At the heart of effective teaching and learning in mathematics are quality programmes underpinned by The New Zealand Curriculum and based on identified student strengths, interests, and needs. Many research studies, including those informing Ka Hikitia, confirm the importance of quality teaching and show that it is critical to the improvement of student outcomes (for example, "Quality teaching for diverse students in schooling: Best evidence synthesis iteration" and "What are the attributes of excellent teachers?" (PPT 360KB). The standards for mathematics have been developed on this basis.
Classrooms are complex social situations in which students’ learning is influenced by their interactions with their social and cultural environments and by the degree to which they actively manage their learning. Much is known about the features of teaching that acknowledge this complexity and that improve outcomes for diverse learners. The mathematics Best Evidence Synthesis evaluates, analyses, and synthesises New Zealand and international research on quality teaching in mathematics. Research findings from the Numeracy Development Projects confirm the importance of quality programmes in mathematics and outline their components.
These include the following seven teacher activities and their descriptions from Book 3: Getting started (PDF 463KB, pp. 3–4) from the Numeracy Development Projects.
An inclusive classroom climate
Successful teachers create social norms in their classrooms that give students the confidence and ability to take risks, to discuss with others, and to listen actively (Cobb, McClain, & Whitenack, 1995). High expectations for student behaviour and provision of a well-organised environment that maximises students’ learning time are critical. The valuing of student diversity – academically, socially, and culturally – is fundamental to the development of positive relationships between teacher and students (Bishop et al., 2003). [The Māori education strategy: Ka Hikitia - Accelerating Success 2013 -2017 and Pasifika Education Plan 2013-2017 support schools to provide inclusive classroom climates for all students.]
Use of a variety of assessment methods, both formal and informal, to identify the needs of students is critical to quality teaching. From this data, successful teachers target concepts and processes to be taught/learned and plan carefully sequenced lessons. They develop learning trajectories that map potential growth paths and can "unpack" these trajectories in detail if needed. Students are aware of (and sometimes set) the learning goals. These goals change and grow as learning occurs.
Cross-national comparisons show that students in high-performing countries spend a large proportion of their class time solving problems (Stigler & Hiebert, 1997). The students do so individually as well as co-operatively. Fundamental to this is a shared belief, between teacher and students, that the responsibility for knowledge creation lies with the students (Clarke & Hoon, 2005).
Responsiveness requires teachers to constantly monitor their students’ thinking and to react by continually adjusting the tasks, questions, scaffolding, and feedback provided. To this end, quality teachers create a variety of instructional groups to address specific learning needs.
Askew et al. (1997) report that successful teachers of numeracy are "connectivist". Such teachers use powerful representations of concepts and transparently link mathematical vocabulary and symbols with actions on materials. The use of realistic contexts helps students to connect mathematics with their worlds.
Quality teachers ask questions that provoke high-order thinking skills, such as analysing, synthesising, and justifying, and they have high expectations for student achievement. They encourage students to regulate their own learning, make their own learning decisions, and be self-critical. Successful teachers provide incentives, recognition, and support for students to be independent learners.
Success for all students is a key goal, and quality teachers provide extra time for students with high learning needs. They promote respect and empathy in their students for the needs of others.
To understand equity, the focus needs to be "not only on inequitable social structures and the ideologies that prop them up but also on how such realities play out in the everyday activity within classrooms and other cultural practices" (Effective pedagogy in mathematics/pāngarau: Best evidence synthesis - section 1 (PDF 925KB, p. 9). In this regard, Te Maro, Higgins, and Averill ("Creating strong achievement gains for Māori children in English-medium mathematics classrooms" PDF 86KB) found that particular characteristics of the school environment, the orientation of the teacher towards using culturally responsive actions, and certain personal qualities of the teacher (including a focus on developing relationships) produced strong achievement gains for Māori students. It is essential that teachers respect and value each learner for who they are, where they come from, and what they bring with them. The key priority is to ensure that, as part of their professional practice, teachers focus on Māori learners "enjoying education success as Māori".
In order to make judgments in relation to the mathematics standards, it is essential that teachers understand the mathematical and statistical content that they are teaching. However, content knowledge is not sufficient in and of itself. Uniformly, the research on quality teaching stresses the importance of teachers’ pedagogical content knowledge. Shulman (1987) defines pedagogical content knowledge, in part, as a teacher’s 'understanding of how particular topics, problems, or issues are organized, presented, and adapted to the diverse interests and abilities of learners, and presented for instruction' ("Knowledge and teaching: Foundations of the new reform"). Teachers must ensure that they understand the conceptual difficulties that students may be having and be able to plan coherent, targeted teaching to address those difficulties.
Published on: 13 Oct 2009
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