Students' developing knowledge in a subject discipline: insights from combining quantitative and qualitative methods

In this paper we describe an example of research that combined quantitative and qualitative methods in order to investigate students' developing mathematical reasoning over time and to identify factors that were influential in this developmen

Software tools for geometrical problem solving: potentials and pitfalls

Dynamic geometry software provides tools for students to construct and experiment with geometrical objects and relationships. On the basis of their experimentation, students make conjectures that can be tested with the tools available. In this paper, we explore the role of software tools in geometry problem solving and how these tools, in interaction with activities that embed the goals of teachers and students, mediate the problem solving process. Through analysis of successful student responses, we show how dynamic software tools can not only scaffold the solution process but also help students move from argumentation to logical deduction. However, by reference to the work of less successful students, we illustrate how software tools that cannot be programmed to fit the goals of the students may prevent them from expressing their (correct) mathematical ideas and thus impede their problem solution

Difference, inclusion and mathematics education: launching a research agenda

The round-table discussion on difference, Inclusion and mathematics education was in included in the scientific programme of VI SIPEM in recognition and celebration of the emerging body of research into the challenges of building a culture of mathematics education which values and respects the diversity of learners in different educational contexts – in Brazil and beyond. This paper presents the contributions to the discussion, which focus on the problematisation of the term “inclusion”, explorations of how the practices of previously marginalized students can bring new resources to the teaching and learning of mathematics and reflections upon the potentially discriminatory nature of the structures which currently mould school mathematics. The paper aims to serve as material for the developing research agenda of the thirteenth working group of the Brazilian Society of Mathematics Education, which met for the first time during the event

Multimodality and mathematical meaning-making: blind students’ interactions with symmetry

In this paper, we examine the claim that mathematical cognition is embodied by exploring the co-ordinations of multimodal resources which characterise dialogues between researchers and blind mathematics students. We begin by considering approaches to understanding the relationship between perception and conception in different academic fields, notably philosophy and neuroscience. This leads us to adopt an embodied perspective on mathematical cognition, with roots in the phenomenology of merleau-ponty. We illustrate how the lived-in bodies of the two blind students interviewed impinged upon their mathematical activities as they worked on a series of task involving symmetrical figures and geometrical transformations – and how the practices of the student with no visual memories differed from those of the student who had more recently lost his sight

Ensaio sobre a inclusão na Educaçâo Matemática

O contínuo movimento das políticas públicas relativas à educandos com necessidades educacionais especiais tem conduzido a um incremento significativo da presença desses aprendizes em salas regulares. Neste artigo discutimos alguns dos desafios associados à inclusão de alunos sem acuidade visual nos processos de ensino e aprendizagem de matemática. Apresentamos as vozes dos atores envolvidos nesses processos: professores, alunos e pesquisadores e analisamos aspectos relativos às avaliações aos quais esses aprendizes são submetidos em nosso país

A relação corpo, cognição e cultura e a natureza multimodal e multissensorial do conhecimento matemático

Neste artigo, apresentamos investigações relacionadas às práticas matemáticas de alunos com limitações sensoriais. Compartilhamos nossas interpretações sobre os processos de mediação do conhecimento matemático, que caracterizam as interações com aprendizes que usam suas ferramentas corporais para suprir as funções de órgãos sensoriais não funcionais. Acreditamos que os significados matemáticos estruturam-se a partir dos nossos encontros com o mundo, e reconhecemos a matemática como uma disciplina constituída culturalmente. Vemos a aprendizagem como um processo delicado, no qual os aprendizes tornam-se conscientes de como seus sentidos subjetivos dos objetos matemáticos conectamse aos significados culturais enfatizados na matemática escolar. Tais aspectos nos levam a considerar que a cognição matemática é mediada culturalmente e corporalmente e tem natureza multimodal e multissensorial. Selecionamos episódios que mostram como essa natureza pode ser explorada na elaboração de cenários para aprendizagem, nos concentrando nos processos de apropriação quando aprendizes com limitações sensoriais são convidados a ver e ouvir os objetos matemáticos. As análises dos processos de resolução das tarefas propostas têm confirmado a centralidade dos aspectos corporais nas práticas dos aprendizes. As falas, os gestos, as expressões faciais e a manipulação dos materiais revelam que a relação entre ação e cognição mostra a indissociabilidade entre fazer e imaginar

