Putting socio-cultural theories to work in supporting mathematics teachers' professional development

We discuss the contributions of socio-cultural theories to research and design of interventions directed at the professional development of mathematics teachers. We explain how these theories have been put to work in the field. We also bring to attention specific issues arising in the field for which development and adaptation of socio-cultural theory might be a useful resource

Building learning opportunities in classrooms of disadvantage: rethinking the learning trajectories

Researching learning trajectories in classrooms of disadvantage introduces specific challenges as well as opportunities. Situating our work within design research, we illustrate the power of theoretical approaches in which close attention is paid to both learners' conceptual developments and the means capable of supporting such developments for all learners. We illustrate how considerations of teachers' learning can and should inform the formulation of (students') learning trajectories, if these are to become viable outside of research studies

Co-teaching in mathematics education: IMSITE project experience

Problem We report on co-teaching experience between a university-based mathematics educator (UME) and a secondary mathematics teacher (SMT) in preparing future secondary teachers of mathematics. This collaboration is part of an OLT-funded project Inspiring Mathematics and Science in Teacher Education (IMSITE), which aims at enhancing teacher education by transcending traditional disciplinary boundaries. The project explores ways of combining experiences of university- and school-based mathematics educators in designing learning experiences, which are both grounded in mathematical content, and meaningful from learners’ point of view. The target course was a mathematics curriculum course with focus on middle years of schooling. Majority of the 50 participating students took this course as an elective, preparing for the reality where many secondary teachers without mathematics qualification are asked to teach middle years mathematics. Plan In the first semester of the collaboration, the plan was to: (a) familiarise SMT with course content, goals, and limitations; (b) familiarise UME with tools and resources currently available and actively used by QLD mathematics teachers; (c) share and compare experiences, believes, and practices as educators from different communities by day to day collaboration in planning, task choice and monitoring students’ progress and achievements; and (d) develop collaborative reflective practices which would enable genuine, in depth discussions about pedagogies and students’ mathematical understandings (Chapman, 2009; Sakonidis & Potari, 2014). Action For 8 weeks of the accelerated semester, SMT and UME met on a weekly basis to discuss the goals for the week, activities prepared by UME, and possible improvements that combined the expertise of both co-teachers. The data consists of the electronic log of actual course activities and resources, as well as reflective notes by both co-teachers that focus on changes needed for future course iterations and on reflections of the collaboration. The poster will report on resulting course improvements, including updated digital tools for supporting learning, improvement of student reflection and professional reporting, and grounding all workshop activities in mathematical problem-solving. Reflection Relationships and interactions between SMT and UME made the dual identities of pre-service teachers (as ‘students’ and as ‘future teachers’) more visible, helping us to shape the interactions with students more productively. Implications for the next iteration of co-teaching will be discussed, including role of mathematics and role of course assessment. Proceedings of the Australian Conference on Science and Mathematics Education, The University of Queensland, Sept 28th to 30th, 2016, page X, ISBN Number 978-0-9871834-4-6. REFERENCES Chapman, O. (2009). Educators reflecting on (researching) their own practice. In R. Even & D. L. Ball (Eds.), The professional education and development of teachers of mathematics (pp. 121-126). Boston, MA: Springer. Sakonidis, C., & Potari, D. (2014). Mathematics teacher educators’/researchers’ collaboration with teachers as a context for professional learning. ZDM Mathematics Education, 46(2), 293-304

Reasoning with fractions: supporting pre-service teachers’ learning

We report on a mathematics education course for primary pre-service teachers (PSTs) in which both mathematical and pedagogical learning is essential. Part of this course is devoted to supporting PSTs in (a) strengthening conceptual understanding of fractions and (b) coming to imagine ways in which fractions can be effectively introduced in primary classrooms. In collaborative group work on fraction activities, PSTs generated solutions that were very different from those of year 3-5 pupils. This was unexpected and led to new insights and learning for the instructors. We draw implications about supporting the PSTs’ development of deeper mathematical reasoning in circumstances where prior mathematical learning limits their problem-solving skills and creativity. This work contributes to a larger effort of developing resources that could enhance adults’ learning across STEM disciplines

Resources for teaching: supporting a Mexican teacher’s learning

We analyze the role played by a teaching resource in effectively supporting a professional development collaboration with Irene, a Mexican public-school teacher. The resource is an instructional sequence on fractions that was developed through a series of design experiments in Mexican classrooms. As a result of this collaboration, Irene modified significantly her instructional practices. We discuss how the instructional sequence contributed to Irene’s renewed view of a mathematics classroom by providing her with guidance that was explicit, specific, and achievable

Reciprocal relations of relative size in the instructional context of fractions as measures

The presented study is part of a bigger design and research enterprise in the teaching of fractions as measures. We analyze extracts of a teaching session with a single fifth grade student, in which he flexibly compared the relative sizes of the lengths of three drinking straws, skillfully using unitary, proper, and improper fractions. We identify aspects of his prior instructional experiences that supported the emergence of his relatively sophisticated ways of reasoning. Findings suggest that supporting students' reasoning about reciprocal relations of relative size can be a viable goal in an instructional agenda on fractions as measures

La equipartición como obstáculo didáctico en la enseñanza de las fracciones

Se plantea la conjetura de que el uso de la equipartición en la enseñanza inicial de las fracciones constituye un obstáculo didáctico. Retomando los análisis del concepto de fracción realizados por Hans Freudenthal, Patrick Thompson y Luis Saldanha, se explica por qué es razonable esperar que la equipartición oriente a los estudiantes a entender las fracciones en formas que dificultan el desarrollo de concepciones maduras de los números racionales