Numeracy in practice: teaching, learning and using mathematics
The following article is adapted from the report of the same name produced by the Victorian Department of Education and Early Childhood Development
Numeracy in Practice: Teaching, Learning and Using Mathematics is a research and policy-based resource for teachers of numeracy in Years P–10. It is an initiative of the Victorian Department of Education and Early Childhood Development, and intended to be a companion volume to Literacy Teaching and Learning in Victorian Schools.
The report is based on a focused literature search undertaken to identify and present findings from local and international research relevant to teaching, learning and using mathematics in the 21st century. It highlights those aspects that make a difference to student numeracy outcomes. Numeracy in Practice: Teaching, Learning and Using Mathematics focuses on the characteristics of effective numeracy teaching and addresses key classroom issues including: what to teach, how to teach numeracy, how to cater for diversity and how to make best use of technology. The report also focuses on the ways in which the school and the community can support effective teaching of mathematics.
Separate sections of the report explore key areas of research relevant to the teaching and learning of mathematics in Victorian schools.
Numeracy and mathematics
Across the world, while it is clear that not everyone uses the term 'numeracy', there is a strong consensus that all young people need to become competent and confident users of the mathematics they have been taught. Numeracy is best described as a key outcome of how mathematics is taught and learned – it bridges the gap between mathematics learned at school and the variety of contexts where it needs to be used in everyday life.
Mathematical knowledge that is seen as isolated from its applications, from other school subjects and from life outside school does not do justice to the important role that mathematics has in schooling and in the future life and work of all our students.
Australian performance in international studies
Australia has been consistently above the international average in both TIMSS and PISA tests. Nevertheless, there are aspects of our performance that on closer inspection call for action. In particular, the performance of Indigenous students and those students living in remote and very remote locations is significantly lower than that of students in the rest of the nation.
Compared to those countries that are consistently high performing in these international assessments, Australian students are under-represented in the top performing group and over-represented in the lower performing groups, with a large proportion of students falling in the middle.
The National Reform Agenda and Victoria's plan to improve literacy and numeracy outcomes reflect a commitment by governments to keep improving performance in order to remain competitive.
The agenda for reform outlined in the 2008 Blueprint will focus on expanding the resources and opportunities for improving outcomes in mathematics and science, articulated in a mathematics and science strategy and a statement on Victoria’s approach to literacy and numeracy.
The 2008 TIMSS Video Study, moreover, offers important insights into how mathematics is taught in typical classrooms in other countries. There are lessons to be learned from these countries that Australian schools might take to heart – in particular, more real-life connections, more mathematical connections and more high-level questioning.
Australian approaches to numeracy
Both the Victorian Early Numeracy Research Project and the Middle Years Numeracy Research Project provided evidence-based recommendations about school organisation and structures that support achievement in student learning outcomes in mathematics. The student learning data collected showed a seven-year range of student achievement in many middle years' classes. They also found that a whole-school approach to numeracy improvement, supported by effective leadership, was a key element in achieving improvement in numeracy outcomes.
Each of these research projects embodied high levels of collaboration between researchers, schools systems and participating schools. Individual schools are simply not in a position to carry out similar research on their own. In making use of what has been learned from these projects, individual schools have to decide what to draw on, how that fits in with their own priorities, and what outside support is needed to get under way.
Outside support – whether from the region or network – is likely to be most effective when individual schools set their own clear priorities for promoting numeracy, adopt a whole-school approach to effective teaching, and use classroom assessment to assist planning for instruction and to promote student learning. Schools need to make provision to support students who are identified as underachieving and others who may need to be challenged. Mathematics teaching and assessment need also to be linked to frameworks for reporting such as the Victorian Essential Learning Standards. These issues will be discussed in following sections.
Effective numeracy teaching
From the early years of schooling students need to be provided with higher level problems and questions, which help them make connections between key concepts and procedures, rather than instruction that is focused on routine procedural tasks. Students need to see the mathematics they are doing as important and relevant, and themselves as capable of thinking and working mathematically.
Working collaboratively in mixed ability groupings is generally to be encouraged with opportunities for students to support one another and to share explanations.
Serious questions remain about the practice of more or less fixed-ability groupings, either in the same class or placing students in different classes according to ability. This practice is not supported by research. On the contrary, it appears to contribute to negative attitudes and lowered attainment for less well-achieving students and to yield limited benefits for others.
ICT in its various forms has, and will continue to have, an important place in the teaching and learning of mathematics. New forms of web-based technology have the potential to create new 'spaces' for learning and communication in all subjects. In particular, they have the potential to engage students as active contributors in their own learning, and to re-define the times and spaces when and where learning occurs.
Continued advances in technology itself and changed contexts in its use in schools create problems for longitudinal research studies of effectiveness that can confidently be ascribed to the use of technology itself. However, there are many formal and informal measures of student engagement, motivation and achievement that can be used to monitor the use of technology.
There is evidence of gender differences in the way technology is used. These need to be monitored carefully at classroom and school levels. Access by teachers to appropriate professional development in the effective use of technology – especially in promoting higher level mathematical thinking – is also important. Schools that demonstrate high performance in the numeracy domain develop a shared vision with goals that:
Differentiating support to improve student learning
Differentiated teaching is a powerful classroom strategy that aims to increase effective learning for all students. Careful use of tasks and teacher prompts are needed to ensure that all students can engage with and benefit from the mathematics they are learning. Differentiated teaching usually relies on a mix of whole-class and small-group work based on short-term flexible groupings according to particular tasks and learning goals.
For at-risk students, research-based withdrawal programs – working either on an intensive individual basis or in small groups – are able to produce significant improvement in mathematical understanding and attainment. The focus of these programs is building up students' conceptual knowledge so that they can become proficient and engaged in learning and using mathematics. There is also evidence that well-designed and well-supported classroom approaches are effective. These latter approaches need sustained teacher professional development, but this has the effect of building the capacity of all teachers of mathematics across the school.
Purposes of assessment
Assessment may have different purposes and no single assessment approach can fulfil all of them. Externally administered, standardised testing programs such as NAPLAN can help schools to set broad directions for curriculum planning and focus on areas of the curriculum where the school may not be performing as well as expected. Effective assessment practice in the classroom is the next step in ensuring that teaching is appropriately directed to the learning needs of individual students. The relationship between formative and summative assessment does not have to be contradictory; indeed, research shows that formative assessment practices can be helpful when preparing for national testing programs. Teachers just need to be clear on the difference in purpose between different assessment approaches, how they affect teaching practice, and their impact on students. The closer any assessment approach is to students' thinking, the more effective it is likely to be.
A responsibility for all those engaged in schools
Promoting numeracy is a task for all who are involved with schools. It is a key task for those engaged in school leadership positions – principals and curriculum leaders – in developing school policies, in allocating resources and supporting teachers. Promoting numeracy is also, of course, a key responsibility for teachers. All teachers should see themselves as making a contribution to children's numeracy. For students to become numerate, they must be given opportunities to practise and apply the mathematics they have learned; this should take place not only in the mathematics classroom but in other areas of the curriculum.
School councils too have an important role in supporting the development of appropriate policies and ensuring that achieving high standards of numeracy is incorporated into the school's cycle of goal setting, planning for school improvement and cyclical review of performance in these areas. Parents also need to be involved. All these areas call for a whole-school commitment and cannot be left to a few teachers.
Collaboration between primary and secondary schools is important, especially across the transition years. Sharing of good practice with other schools helps to foster teacher professional development. Supporting all these directions is a key task for those who work at the regional and network levels.
Key Learning AreasMathematics