Reflexões de licenciandos de matemática sobre os desafios do ensino de matemática em aulas inclusivas

Vivemos em um mundo no qual a deficiência tende a ser considerada uma condição lamentável, uma desvantagem que deve ser superada. Na educação, tal visão resulta em preconceito institucional e pessoal contra os aprendizes com deficiência, podendo ter um efeito marcante em suas trajetórias acadêmicas. Este projeto propõe uma investigação sobre como as perspectivas relacionadas a inclusão de aprendizes com deficiências impactam no ensino de matemática, uma parte fundamental do currículo, e uma disciplina na qual frequentemente as habilidades são vistas como inatas. Neste artigo apresentamos nossas tentativas a desenvolver, experimentar e avaliar cenários que convidam professores e futuros professores a refletir sobre os desafios associados ao ensino de matemática em salas de aula inclusivas

Attuning to the mathematics of difference: Haptic constructions of number.

CAPTeaM develops and trials activities that Challenge Ableist Perspectives on the Teaching of Mathematics. The project involves teachers and researchers from the UK and Brazil in reflecting upon the practices that enable or disable the participation of disabled learners in mathematics. In this paper, we focus on two themes that emerged from data analyses generated in the first phase of the study: deconstructing the notion of the normal mathematics student/classroom and attuning mathematics teaching strategies to student diversity. Here, we address these themes through exemplifying participants’ haptic constructions of number in the context of a multiplication task in terms of four strategies they devise: “counting fingers”; “tracing the sum”; “negotiating signs to indicate place value”; “decomposing”

Challenging ableist perspectives on the teaching of mathematics through situation-specific tasks

CAPTeaM (Challenging Ableist Perspectives on the Teaching of Mathematics) investigates how ableist perspectives – according to which to be able-bodied is the norm and disability is a disadvantage that must be overcome – impact upon the teaching of mathematics. CAPTeaM is a partnership between researchers in the UK and Brazil which brings together approaches to investigating and transforming teacher beliefs and research into the mathematical learning of disabled students. We develop and trial situation-specific tasks that invite teacher reflection on incidents of disabled students’ mathematical contributions. In this paper we present two types of tasks and illustrate analyses of data collected from 81 teachers that explore their views on including these contributions in their mathematics classrooms

Interdependency, alternative forms of mathematical agency and joy as challenges to ableist narratives about the learning and teaching of mathematics

Catering for the mathematical needs of disabled learners equitably and productively requires the anti-ableist preparation and professional development of teachers. In CAPTeaM (Challenging Ableist Perspectives on the Teaching of Mathematics), we design tasks that emulate inclusion-related challenges from the mathematics classroom, and we engage teachers with these tasks in workshop settings. In this paper, we focus on evidence from one type of task in which participants engage in small groups with solving a mathematical problem while at least one of them is temporarily and artificially deprived of access to a sensory field or familiar channel of communication. In this paper, we focus on evidence of emerging resignification – discursive and affective shifts in the participating teachers’ sense-making about what makes the construction of mathematical meaning possible and valuably different – as they work on the tasks. By linking Vygotsky’s vision about the educational changes required to empower and include disabled learners with more contemporary ideas from embodied cognition and disability studies, our analyses show how engagement with the tasks affects participants’ realisation and appreciation of interdependencies between learners, teacher, resources, and emotions, highlights alternative forms of mathematical agency and gives opportunities to turn initial sense of impasse and despair into joy