Research Activities

Expanding the CAPTeaM Plan of Action, where activities were developed and trialled for the purpose of challenging the perspectives of pre- and in- service mathematics teachers, this next stage involves the collaborative developing and trialling of activities aimed at mathematics learners.

Specifically:

As the following summary of the project’s Year 1 activities indicates, the original aims of the project were steadily achieved. Across the three CAPTeaM years, in both countries, we worked with a small group of secondary mathematics teachers, from initial teacher training through their first years in the classroom, who were partners with us on the development of more tasks and classroom trials that aimed to challenge ableist perspectives on the teaching of mathematics.  

Expanding the 2014-15 CAPTeaM action plan, where activities were developed and trialled for the purpose of challenging the perspectives of pre- and in- service mathematics teachers, Years 1-3 of this second phase of CAPTeaM also involve the collaborative developing and trialling of activities aimed at mathematics learners. In line with this overall plan, in Year 1, we recruited participating teachers in each country (a mixture of pre- and in-service). For example, a key new member of our team in the UK is Mr Malcolm Sinclair, peripatetic mathematics teacher of the deaf who has been instrumental in our liaising with the teacher community. Mr Sinclair was a participant in one of CAPTeaM’s 2014-15 event and has rejoined us as a team member for the second phase. 

The team met approximately once a month (see Section 11 also for current and future meetings) to discuss existing tasks and research results that emerged from the analyses of teacher responses to CAPTeaM tasks; evaluate new tasks and small-scale classroom activities produced by the researchers on the project; meet members of the disabled community and those involved in special education in order to trial the new tasks and classroom activities with small groups of learners (with and without disabilities); and, become involved in the design and delivery of the day events – initial plans for one Mathematics Day for disabled learners (July 15) changed to two events (also Oct 19), following requests by participants in the first event. The second event involved a team of British Sign Language (BSL) interpreters with experience and interest in mathematics communication for the deaf and hearing impaired in the classroom.

We note that the bulk of the UK-based events in Year 1 have involve learners, their carers and their teachers from the deaf community, mainly because of the momentum gained in this community through the CAPTeaM 2014-15 events. Through the now fast developing doctoral thesis of team member Angeliki Stylianidou, we now plan that Years 2 and 3 will also include a strong focus on the blind and visually impaired community.

The visit of the Brazil-based co-I (Healy) took place in December 2016 and the reciprocal visit (Nardi, Biza) of the UK PI and team member to Brazil took place in May 2017. Workshops, seminars and lectures on both sites as well as in other locations where team members were invited to disseminate CAPTeaM materials and findings include: 

10 Apr: Irene Biza addressed ATDM9 (le 9eme séminaire national de L’Association Tunisienne de Didactique des Mathématiques) with a plenary talk that introduced the four strands of the MathTASK programme, including CAPTeaM, to a broad audience of researchers, practitioners and educational professionals (2h, Apr 10, ~50 participants).

23 May: Public lecture (2h, ~100 participants). Evento de Comemoração ao Dia da Matemática: Diálogos sobre Ensino de Matemática, UFF – Federal University of Fluminense (Santo Antônio de Pádua, UFF), Brazil.

24 May: Workshop (2h, May 24, ~20 participants). Evento de Comemoração ao Dia da Matemática: Diálogos sobre Ensino de Matemática, UFF – Federal University of Fluminense (Santo Antônio de Pádua, UFF), Brazil.

15 July: CAPTeaM Workshop for teachers (2h, 15 participants)., by Irene Biza, Lina Kayali, Elena Nardi, Malcolm Sinclair, Angeliki Stylianidou, Athina Thoma. University of East Anglia, UK.

July – Sep: Initiation of research project The Process of Learning to Teach Mathematics and the Student Diversity. Local research group is formed by: 5 lecturers of the UFF, 5 pré-service teachers, 1 teacher representative of teachers who teach Math in elementary school, 1 representative of the support nucleus of school inclusion in Padua, and Brazilian CAPTeaMers who participate in this group as external collaborators.  The project was approved by the plenary of the Department of Exact, Biological and Earth Sciences at UFF in August 2017. Presentation of the project proposal for members of the group on 19 September 2017. Brazil.

3 Oct: Public lecture, Mathematics Activities using an inclusive perspective by Érika Silos (2h, ~40 participants). Tecendo redes: construção de apoio à inclusão - Curso de formação continuada em Educação Inclusiva (Weaving Networks: developing support for inclusion - Continuous Teachers Education Course in Inclusive Education), Fluminense Federal Institute (IFF, Pádua) Brazil.

