Critical Mathematics Research Articles

Mathematical modelling: a methodology favourable to the manifestation of critical mathematics consciousness

This study aims to characterise and understand the manifestation of critical mathematics consciousness (CMC) in the modelling process and the relationships that are established between mathematical modelling as a teaching methodology and the development of critical consciousness. Based on a contextualised topic of interest, the students produced mathematical models, and an improved analytical framework based on education for critical mathematical consciousness was used to analyse the interpretations and validations produced. In addition, a questionnaire was applied to ascertain consciousness at an individual level. The results show that the application of the analytical framework generated insights into the development of critical mathematics consciousness. Furthermore, it was noted that the use of questions seems to help in the development of mathematical modelling by deepening discussions and benefiting the development of CMC. This suggestion contributes to the evolution of CMC, through the reflection on social issues in the production of a model. It appears that mathematical modelling is favourable to the manifestation of CMC.

Teaching Constant Rate-of-Change Problem-Solving to Secondary Students With or at Risk of Learning Disabilities.

Rate of change (i.e., slope) is a critical mathematics concept for success in everyday life, academics, and professional careers. Students with or at risk of learning disabilities struggle with solving rate-of-change problems, especially word problems. Interventions that incorporate representations and problem-solving strategies are effective for improving the word problem-solving performance of students with disabilities. This multiple-probe, multiple-baseline, single-case design study evaluated the effects of an intervention that included an integrated, concrete-representational-abstract teaching framework with an embedded problem-solving strategy (POD Check) on students' rate-of-change word problem-solving performance. The intervention was delivered virtually via video conferencing technology. Four middle- and high-school students with or at risk of mathematics learning disabilities in the Intermountain West participated in the intervention. Results indicate evidence of a functional relation between the intervention and students' word problem-solving performance, and effects were maintained 2-4 weeks after the intervention. The findings of this study provide implications for mathematics intervention research and practice for students with learning disabilities.

Black adolescents’ motivation to resist the false dichotomy between mathematics achievement and racial identity

This study investigates the racial-mathematical identity profiles of Black American adolescents. Survey data were collected in five schools across one U.S. urban school district at two time points (spring 2018 [n = 197] and spring 2019 [n = 210]). Based on extant research regarding psychological response patterns to racialized school stress, we investigated the existence of an identity negotiation pattern in which students were motivated to resist negative stereotypes about Black people by achieving well in mathematics. We conducted a latent profile analysis combining students’ self-beliefs across five indicators: racial centrality, racial public regard, mathematics attainment value, mathematics mastery experiences, and resistance motivation. Three distinct racial-mathematical identity profiles emerged: (1) Mathematics Devalued/Ambivalent, (2) Moderately Math Attained, and (3) Resistors. We found associations between profile membership and students’ gender, negative math emotions, and their receipt of cultural and critical mathematics instruction. We also found an association between the identity profiles and school type (academically selective “magnet” schools vs. open-enrollment neighborhood schools), but not in the direction that might be assumed. Moreover, we found that certain school environment factors (i.e., racial stereotyping and cultural and critical mathematics instruction) were significantly different in racially diverse magnet schools than in the neighborhood schools. Overall, our data reveal the existence of a highly motivated Resistor profile among Black students, that is predicted by cultural and critical mathematics instruction but underrepresented within this district’s selective magnet schools.

Algorithm Society and the Critical Mathematics Education

Resumo O avanço tecnológico vem se desenvolvendo de forma acelerada e os algoritmos são basilares nessa estrutura, contribuindo para sua formatação social. A partir desse contexto, teve-se como objetivo neste artigo buscar subsídios que impulsionem reflexões sobre as implicações sociais da Matemática na sociedade do algoritmo, bem como sobre o papel social da Educação Matemática nesse cenário. O artigo trata-se de um ensaio teórico, uma vez que se caracteriza por uma natureza reflexiva e interpretativa. Este ensaio é fundamentado na perspectiva da Educação Matemática Crítica e na relação Ciência Tecnologia e Sociedade, particularmente sobre a denominada Equação Civilizatória. De forma a exemplificar as reflexões teóricas-conceituais levantadas no artigo, apresenta-se também os resultados de um estudo empírico, cujo objetivo foi o de investigar como estava a compreensão de alguns sujeitos sociais, usuários das tecnologias digitais, sobre as implicações sociais da modulação algorítmica, atrelada ao advento da revolução digital. Conclui-se que há carência de discussões críticas sobre a imbricação entre a tecnologia e a Matemática como ferramenta basilar na construção dos modelos sociais. Com isso, propõe-se para o campo da Educação Matemática a aproximação com as preocupações da Educação Matemática Crítica imbricada à Equação Civilizatória, de modo a problematizar as aplicações sociais da matemática e promover reflexões sobre suas implicações.

