Aims

What were the main aims of the initiative?

This example outlines a new mathematics learning paradigm. According to socio-epistemological theory, the mathematics knowledge learning process in schools gives meaning to mathematical objects and the use of mathematical knowledge. A focus on Things that I do allows students to build knowledge and to develop mathematical thinking. Based on this paradigm, this example proposes professional development experiences for in-service teachers, from Oaxaca State secondary basic education level in México. The authors studied their formative experience in order to identify the factors that support their empowerment process, specifically in the field of school mathematics teaching.

Themes

The aim of this project is to promote participation in practices that enable teachers to develop their students’ ‘social construction of mathematical knowledge’. As already reported by socio-epistemological theory, this approach allows the democratisation of learning, as teachers can design learning situations based on the real life experiences of their own students. In this way, the use of mathematics is built into the practice.

The aim is to study the collective design of learning situations and socially shared practices, as for example in: the construction of a symbolic language for elementary algebra from experiences of construction in masonry; the study and/or recognition of geometrical patterns in the practice of embroidery; the constitution of mathematical concepts of volume and physical space through ancestral community practices like the jícara (container for drink) and the cuartillo (container to store seeds). These designs were introduced into classrooms in different regions of the State, with different school systems (technical, general and tvsecondary) and in different stages of secondary education.

The teachers take an alternative approach to the educational reforms implemented at national level, which require the design of innovative learning situations based in relevant contexts that value the use of knowledge and the mainstreaming of all learners.

The main objective is to recognise that you can learn mathematics from practical concepts. For example, rather than abstract ideas of proportionality, in practical terms, students might explore comparisons, equalities and construction of units of measure. A practical approach would, for example, allow students with diverse cognitive disabilities to find meaning in these ideas through relevant activity rather than being excluded by a focus on abstract thought. To support this approach, a study of the practices associated with mathematical objects is essential.

The second aim is to build together with the teachers a framework that allows them to transform daily tasks through autonomous professional development, that begins by questioning the objectives of their daily work: the development of mathematical knowledge.

Background

Location, setting, Scope, key events etc.

The state of Oaxaca in Mexico is an area of great cultural diversity. It has a high proportion of speakers of languages other than Spanish and many indicators of marginalisation. It possesses a rich historical and cultural background and has kept many of its local traditions. It resisted many of the structural reforms of the Mexican government and has a high number of semi-autonomous local authorities.

Regarding education, Oaxaca follows its own curriculum and the work force is opposed to the traditional Mexican union – the SNTE (National Union of Workers of the Education).

ISSUES ADDRESSED

What issues/challenges does the example address?

The professional development courses study the learning of specific concepts. While many courses conclude with a summary of what the teachers know or do not know, this course tackles the actions embedded in educational professional practice, considering the mathematical knowledge that is an indispensable element and that can transform the profession. Examples include: the incorporation of teachers into a scientific domain called Mathematics Education; the active participation in academic events and national or international congresses; design, implementation, analysis and dissemination of the results of the study of learning situations in such events; construction of groups of teachers that help them to form a community of transformation at institutional, local or regional level.

 

Implementation

How was the Initiative implemented?

The programme reported here is a two-year course, with most of the time devoted to the preparation, evaluation and presentation of an investigation to obtain a master degree. During the three first semesters there are 9 seminars, with a time commitment of 40 hours. The teachers take courses on Friday, Saturday and Sunday, every two weeks. However, the times are flexible. The 9 seminars problematise school mathematics, including proportional thought, variational thinking and language, trigonometric thinking and exponential growth.

This problematisation consists of questioning traditional school mathematics generally used by teachers in classrooms. This school mathematics is based on a conceptual evolution of mathematical objects, whereas the paradigm in the courses described here proposes a more practical approach. Here, meaning is given to objects through use, recognising the epistemological nature of the construction of knowledge. This work ensures that the theory studied during the project is consistent with practice.

Later, when writing up their investigations, the teachers investigate the theoretical approaches learnt, but above all, they correlate theory with practice: the teacher accepts that mathematical knowledge can be built through practice and design, based around ad hoc situations in the classroom.

With the aim of sustaining design that supports socio-epistemological theory, teachers read widely about Mathematics Education and argue about the difficulties and learning strategies that the research community has reported previously. In this way, the teachers ‘professionalise’ tasks, study the educational phenomena, and go back to school with a ‘critical eye’ to their practice. The key is that they go back with their new designs to be active: they transform the paradigm of construction of mathematics and use innovative didactic tools to create learning opportunities according to the context.

Once they have finished the course, some teachers continue with doctoral studies but all continue with the active participation in congresses and academic events. That is to say, they join a scientific community and become the main actors in analysing their practice.

KEY OUTCOMES & IMPACT

What where the key Outcomes? What impact/added value did they prove? What were the biggest challenges?

The most outstanding result has been the formation of a professional community of educational mathematics at secondary school level that supports the design of innovative educational intervention. The investigation team, as a result, has a better understanding of the phenomenon of teacher empowerment and the factors that motivate a change of practice in particular in relation to teachers’ school mathematical knowledge. Teacher colleagues have formed new networks to extend their achievement and find mutual support for professional growth. They discuss their work at conferences and write up the results of investigations that give an account of the process of empowerment leading to the transformation of real school practice. They can provide examples of how their idea of education has changed, based on the idea of ‘autonomy’ or ‘relative autonomy’: the teachers build bridges to develop professionally in an autonomous and collegiate way.

EVALUATION

Has the initiative been evaluated or are there plans for this in the future?

The work is, in part evaluated by the investigations presented by teachers for their degree. The active participation of teachers in professional development, attendance at conferences and collegiate and academic meetings, provides an opportunity to present proposals on improvements to education and to defend and improve ideas through community dialogue.

One of the greatest difficulties has been combining work time with time for professional development, as in both cases the load was extensive.

FUTURE DEVELOPMENTS / SUSTAINABILITY

Have any plans been made for future direction of the initiative?

One way that change has been evidenced in relation to the problematisation of mathematical knowledge is that teachers recognise and are incorporated into the Mathematics Education scientific domain. This fact allows for the continuity and sustainability of the teacher empowerment. For the authors, teachers must not only be empowered – but also empowering. Teachers should question the traditions of school mathematics as necessary to design learning appropriate to the context of their students. In this way, any problems with education and learning are not attributed to the students. There should no longer be students who do not want to learn, or teachers who do not know how to teach if they work with mathematics in this way.

If the project is sub-divided into phases of development, one could say that there is a general phase of knowledge of the field; a phase of ‘deepening’ and a phase of design. In this way, the continuity of the project progresses.

LEARNING POINTS

What are the main learning points?

As teachers’ articulated knowledge gained from their investigations, the authors learnt that the change of teacher practice does not come from theoretical questions, but from shared learning – in this case, from designing educational interventions.

Building educational knowledge can modify practice, but is only consolidated when it is shared in a community of reference. This process can be generalised to other branches of knowledge and to other educational experiences, for example workshops, diplomas or specialist courses. These actions will serve to bring about a big process of cultural change through an understanding of what produces that change. For mathematics education, the inappropriate use of knowledge restricts teachers to repetition and the exercise of power. Teacher empowerment encourages mathematics teachers by promoting autonomy and transforming didactics through innovation.

Materials

Are there further information about supporting materials?

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Daniela Reyes Gasperini, Ricardo Cantoral, Gisela Montiel

Departamento de Matemática Educativa del Centro de Investigación y de Estudios Avanzados, México

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