3 Oct: Survey about students with disabilities in Pádua schools (presentation was held by the representative of mathematics in elementary school and by the representative of the Pádua support nucleus of school inclusion), Brazil.

24 Oct: Discussion of a type 1 and type 2 tasks with groups of participants and with pre-service teachers during the National Science and Technology Week, Brazil.

6 Nov: Invited lecture by Leo Akio (RUMO Project) on Mathematics and Down Syndrome (2h, ~25 participants), Brazil.

19 Oct: CAPTeaM event for Year 8+ deaf/hearing-impaired students and BSL interpreters for mathematics (2h, 15 participants). UEA, UK.

Oct 24: Workshop entitled “When Mathematics of Difference Makes the Difference”, By Érika Silos (2h, ~25 participants). Semana Nacional de Ciência e Tecnologia. Tema: “A Matemática está em Tudo” (National Science and Technology Week 2017. Theme: “Mathematics is in Everything”), UFF – Federal University of Fluminense (Santo Antônio de Pádua, UFF), Brazil.

Year 2

As the following summary of the project’s Year 2 activities indicates, the original aims of the project continued to be steadily achieved and its dissemination and impact to grow at an increasing rate. No significant problems arose in doing so and the minor amendments to the dates of reciprocal visits (some moved to Year 3 due to maternity leave by key team members based in Brazil) were overall in line with the original project plan. 

In Year 2, we continued to work, in both countries, with primary and secondary mathematics teachers, from initial teacher training through their first years in the classroom, and we continued to development tasks and classroom trials that aimed to challenge ableist perspectives on the teaching of mathematics. Expanding the 2014-15 CAPTeaM action plan, where activities were developed and trialled for the purpose of challenging the perspectives of pre- and in- service mathematics teachers, in Years 1-3 of this second phase of CAPTeaM also involved the collaborative developing and trialling of activities aimed at mathematics learners. In line with this overall plan, in Year 1, we recruited participating teachers in each country (a mixture of pre- and in-service). In Year 2 we continued to work with Mr Malcolm Sinclair, peripatetic mathematics teacher of the deaf who has been instrumental in our liaising with the teacher community. Mr Sinclair was a participant in one of CAPTeaM’s 2014-15 event and has rejoined us as a team member for the second phase. The team met at UEA once a month to discuss and plan project activities and events. A notable element of progress in Year 2 was the design and completion of fieldwork for the doctoral thesis of team member Angeliki Stylianidou, which focused on the blind and visually impaired community.

The visit of the UK PI and team member (Nardi, Biza) to Brazil took place in May 2018. Workshops, seminars and lectures on both sites as well as in other locations where team members were invited to disseminate CAPTeaM materials and findings are listed in what follows. We also list the events led by the PI and key UK-based members of the team (Nardi and Biza, assisted by doctoral students and RAs to the project Athina Thoma, Lina Kayali and Angeliki Stylianidou).

27 Nov 27: Oral communication and publication entitled "Exploring Inclusive Perspectives for Teaching Mathematics: Brazilian actions of the CAPTeaM Project" by Aline Simas, Érika Silos, Gisela Pinto and Leiliane Ramos. II Seminário: Desenvolvimento Curricular, Formação de Professores e Tecnologias em Educação Matemática (II Seminar on Curriculum Development, Teacher Education and Technologies in Mathematics Education (15 min, ~20 participants). Brazil.

30 Nov 2017: Workshop entitled “Challenges of Mathematics Teaching in an Inclusive Classroom” (Brazilian version of the CAPTeaM Teacher Workshop). II Seminário: Desenvolvimento Curricular, Formação de Professores e Tecnologias em Educação Matemática (II Seminar on Curriculum Development, Teacher Education and Technologies in Mathematics Education), (2h, ~22 participants) UFF – Federal University of Fluminense (Santo Antônio de Pádua, UFF), Brazil.

1 Nov 2018: MathTASK professional development event for local mathematics teachers (2h, 27 participants), UEA, Norwich, UK.

1 Dec 2018: CAPTeaM+ Workshop, jointly with Maria Toultsinaki and Panayiotis Stavropoulos. The 7th congress of the Greek Association for Mathematics Education (GARME), (1.5h, 20 participants), University of Athens (UoA), Greece.

3 Dec 2018: Presentation on CAPTeaM and MathTASK in the 7th congress of the Greek Association for Mathematics Education (GARME), (50 participants), University of Athens (UoA), Greece.