Bringing Critical Mathematics Education and Actor–Network Theory to a Statistics Course in Mathematics Teacher Education: Actants for Articulating Complexity in Student Teachers’ Foregrounds

In this paper, we discuss how critical mathematics education (CME) and actor–network theory (ANT) come together in a mathematics teacher education course that focuses on the thematic context of climate change to study statistics. Acknowledging the complexity that student teachers encounter when asked to move from a mainly instrumental treatment of statistics toward a critical foreground of data in society, we turn to explore the actant networks, as theorized by ANT, utilized by student teachers when asked to imagine teaching from a CME perspective. For this, our study is based on a series of interviews with student teachers who participated in a statistics course where pollution data graphs were discussed, inquiring about their role as future critical mathematics teachers. The transcribed interviews, analyzed through ANT, inform us as to how student teachers’ foregrounds are being shaped by actants such as the curriculum, social justice, democracy, and source critique, among others. Based on the above, we recommend that teacher education should invite active discussion of the complexity created when a CME perspective is required. This move would allow for a critical approach to critical mathematics education itself that could prepare student teachers to navigate, instead of ignoring or opposing, such complexity.

Contributions of the Theory of the Inclusion of the Other to Inclusive Mathematics Education

Background: The post-colonial and anti-colonial theories in mathematics education, difference and inclusion led Souza and Skovsmose to create the term deficiencialism. Objective: To present the potential of Jurgen Habermas’s theory of the inclusion of the other to contribute to concepts of inclusive mathematics education. Design: Considering that Habermas is a German philosopher who defends ethical communication to solve social problems, we believe that his concepts can help understand the idea of inclusion in teaching to guide the academic community towards a better understanding and positioning about who the Other is. Setting and participants: Jurgen Habermas (2018, 2019) and Ole Skovsmose (2014). Data collection and analysis: Bibliographical and theoretical study. Results: We found possible similarities between Habermasian theories and the critical mathematics education by Ole Skovsmose, each concept with its particularities converging on ethical communication that can favour a more inclusive mathematics education.

Book review: A life in critical mathematics education. Ole Skovsmose (2023) Critical Mathematics Education. Springer

Book review: A life in critical mathematics education. Ole Skovsmose (2023) Critical Mathematics Education. Springer

Teacher Learning towards Equitable Mathematics Classrooms: Reframing Problems of Practice

This study responds to the debate on understanding and evaluating teacher learning in professional development programmes, with particular reference to the development of equitable mathematics classrooms. Conducted in the context of a year-long PD mathematics programme for primary teachers in Norway, designed to disrupt teachers’ assumptions about mathematics pedagogy and how it relates to students’ mathematical thinking, this study takes teachers’ entry goals as its point of departure. Sixteen teachers participated in interviews at the end of the course. Recognising the situated nature of the development of pedagogic judgement in our analysis of teachers’ reflections on their learning, we report on the shift in their “problems of practice” towards actionable concerns about student inclusion. We argue that this shift underpins a fundamental change in their assumptions about teaching and learning and a critical stance towards their own professional practice, suggesting an important indicator of what constitutes sustainable professional development for critical mathematics education.

Remote teaching in the Mathematics degree course at the Federal University of Acre: perspectives, difficulties and future possibilities

This research aimed to identify potentialities and protect from remote moments between professors and students of the Mathematics Degree Course at the Federal University of Acre during the pandemic moment, as well as actions that can be worked on by the subjects for a “next” post-pandemic. As methodological resources and source of information, teachers and students were consulted through an intuitive command to identify difficulties/concerns and possibilities with respect to development actions in the period called Emergency Remote. This investigation was qualitative in nature, as I understand that I deepened the understanding of the social group in question and its trajectory does not require quantification. The information was processed in the light of the Philosophy of Mathematics Education, Critical Mathematics Education and Digital Technologies in Mathematics Education. The quality of the students' internet and the possibilities for evaluating students by teachers represented the greatest difficulties encountered during the pandemic. representaram as maiores dificuldades encontradas no momento pandêmico.

