The Australian Government Department of Education, Science and Training commissioned the Victorian Department of Education and Training, the Catholic Education Commission of Victoria and the Association of Independent Schools of Victoria to undertake a project to identify effective classroom teaching approaches in mathematics for primary school students in a range of Victorian schools. The project was conducted in partnership with a research team from RMIT University from September 2001 to April 2003.
The major outcome of this research is the identification, description and elaboration of twelve scaffolding practices that contribute to improved student learning outcomes. These practices describe a range of communicative practices that teachers use to support students’ mathematics learning. They can be selected and used appropriate to purpose, for example, to explore / make explicit what is known, challenge / extend students’ mathematical thinking, demonstrate the use of a mathematical instrument, or to assist students arrive at a key generalisation. In particular, they support teachers to make more informed decisions about how they will meet the learning needs of all students in the most appropriate way possible.
A major policy objective of the Australian Government is to ensure that all students attain sound foundations in literacy and numeracy. In 1997 all Education Ministers agreed to a National Literacy and Numeracy Plan which provides a coherent framework for achieving improvement in student literacy and numeracy outcomes. The 1999 Adelaide Declaration of National Goals for Schooling in the Twenty-First Century contains the national literacy and numeracy goal that students should have attained the skills of numeracy and English literacy, such that every student should be numerate, able to read, write, spell and communicate at an appropriate level.
In support of the numeracy component of the National Plan, in 2001 the Australian Government implemented the Numeracy Research and Development Initiative. This Initiative consisted of two complementary strands – a national project strand and a strategic State and Territory projects strand. The Researching Numeracy Teaching Approaches in Primary Schools Project is one of ten strategic research projects undertaken by State and Territory education authorities across Australia. The purpose of these projects was to investigate a broad range of teaching and learning strategies that lead to improved numeracy outcomes. The Researching Numeracy Teaching Approaches in Primary Schools Project was conceptualised as a cross-sectoral project by the Victorian Department of Education & Training, the Catholic Education Commission of Victoria and the Association of Independent Schools of Victoria, and conducted in partnership with a research team from RMIT University from September 2001 to April 2003.
The project aimed at researching numeracy teaching practice through the identification of effective classroom teaching approaches in mathematics for students in the early years (Prep – Year 4) and the middle years (Years 5 and 6) in a range of Victorian schools. It was also aimed at determining the potential of these approaches for improving student outcomes.
The action research component involved the research team working with teachers from the 16 research schools as they enacted their action plans and helped identify and describe a range of numeracy teaching approaches. A range of measures were used to explore the research questions including a Behind-the-screen process, which involved the structured observation of a group of teachers by their peers facilitated by members of the research team. To evaluate the effectiveness of the proposed numeracy teaching approaches, sample based, student interview data were collected at the beginning and end of the project from both the research schools and a matched set of reference schools.
The research is expected to influence classroom practice and impact on student numeracy outcomes in at least seven ways.
- The identification and elaboration of a range of interaction patterns or scaffolding practices (described below) will help teachers make more informed decisions about how to address specific learning needs and promote and sustain mathematical thinking.
- Access to an emergent professional language will encourage and facilitate increased professional discussion, reflection and critical review of ‘taken-forgranted’ teaching practices in mathematics - a first step in improving practice.
- Participation in a Behind-the-screen process or similar opportunities for peer observation and review will develop and deepen teachers’ understanding of their practice, and contribute to the ongoing development of a professional language.
- Recognition of the critical importance of teachers’ pedagogical content knowledge will encourage professional learning teams to identify their learning needs and initiate action as appropriate (eg, mentoring, team-teaching and/or targeted professional development).
- Recognition of the dynamic relationship between classroom cultures and scaffolding practices will encourage teachers and professional learning teams to examine the type of classroom cultures they establish and the nature and role of interaction in the construction of mathematical meaning.
- Recognition of the complexity of classroom organisation and structure will encourage teachers to select lesson structures and groups specific to purpose. That is, according to the nature of the task(s) and scaffolding practices chosen to meet specific learning needs.
- The demonstrated value of a whole school approach, supported by effective leadership and shared expectations will inform the work of professional learning teams and encourage then to engage with practice in a more open and critical way.
The major outcome of this research is the identification, description and elaboration of twelve scaffolding practices that contribute to improved student learning outcomes in a range of Victorian primary school settings including a special school. They essentially describe a range of communicative practices that teachers use to support students’ mathematics learning. The scaffolding practices can be selected and used appropriate to purpose, for example, to explore / make explicit what is known, challenge / extend students’ mathematical thinking, demonstrate the use of a mathematical instrument, or to assist students arrive at a key generalisation. In particular, they support teachers to make more informed decisions about how they will meet the learning needs of all students in the most appropriate way possible. The identification of these scaffolding practices provided teachers in the research project with a professional language to discuss teaching practices. The twelve scaffolding practices identified by the research are summarized below.
