1 Danish School of Education - Research Programme in Teaching and Learning in the Disciplines, Danish School of Education, Arts, Aarhus University2 The University of Queensland3 Danish School of Education - Research Programme in Teaching and Learning in the Disciplines, Danish School of Education, Arts, Aarhus University
A collaborative practitioner-research based project
Numeracy (mathematical literacy) is an essential skill in life and work. Lack of numeracy has been linked to poor health and work outcomes, and diminished social and civic participation. A key aspect of numeracy, which is not often explicitly mentioned in school curricula, is proportional reasoning. Proportional reasoning is the ability to understand, interpret, and solve problems related to situations of proportion, using comparison and relative and multiplicative thinking. It relies on numerous foundational skills including fractional thinking and an understanding of ratio, scale, decimals and multiplicative structures. Research has highlighted time and again the difficulties that students and teachers experience in proportion and proportional related tasks. This deficit has also been identified in national and international tests, such as NAPLAN in Australia and PISA and TIMMS assessments internationally. Research has also shown that while proportional reasoning develops in students from Years 5 to 9, this development does not always happen naturally. Further, research suggests that targeted teaching can assist students to develop better proportional reasoning skills. This multi-state Australian project responded to these findings through an ongoing professional development program for middle school teachers. A design-based research approach was utilised in which over 120 teachers and school leaders from almost 30 schools participated in multiple workshops over the course of two years (eight half-day workshops in Queensland and four full-day workshops in South Australia). Between workshops, teachers designed and trialled teaching approaches and learning experiences in their classrooms to target their students’ identified proportional reasoning learning needs and capabilities. Data were collected from teachers through feedback sessions, surveys, interviews, and practical presentations. Data were collected on student learning outcomes through interviews, diagnostic instruments, and classroom observations. The initial findings revealed that students and teachers had relatively poor proportional reasoning skills and teachers tended to rely on algorithmic approaches rather than focusing on conceptual development. These findings informed the design of an ongoing professional development program and the collaboration between teachers and researchers led to the development of a range of evidence-based learning materials and teaching resources to promote proportional reasoning across all curriculum areas in multiple year levels. These resources are now freely available for teachers beyond the project and the findings have been widely disseminated through journal publications and local and internatinal conference presentations.
Proportional reasoning; professional learning; practitioner research