14 Dec 2018: Poster presentation on MathTASK and CAPTeaM in the Mathematics Education Symposium: ‘Bringing together research and practice: Critical perspectives and ways forward’, (50 participants) UCL Institute of Education, London, UK.

3 May 2018: Workshop for pre- and in- service mathematics teachers, 13:00-17:00: “MathTASK programme, Task methodology and data analysis”. Postgraduate workshop (24 Participants). UFRJ – Universidade Federal de Rio de Janeiro, Brazil.

4 May 2018: Workshop for mathematics teachers: 16:00-18:00: “MathTASK: Transforming mathematics teachers aspirations into effective strategies in context” (60 participants). UNIRIO – Universidade Federal do Estado do Rio de Janeiro, Brazil.

4 May 2018: Workshop for mathematics teachers: 18:00-20:00: “CAPTeaM: Changing Ableist Perspectives on the Teaching of Mathematics” (60 participants), UNIRIO – Universidade Federal do Estado do Rio de Janeiro, Brazil.

8 May 2018: "Lecture for mathematics teachers: 10:00-11:30: Lecture “CAPTeaM: Changing Ableist Perspectives on the Teaching of Mathematics” (40 participants). UFRRJ – Universidade Federal Rural do Rio de Janeiro, Seropédica, State of Rio de Janeiro, Brazil."

8 May 2018: "Workshop for mathematics teachers: 13:00-15:00: Workshop on CAPTeaM activities" (40 participants).  UFRRJ – Universidade Federal Rural do Rio de Janeiro, Seropédica, State of Rio de Janeiro, Brazil.

21 June 2018: “Thinking and Communicating about Commognition: Workshop (including CAPTeaM activities), (4h, 20 participants), UEA.

22 June 2018: “Thinking and Communicating about Commognition: Round Table Discussion (including examples from CAPTeaM), (2h, 20 participants), UEA.

12 July 2018: Workshop for secondary mathematics teachers and primary mathematics specialists: (3h, 24 participants). “CAPTeaM: Challenging Ableist Perspectives on the Teaching of Mathematics”, UEA, Norwich, UK. 

June: Monthly meetings of the UEA-based cohort of team members: ten meetings per academic year, September – June, 90 minutes each (8-12 participants)

Team member Lulu Healy (now based in the UK) delivered the following events:

14 Dec 2017. Plenary lecture: Inclusive mathematics education in Brazil: From school-based case studies to a research field. Lulu Healy presented a lecture at Mathematics Education Symposium at the UCL Institute of Education (London): Bringing together research and practice: Critical perspectives and ways forward’. This lecture focussed on the Brazilian strand of the CAPTeaM and its origins in the research programme Towards an Inclusive Mathematics Education (~120 participants).

5 April 2018. CAPTeaM Workshop, Including disabled learners in school mathematics, at the Ninth British Congress on Mathematics Education at Warwick. Co-led with Irene Biza.

30 May 2018. Lulu Healy ran a CAPTeaM Workshop for 50 PGCE mathematics students at King’s College, London.

8 October 2018. Lulu Healy presented aspects of the CAPTeaM project as part of a lecture on Inclusion and challenging ableism in schools to 200 PGCE students at King’s College London.

31 October 2018. Lulu Healy discussed contributions of the activities undertaken during the CAPTeaM project at her seminar entitled How can we avoid disabling mathematics learners, in the Mathematics Education Seminar Series of the University of Cambridge (~30 participants), UK.

Course lectures

In this period, all team members included CAPTeaM-related lectures in the courses they deliver in their respective institutions.
For example:

• Elena Nardi dedicates Week 9 (4h, 21 students) of her undergraduate module on mathematics education to CAPTeaM.
• Solange Hassan Ahmad Ali Fernandes delivered the following lectures in her institution:

a. Fernandes, Solange Hassan Ahmad Ali. Por uma aula de matemática para todos. 2017. (Apresentação de Trabalho/Conferência ou palestra).

b. Fernandes, Solange Hassan Ahmad Ali; MUNIZ, C. POR UMA MATEMÁTICA ESCOLAR APRENDÍVEL. 2017. (Apresentação de Trabalho/Conferência ou palestra).

c. Fernandes, Solange Hassan Ahmad Ali. A Educação Matemática inclusiva e a pesquisa. 2017. (Apresentação de Trabalho/Conferência ou palestra).

d. Fernandes, Solange Hassan Ahmad Ali. EDUCAÇÃO MATEMÁTICA + INCLUSÃO: COMO VOCÊ RESOLVE PROFESSOR?. 2017. (Apresentação de Trabalho/Conferência ou palestra).