Excavating
| drawing out, digging, uncovering what is known, making it transparent |
Teacher systematically questions to find out what students know or to make the known explicit. Teacher explores children’s understanding in a systematic way |
Modelling
| demonstrating, directing, instructing, showing, telling, funnelling, naming, labelling, explaining |
Teacher shows students what to do and/or how to do it. Teacher instructs, explains, demonstrates, tells, offers behaviour for imitation. |
Collaborating
| acting as an accomplice, co learner/ problem-solver, co-conspirator, negotiating |
Teacher works interactively with students in-the-moment on a task to jointly achieve a solution. Teacher contributes ideas, tries things out, responds to suggestions of others, invites comments/opinions in what she/he is doing, accepts critique |
Guiding
| cuing, prompting, hinting, navigating, shepherding, encouraging, nudging |
Teacher observes, listens, monitors students as they work, asks questions designed to help them see connections, and/or articulate generalisations |
Convince Me
| seeking explanation, justification, evidence; proving |
Teacher actively seeks evidence, encourages students to be more specific. Teacher may act as if he/she doesn’t understand what students are saying, encourages students to explain, to provide/obtain data, … |
Noticing
| highlighting, drawing attention to, valuing, pointing to |
Teacher draws students attention to particular feature without telling students what to see/notice (ie, by careful questioning, rephrasing or gestures), encourages students to question their sensory experience |
Focussing
| coaching, tutoring, mentoring, flagging, redirecting, revoicing, filtering |
Teacher focuses on a specific gap (ie, a concept, skill or strategy) that students need to progress. Teacher maintains a joint collective focus and provides an opportunity for students to bridge the gap themselves |
Probing
| clarifying, monitoring, checking |
Teacher evaluates students understanding using a specific question/task designed to elicit a range of strategies, presses for clarification, identifies possible areas of need |
Orienting
| setting the scene, contextualising, reminding, alerting, recalling |
Teacher sets the scene, poses a problem, establishes a context, invokes relevant prior knowledge and experience, provides a rationale (not necessarily at the beginning of the lesson, but at the beginning of a new task/idea) |
Reflecting/Reviewing
| sharing, reflecting, recounting, summarising, capturing, reinforcing, reflecting, rehearsing |
Teacher orchestrates a recount of what was learnt, a sharing of ideas and strategies. This typically occurs during whole class share time at the end of a lesson where learning is made explicit, key strategies are articulated, valued and recorded |
Extending
| challenging, spring boarding, linking, connecting |
Teacher sets significant challenge, uses open-ended questions to explore extent of children’s understanding, facilitate generalisations, provide a context for further learning |
Apprenticing
| Inviting peer assistance, peer teaching, peer mentoring |
Teacher provides opportunities for more learned peers to operate in a student-as-teacher capacity, endorses student/student interaction |
As a consequence of this work, the notion of numeracy teaching approaches was broadened to encompass the communicative acts teachers engage in as they support students in their mathematical learning.
Additional data from the action research component of the project indicate that deep pedagogical content knowledge and appropriate classroom cultures are needed to support effective scaffolding practices. In the context of this research, pedagogical content knowledge refers to knowing how to represent and formulate the subject so that it is comprehensible to others. In particular, it was evident that where teachers were aware of students’ prior knowledge and experience and had a well developed understanding of relevant learning trajectories, they were more likely to choose and use appropriate mathematical learning activities. Where there was evidence of a mutually respectful learning environment in which the teacher and students were expected to formulate, share and justify their thinking, it was more likely that the mathematical potential of the activities would be realized and interactions would be more deeply focused on the mathematics. Where these were in place, it was clear that scaffolding practices were likely to be used to greater effect and teachers were more likely to remain focused and press for understanding.
Considered overall, the outcomes and findings of this project clearly suggest that access to a professional language in conjunction with opportunities for sustained, collective reflection on practice powerfully impact on teachers' knowledge base for teaching mathematics. While an important prompt for this was the requirement to plan for, implement and reflect on one’s communicative practices, it was not until such reflections were shared, and scaffolding practices became the object of inquiry that teacher’s knowledge was substantially shifted. While targeted professional development in key areas identified by the project can and will make a difference, ultimately, a change in how teachers see themselves and the nature of their work is required. It is suggested that teaching needs to be seen as a social, not individual practice, that shapes and is shaped by the culture in which it is embedded. As a consequence, attempts to improve teachers’ knowledge will need to be multifaceted, focusing as much on the knowledge and skills of individuals, as the culture of the community in which those knowledge and skills are exercised.
Qualitative data supported an observable improvement in numeracy outcomes from the perspective of teachers and the schools involved. Quantitative data collected from students demonstrated important growth for all year levels and all domains assessed, in research and reference schools, over the course of the project as measured by the Early Years Numeracy Interview and the Success In Numeracy Education Assessment Interview. There was a trend in the research school data to suggest that the tail of the distribution was shorter. This may be because research school teachers’ increased awareness of scaffolding practices encouraged more supportive interactions with lower performing students.
A number of key suggestions are made in relation to the dissemination of project findings, the use and further development of the Behind-the-screen process, the institution of a reflective professional practice, strategies for implementation, and further work and future research.