crucial role of contradictions• the landscape of possibilities of

transformation• the importance of assuming an

alignment with a critical positioning• the importance of taking risks

seeking for a better life!

3 key questions

• what makes mathematics education critical?

• who makes mathematics education critical?

• who benefits from making mathematics education critical?