• Gisela Pinto delivered the following lectures in her institution:

a. Pinto, G. M. F. Espaços Formais E Não Formais De Educar Em Ciências E Matemática, 2018. (Conferência ou palestra,Apresentação de Trabalho)
b. Pinto, G. M. F. Matemática e Surdez: o que fazer, 2018. (Outra,Apresentação de Trabalho)
c. Pinto, G. M. F. Desafios Do Ensino Em Matemática Em Uma Sala De Aula Inclusiva, 2017. (Outra, Apresentação de Trabalho)
d. Pinto, G. M. F.; SEGADAS, C. Educação Matemática Inclusiva E A Pesquisa, 2017. (Conferência ou palestra, Apresentação de Trabalho)
e. Pinto, G. M. F. Ensino De Matemática Para Cegos E Surdos: Algumas Reflexões, 2017. (Outra, Apresentação de Trabalho)

Other Brazil-based members of the team have also led, or participated in, the following CAPTeaM-related events:

• Érika Silos leads the regular meetings of the CAPTeaM associated research group at the UFF of Santo Antônio de Padua, Brazil (in addition to project team members: 5 faculty members, 14 pre-service teachers, 1 representative of the support nucleus of school inclusion in the region).
• Gisela Pinto participated in or led the following national events/meetings:

o Conferencista no(a) diálogos sobre o pibid na formação inicial de educadores, 2017. (encontro) matemática e inclusão: algumas reflexões.

o Desenvolvimento curricular, formação de professores e tecnologias em educação matemática, 2017. (encontro) desafios do ensino em matemática em uma sala de aula inclusiva.

o Conferencista no(a) desenvolvimento curricular, formação de professores e tecnologias em educação matemática, 2017. (encontro) tecnologia no ensino, currículo e na formação de professores: algumas reflexões. o Conferencista no(a) i encontro de educação matemática nos anos iniciais do colégio pedro ii, 2017. (encontro) matemática inclusiva, currículo e avaliação: diálogos permanentes no contexto dos anos iniciias.

o Conferencista no(a) ii encontro fluminense das licenciaturas, 2017. (encontro) o Ensino de matemática para cegos e surdos: algumas reflexões.

o Ii workshop dos programas de p´os-gradua¸c˜ao em ensino do estado do rio de janeiro – o Wppgerj2, 2017. (encontro) int´erprete educacional de libras e o desafio da interpreta¸c˜ao na aula de matem´atica em contexto inclusivo.

o Ii workshop dos programas de p´os-gradua¸c˜ao em ensino do estado do rio de janeiro – wppgerj2, 2017. (encontro).

o Conferencista no(a) iv colóquio de educação matemática inclusiva, 2017. (outra) a educação matemática inclusiva e a pesquisa.

o Conferencista no(a) iv semat - semana da matemática, 2017. (encontro) inclusão e educação matemática: algumas reflexões.

o Vi encontro de educação matemática de ouro preto, 2017. (encontro).

o Vii encontro de ensino e pesquisa em educação matemática, 2017. (encontro)

Years 3-4

In Years 3-4, activities were in line with the original application. We have augmented the Year 1 and Year 2 activities with the design of materials for mathematics teacher education and trialled these materials in the respective programmes in the UK and Brazil. Workshops, seminars and lectures held to disseminate CAPTeaM materials and findings included: 

4 April 2019: “Exploring secondary students’ readiness for mathematical proof through an enrich application of the proof schemes taxonomy” (2h). Elena Nardi and Irene Biza. UNIRIO – Universidade Federal do Estado do Rio de Janeiro, Brasil.

5 April 2019: “Scripting the experience of mathematics teaching: Analysing mathematics teachers’ production of reflective accounts” (3h). Irene Biza and Elena Nardi. UNIRIO – Universidade Federal do Estado do Rio de Janeiro, Brasil.

10 April 2019: “From resource to document: Examples from the use of the documentational approach in research”, Elena Nardi and Irene Biza. Departmental seminar (2h) to the postgraduate research programme (Programa de Pós-graduação em Ensino de Matemática (PEMat). UFRJ – Universidade Federal de Rio de Janeiro, Brasil.