The Fascists Are Coming! Teacher Education for When Right-Wing Activism Micro-Governs Classroom Practice

U.S. educational reform is often the harbinger of global demands on mathematics education practices globally. It behooves teacher education to ‘catch up’ on current trends, hopefully, to stave off the worst of the fascist tendencies of contemporary politics of education. Past foci on research-based ‘best practices’ and ‘mathematics for all’, grounded in liberal multiculturalism (confirming expectations from critical mathematics education scholarship), have become the targets of activists and politicians, turning once-exemplary teachers and their students into casualties. The four phases of currere are employed to study this phenomenon and to identify strategies and tactics for teacher education programs. The currere methodology indicates that the content of such programs must reduce time devoted to evidence and research-based practice in order to accommodate techniques and knowledge bases for the recognition of right-wing tactics, clowning, slogan parody, and political organizing. Teacher education must further place mathematics teachers’ embrace of expertise, authority, and neutrality within broader perspectives on the politics of education, organizational infrastructure strategies and tactics, resource curation, and personal safety planning. Teacher educators themselves must prepare responses to threats on their careers, lives, and families, and proactive ‘game plans’ for the development of new program curricula.

Peer-Tutor Assisted Problem-Based Learning Model on Mathematics Critical Thinking

The mid-semester summative mathematics results stated that grade IV students needed remedial because the ability to solve problems was still low, indicating low critical thinking skills. Based on observations, this occurs because of the need for more interaction that activates students, and the learning process does not invite students to solve problems. The application of learning models affects the improvement of critical thinking skills and being able to activate learning. This study aimed to analyze the significant effect of the Peer Tutor assisted model on the Ability to Think Critical Mathematics in Grade IV Elementary School. This type of research used quasi-experimental (quasi-experimental) with a nonequivalent posttest-only control group design. The research population was ten groups of class IV elementary schools in Cluster IV. Determination of the sample using a random sampling technique with 2 groups, namely experimental and control. The data collection method is a description test method of 6 items. Data analysis was carried out descriptively and inferentially. This study's results are the experimental group's average posttest score, 90.20, and the average posttest score of the control group, 52.94. So, the average post-test score of the experimental group is greater than the control group. The results of the hypothesis show a significant effect of the peer tutor-assisted model on the critical thinking skills of students in grade IV elementary school. It was concluded that the peer tutor-assisted model significantly improves critical thinking skills in mathematics.

Students’ perspectives on Critical Mathematics Education

Theoretically, critical mathematics education (CME) differs markedly from traditional, teacher-centered mathematics teaching approaches. In addition to meeting mathematical goals, a main focus of CME lies on fostering students’ critical consciousness and positioning them as active and informed actors in the classroom and beyond. However, only few empirical studies explicitly focus on how students experience CME instruction and curriculum. In this contribution, we draw on interview data to examine how K-12 students in one Austrian and one American school setting respond to and perceive CME lessons. The analysis revealed that, within both classroom settings, students’ perceptions vary greatly, with some perceiving CME lessons as being completely different from prior experiences in school mathematics to some seeing little-to-no difference. Additionally features of CME instruction that mathematics teachers and researchers might consider to be the most salient are not necessarily the ones that students report attending to. Reasons for that might be manifold, and students might need more time with CME instruction and especially with reflecting on such lessons to identify the rationale behind the instructional approach. Moreover, researchers should be aware that students might not share their understanding of critical instructional reforms and might have diverse or even divergent perceptions.

Experiencing Critical Mathematics Education

When students ponder why they consider it relevant to learn math it becomes apparent that their attributions of relevance do not meet what educational policies state as goals. While they generally consider the subject to be important, their explanations why they do so are limited to only elementary mathematical skills needed in everyday life or unspecified skills for later work life, rarely connecting them to broader societal topics. Integrating Critical Mathematics Education (CME) tasks into math lessons might be a chance to let attributions of relevance evolve further. This contribution shows in how far the students’ perspectives on the relevance of math changed after they experienced several CME units. 16 students from three different schools have participated in two rounds of interviews where they have been asked about their image of math and math learning and if and what they consider relevant. Within the second round of interviews, after they experienced several CME units, additional questions about their experiences in these lessons have been added. The analysis shows that students’ general attribution of relevance did not change considerably. However, effects could be identified in their reflections about the CME units. Students talked about how these units let them experience a connection between math and societal topics that leads to a more personal and direct relevance of math for their lives. However, their understanding of what counts as doing math might hinder them to easily transfer their experiences within these units to their general attributions of relevance of math. If teachers regularly include CME tasks into their math lessons and make reflections on what mathematical activities have been applied to make sense of them an integral part of instruction, CME seems to offer the opportunity for students to broaden their conceptions of math and experience connections between math and societal topics more clearly.

