Periodic Reporting for period 1 - LI-PrimaryTeachers (Contributions to the in-service education of primary school teachers from their engagement in mathematics landscapes of investigation)
Reporting period: 2024-03-01 to 2025-02-28
Critical Mathematics Education can be understood as an expression of concerns regarding mathematics education and the different sociopolitical roles it can play in society. These concerns encompass what happens in mathematics classrooms and the opportunities in students’ future lives; socioeconomic exploitation, racism, sexism, homophobia, xenophobia, and violence; mathematics itself—not only the school-taught variety but also the mathematics used in different contexts and jobs—, which directly impacts people’s lives; democracy and social justice; and the connection of mathematics education with issues such as equity, inclusion, power relations, students’ and teachers’ foregrounds, dialogue, among others. Educational approaches developed from the perspective of Critical Mathematics Education aim to go beyond mere number manipulation and solving of application problems in the classroom. They seek to provide students with opportunities to question the notions of exactness and absolute rationality of mathematics while providing them with mathematical skills to understand the political structures of inequality, social injustice practices, and mechanisms of oppression, and to act towards transforming the world. One such educational approach involves working with Landscapes of Investigation which are learning environments where students are invited to engage in tasks offering opportunities to: (a) participate in exploratory and investigative processes, including activities such as developing lines of reasoning, conjecturing, testing hypotheses, conducting experiments, proposing and defending ideas, constructing new hypotheses, or creating models; and (b) critically explore and reflect on sociopolitical issues, many of which are controversial. In the context of primary school teacher education, existing literature indicates that practices have often failed to fully capitalise on the potential of approaches like landscapes of investigation. In this regard, at the research level, the project Li-Primary Teachers aimed to understand, from the perspective of Critical Mathematics Education, how primary school teachers plan and implement Landscapes of Investigation with their students within a context of in-service professional education and development. The project had the following specific objectives: (a) to review high-impact mathematics education journals to examine the current state of research on the in-service primary school teacher education; (b) to analyse how primary school teachers learn, through continuous professional development, to design tasks based on Landscapes of Investigation focused on exploring social issues; (c) to identify teacher education dynamics that support professional learning; and (d) to examine possible changes in teachers’ didactical conceptions of mathematics based on their involvement in in-service professional development. The data were collected during a year-long in-service teacher education programme involving 12 Portuguese primary school teachers. This programme included stages of study and experimentation, planning and enacting of Landscapes of Investigation with primary school students, and collective reflection on the work undertaken. Interviews were also conducted after the conclusion of the teacher education programme.
The MSCA Research Fellow, Guilherme Henrique Gomes da Silva, PhD, worked at the Instituto de Educação da Universidade de Lisboa (IE-ULisboa), Lisbon, Portugal, under the supervision of Professor João Pedro da Ponte from 01 March 2024 to 28 February 2025. The fellow became a member of and collaborated closely with the Didactics Research Group, part of Education and Training Research and Development Unit (UIDEF) from IE-ULisboa. The research data were collected in the context of a year-long in-service teacher education programme for primary school teachers. Twelve Portuguese teachers participated in the programme, which included 13 in-person sessions of three hours each, alongside meetings dedicated to planning and enacting lessons with the participants' classes. This programme took place within the participants' workplace context as part of a university-school partnership. The teacher education followed a four-stage interconnected model designed to create opportunities for teachers to enact and reflect on their educational contexts, from the perspective of Critical Mathematics Education. Following the programme, interviews were conducted with seven teachers who accepted the invitation. Additional data collection instruments were employed, including the researcher’s notes during the lessons taught by the participants, teaching materials produced by the teachers, and interactions within a virtual environment where the teacher education resources were shared.