11 April 2019: “Current and future research in mathematics education in LaPraME”, Elena Nardi and Irene Biza. Workshop (2h) for the LaPraME (Laboratório de Práticas Matemáticas para o Ensino). UFRJ – Universidade Federal de Rio de Janeiro, Brasil.

12 April 2019: “Commognition: Theory and Methodology” – Workshop (2h), Elena Nardi and Irene Biza. UNIRIO – Universidade Federal do Estado do Rio de Janeiro, Brasil.

16 April 2019:

“CAPTeaM – Desconstruindo a ideia de aluno padrão e sintonizando o ensino de Matemática para a diversidade” (2h), Elena Nardi and Irene Biza

“Officina 1: Refletindo sobre cenários matemáticos inclusivos” (1.5h), Elena Nardi e Irene Biza

“Officina 2: Quando a matemática diferença faz a diferença”,  Érika Silos e Leiliane Ramos.  UFF – Universidade Federal Fluminense, Instituto do Noroeste Fluminense de Educação Superior, Pádua.

17 October 2019: MathTASK/CAPTeaM CPD event for Mathematics Teachers (4h), UEA, Norwich, UK.

25-26 October 2019: CAPTeaM Workshop (4h) for mathematics educators, teachers and researchers - University of Helsinki, Finland.

6-8 December 2019: MathTASK and CAPTeaM session presented at GARME 8 - University of Cyprus, Nicosia, Cyprus.

Across Years 1-4, we have collected and analysed data in order to investigate in more depth the two themes that emerged from the CAPTeaM analyses: deconstructing the notion of the ‘normal’ mathematics classroom/student; and, attuning mathematics teaching to student diversity.

According to the ableist world-view, the able-bodied are the norm in society and disability is an unfortunate failing that must be overcome – rather than a natural consequence of human diversity, akin to gender, race, ethnicity or sexual orientation. Within education, much like broader society, ableism results in institutional and personal prejudice against learners with disabilities, and has a drastic effect on how these learners are taught. We investigate how ableist perspectives impact on the teaching of mathematics, a quintessential part of curricula around the world, and a discipline where public perceptions of ability as innate often shape pedagogical perspectives and practice. Of particular interest to us are mathematical faculties that are typically associated with visual and auditory perception.

In this one-year project, we have established a partnership which combines aspects of Nardi’s approaches to investigating and transforming teachers' pedagogical and epistemological beliefs in the UK and Healy’s work in Brazil with learners with disabilities. In this first year of what we envisage as a longer-term partnership, we have developed and trialled materials that encourage teachers to reflect upon the challenges of teaching mathematics to students labelled as disabled and who may have previously received their education in special schools or classes.

Read the transcript of video 1 (PDF document)

Our research design mirrors that of Nardi and her colleagues in the UK and consists of designing and trialling Tasks with pre- and in-service secondary mathematics teachers in the UK and Brazil. Our Tasks also engage teachers with fictional, yet data-grounded classroom scenarios that aim to identify and challenge ableist perspectives on mathematical learning. The Tasks are informed by the research that has been carried out by Healy and her colleagues in Brazil with mathematics learners with disabilities or with specific difficulties in learning mathematics. In line with the Brazilian research, the mathematical content of the scenarios draws on ideas fundamental in the school mathematics curriculum in both countries. Alongside the conventional mathematics representations associated with these ideas, the activities also present multisensory representations through which learners can experience mathematical structures through touch, sound, movement and the like. The scenarios are based on data collected with students who might be blind, deaf, who experience particular challenges related to the cognitive process of memory and attention or who have other interesting ways of experiencing the world.

Read the transcript of video 2 (PDF document)

Data has been collected in the form of teachers’ written responses to the Tasks and video-recorded group discussions in which these responses are further elaborated. Workshops on each site conclude teacher participation and open up issues that our Task design for subsequent (beyond this first year) phases of the project will focus on.

Read the transcript of video 3 (PDF document)

The 2014-15 research programme consisted of: two visits between UK and Brazil: one each way; from the UK, the PI and one team member (Biza); from Brazil, the Co-I and one Brazil team member (Fernandes); and, before, interim and post-visit work on: Task design, data collection and analysisi; and, dissemination of results. Intra-regional collaboration is reinforced through a multilingual (English / Portuguese / Brazilian and British Sign Languages) website.

Below are documents relating to this project:

• A description of the five phases of the project (PDF) 
• The preliminary results of the project (PDF) 
• A list of the outputs of the project (PDF) 
• The final report of the project (PDF)