Mathematics and Society: Towards Critical Mathematics Research and Education

Mathematics and Society: Towards Critical Mathematics Research and Education

Describing critical statistical literacy habits of mind

Given the vast number of data representations that people encounter daily, it is imperative that people become critical consumers of the representations they will face. This requires the development of particular habits of mind. The purpose of this paper is to share the critical statistical literacy habits of mind framework. We articulate how we drew on the literature related to statistical literacy, critical mathematics, and critical statistical literacy to identify the habits of mind needed to enact critical statistical literacy in the context of consuming data representations. We describe the refinement process using qualitative interview data. To illustrate what each of the critical statistical literacy habits of mind looks like when enacted, we share examples from statistics teachers making sense of a data representation.

Number Lines to Support Mathematical Understanding

The number line has been proposed as a central construct used by students to solve a range of mathematics problems. Given the capacity of number lines to represent all real numbers and to be used in a variety of contexts, there have been calls to increase the use of number lines in mathematics instruction. However, due to the recency of these recommendations coupled with the myriad ways in which number lines can be used, little hands-on guidance has been provided how best to leverage number lines in mathematics instruction. This special series details five areas in which teachers can use number lines to support acquisition of critical mathematics concepts and skills.

Affective content knowledge as foundation for critical mathematics pedagogy

ABSTRACT Recent mathematics education research highlights the importance of developing rehumanising and critical mathematics pedagogies. The aim of this study is to develop a framework for affective content knowledge in mathematics and to apply that framework to instruction identified as supporting both mathematical learning (ML) and social emotional learning (SEL). Classroom observation and teacher interview data were collected in one primary and one secondary mathematics classroom in the United States and analysed qualitatively using case study methods. Two main findings are presented: 1) both teachers supported ML and SEL by modelling how to do and talk about mathematics with others; 2) both teachers leveraged affective content knowledge to provide instruction that supports ML and SEL. This study is significant because it describes how teachers in real classrooms are building affective content knowledge as part of a critical mathematics pedagogy that rehumanises the mathematics classroom.

The role of mathematics teacher educators in preparing teachers of mathematics to respond to global challenges within their classrooms

The world is in a period of rapid change. Climate chaos is leading to floods, droughts and exacerbating inequality. In this article, we ask, in such a context, what is the role of mathematics education and, in particular, what can mathematics teacher educators (MTEs) do in supporting teachers to respond to global challenges, and the associated injustices, within their mathematics classrooms? We review work done within critical mathematics education and develop a model for reflection on the role of the MTE. We report on work taking place in one university in the UK where, since 2015, MTEs have been encouraging teachers to address global issues in their classrooms. One role which has emerged for an MTE is in supporting the translation of scientific work on climate change into classroom tasks. In England, the spaces for such work are being squeezed in an education system increasingly subject to conservative political forces. We conclude the article by considering possibilities for MTEs to provoke a generic questioning of assumptions, which we argue is possible even within such constraints.

Mathematical Modeling in the perspective of Critical Mathematics Education and Rural Education: a few approaches

Resumo Este artigo traz resultados de uma pesquisa de mestrado e objetiva apresentar aproximações entre a Modelagem Matemática (MM) na perspectiva da Educação Matemática Crítica (EMC) e a Educação do Campo evidenciadas durante o desenvolvimento de atividades de MM em uma turma do 3° ano do Ensino Médio de uma Escola do Campo do interior do Paraná. Para isso, foi realizada uma pesquisa de natureza qualitativa, a partir do desenvolvimento de duas atividades de MM, conduzidas pelos casos 2 e 3 indicados por Barbosa (2004). Os dados foram coletados remotamente via internet por meio de observação, registrados utilizando ferramentas online e analisados de acordo com a Análise Textual Discursiva de Moraes e Galiazzi (2011). Os resultados apontam que a MM na perspectiva da EMC possibilitou fazer conexões com a Educação do Campo, uma vez que emergiram, por meio do diálogo, discussões democráticas e reflexões críticas a respeito de questões econômicas, ambientais, culturais e sociais, despertando a autonomia durante o desenvolvimento das atividades, cujos temas envolveram situações reais articuladas ao contexto e aos conhecimentos dos alunos.

Between race-evasiveness and the pursuit of racial competence: Secondary mathematics preservice teachers’ understandings of race in an introductory methods course

The purpose of this manuscript is to describe the ways that preservice teachers, in their first mathematics education course, understood race in mathematics classrooms. Through a qualitative document analysis of course assignments, we identify three ways students wrote about race: using race-evasive maneuvers to avoid discussion of race in mathematics education, skimming past racial issues in ways that reduced their importance, and directly engaging with race in the active pursuit of racial competence. Our results suggest ways that critical mathematics topics can encourage students to begin this pursuit and underscore the need for intentionally antiracist-oriented mathematics teacher education.