The research findings reveal the programme's contributions to the teachers' practice, particularly in fostering a shift towards the use of Landscapes of Investigation in primary school mathematics. In this process, four prominent features of the teachers’ practices emerged, which could support the implementation of this educational approach in other contexts. The first highlights the strong connection between the use of Landscapes of Investigation and the problematization of social issues. These issues were not only meaningful to primary school children but also enabled them to use mathematics to engage with the issue. In other words, the teachers enacted the exploration of a social issue that children could observe and engage with. This served as a guiding thread for planning and enacting lessons. In this process, it was necessary to find a balance between the mathematics learning objectives and those related to the social issues addressed. Given that these teachers taught multiple subjects, they demonstrated relative ease in adopting an interdisciplinary approach. However, aligning the mathematical objectives of the tasks proved to be challenging. The second feature involved adapting elements of real-world social issues into fictional scenarios. This approach avoided individualising situations for the children while maintaining the educational purpose. The third feature related to how the mathematical tasks were designed. The tasks provided opportunities for students to employ different solution strategies, included questions with multiple possible answers, and emphasised the power of choice for the children. Such characteristics made the investigative tasks rich in opportunities for mathematical learning. Empowering children with the ability to make choices in their learning represented a shift in the traditional paradigm of mathematics lessons, aligning with the perspective of Critical Mathematics Education. The ability to choose also fostered a sense of social responsibility among students. Finally, the fourth feature linked to the teachers’ shift towards working with Landscapes of Investigation concerns the potential of the tasks to stimulate critical reflections. By designing Landscapes of Investigation that enabled children to critically reflect on social issues, the teachers opened opportunities for discussions on topics that are traditionally do not feature in mathematics lessons.
The research findings reveal the programme's contributions to the teachers' practice, particularly in fostering a shift towards the use of Landscapes of Investigation in primary school mathematics. In this process, four prominent features of the teachers’ practices emerged, which could support the implementation of this educational approach in other contexts. The first highlights the strong connection between the use of Landscapes of Investigation and the problematization of social issues. These issues were not only meaningful to primary school children but also enabled them to use mathematics to engage with the issue. In other words, the teachers enacted the exploration of a social issue that children could observe and engage with. This served as a guiding thread for planning and enacting lessons. In this process, it was necessary to find a balance between the mathematics learning objectives and those related to the social issues addressed. Given that these teachers taught multiple subjects, they demonstrated relative ease in adopting an interdisciplinary approach. However, aligning the mathematical objectives of the tasks proved to be challenging. The second feature involved adapting elements of real-world social issues into fictional scenarios. This approach avoided individualising situations for the children while maintaining the educational purpose. The third feature related to how the mathematical tasks were designed. The tasks provided opportunities for students to employ different solution strategies, included questions with multiple possible answers, and emphasised the power of choice for the children. Such characteristics made the investigative tasks rich in opportunities for mathematical learning. Empowering children with the ability to make choices in their learning represented a shift in the traditional paradigm of mathematics lessons, aligning with the perspective of Critical Mathematics Education. The ability to choose also fostered a sense of social responsibility among students. Finally, the fourth feature linked to the teachers’ shift towards working with Landscapes of Investigation concerns the potential of the tasks to stimulate critical reflections. By designing Landscapes of Investigation that enabled children to critically reflect on social issues, the teachers opened opportunities for discussions on topics that are traditionally do not feature in mathematics lessons.
As regards the benefits to society, the research outcomes and practical implications for primary school teacher education are relevant to a number of stakeholders, including primary school teachers, teacher educators, curriculum designers, researchers in mathematics education, and policy-makers. The communication and dissemination activities carried out during the 12 months of the project clearly indicate the importance of the actions undertaken. The research outcomes highlight the possibilities of enacting Critical Mathematics Education in primary schools through in-service teacher education programs. The engagement of primary school teachers and the incorporation of the Landscapes of Investigation approach into their teaching practices appear to offer a way to move beyond traditional mathematics education, which is often based on repetition and application of algorithms, and instead place students at the centre of the learning process. In this way, mathematics was employed by teachers as a tool for understanding social issues relevant to their students. The practical implications of the teacher education model adopted in the research have the potential to bring about positive changes in mathematics classes in primary schools. The interconnected four stages of the teacher education model demonstrated an effective method for bridging the gap between theory and practice in a productive manner.