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Domain 3: Professional practice
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Professional practicegeneral This domain of the Standards is in many respects the core -- it is what teachers actually do in the classroom to maximise students’ learning in the contexts of the individual students, the school and community. The aspects identified -- environment, planning, teaching and assessment -- are all completely intertwined and inter-dependent. It is likely that individual teachers will work differently in similar contexts. Their approaches will be based on their own knowledge and experience bases and their values as teachers and people. No one approach is ‘right’. Multipl
Excellent teachers of mathematics are purposeful in making a positive difference to the learning outcomes, both cognitive and affective, of the students they teach. They are sensitive and responsive to all aspects of the context in which they teach. This is reflected in the learning environments they establish, the lessons they plan, their uses of technologies and other resources, their teaching practices, and the ways in which they assess and report on student learning.
3.1 The learning environmentExcellent teachers of mathematics create, through negotiation with their students a classroom that reflects their commitment to mathematics and all their students learning of mathematics.
Excellent teachers of mathematics establish an environment that maximises students' learning opportunitiesStudents and teachers work within a set of expectations or ‘rules’. These rules govern the overall ways in which things are done and relate to expectations about mathematical and other behaviours, and ways members of the classroom interact (between students as well as between students and teacher). To a large extent they are derived from the teachers’ professional values (see Domain 2), but in productive and inclusive classrooms the norms are negotiated with and agreed by the students. Maximising students’ learning opportunities is an overriding intention of excellent teachers, and they build this into the core of what the classroom is about, and how it operates. . The psychological, emotional and physical needs of students are addressed and the teacher is aware of, and responds to, the diversity of students' individual needs and talentsThe classroom learning environment cannot remain static. Certainly the basic norms and values can and do remain more or less set, but the nature of the mathematics being learnt and the way it is being learnt -- and individual students’ responses to these -- do changeover time. Through their knowledge of students (1.1), excellent teachers of mathematics strive to ‘set up’ the classroom and the learning in ways that best meet their students’ needs, and which help foster their talents. This ‘setting up’ includes the physical (e.g. can all students access the resources they need?), the emotional (eg in what ways does this enhance students’ love of learning?), the intellectual (e.g. how does this stimulate thinking?) and the psychological (e.g. how does this encourage, support and reward learning?). . Students are empowered to become independent learnersThe classroom learning environment cannot remain static. Certainly the basic norms and values can and do remain more or less set, but the nature of the mathematics being learnt and the way it is being learnt -- and individual students’ responses to these -- do changeover time. Through their knowledge of students (1.1), excellent teachers of mathematics strive to ‘set up’ the classroom and the learning in ways that best meet their students’ needs, and which help foster their talents. This ‘setting up’ includes the physical (e.g. can all students access the resources they need?), the emotional (eg in what ways does this enhance students’ love of learning?), the intellectual (e.g. how does this stimulate thinking?) and the psychological (e.g. how does this encourage, support and reward learning?). . They are motivated to improve their understanding of mathematics and develop enthusiasm for, enjoyment of, and interest in mathematics. In an inclusive and caringThe mathematics classroom is a social environment -- a community -- among the many that students work within. Students need to feel they are a valued member of that community (inclusive). The basic norms and values of the mathematics classroom set the ground rules, but these need to be consistently reflected in the practices of the classroom. Caring has many faces in the classrooms of excellent teachers of mathematics. It can certainly be manifest as gentle encouragement and support, but can equally emerge as firmness and challenge. The care is for the students’ learning of mathematics as part of their overall intellectual and personal development as citizens. atmosphere of trust and belonging, active engagement with mathematicsActive engagement with mathematics may or may not be reflected in physical actions. It always involves intellectual ‘work’ on the part of the student, and often reflects an emotional side with students wanting to learn, understand and know, and feeling good about their achievements. Engagement is consistently expected in the classrooms of excellent teachers of mathematics -- they consistently strive to establish an environment in which their students want to be engaged by the mathematics. is valued, communication skillsMathematics can contribute substantially to an individual’s capabilities as a communicator. An effective mathematics classroom environment encourages and expects high quality communication both about and with mathematics. The forms of communication practised and developed cover the full range of modes — reading, writing, speaking and listening to mathematics — with particular emphasis on specifically mathematical representations such as graphs, diagrams and the use of abstract symbols. fostered, and co-operative and collaborative efforts encouraged.
3.2 Planning for learningExcellent teachers of mathematics plan for their students’ learning by considering and making choices in relation to the actual mathematics, resources and the teaching and learning strategies to be used. Their plans are clear and purposeful, but retain the flexibility to change in response to the context and students’ interests and progress.
Excellent teachers of mathematics plan for coherently organised learning experiencesA key ingredient in good planning (and teaching) of mathematics is purpose. Knowledge of mathematics, students learning of mathematics and the ‘curriculum’ provides the big picture, with teachers responsible for making the choices in terms of the actual learning experiences on a day-to-day and week-to-week basis. Excellent teachers of mathematics strive to ensure that they plan learning experiences that ‘fit together’ to ensure students learn mathematics in ways that help them see and build connections within mathematics (coherent). They also ensure that their plan is practical and can be successfully implemented (organised). For example, an activity that assumes some facility with and access to a particular software package, say, would need to be set up in such a way that these matters are addressed. that have the flexibility to allow for spontaneous, self-directed learning. these learning experiences involve substantive mathematicsVery often school mathematics has been characterised as a set of knowledge and skills. In themselves, skills such as measuring a length, factorising a quadratic or determining an inter-quartile range can be useful, but they are not ends in themselves. The ends are the ‘big picture’ of mathematics -- measurement as quantifying our world; algebra as a powerful tool for modelling and understanding; statistics as a means for quantifying difference. Clearly, the actual mathematics to be taught and learnt is determined by a wide range of factors. Broadly these are the students’ prior knowledge, their interests and aspirations and the curriculum within which the teacher is required to work. Excellent teachers of mathematics use their understanding of these and their own knowledge and values to ensure that they create a plan for students’ learning that sets out to deal with the ‘big ideas’ of mathematics. Their plans and subsequent actions attend carefully to knowledge and skills on the small scale because these are an important part of the ‘big picture’. They do this, however, with a purposeful eye on enabling students to build their own ‘big picture’ of what we call mathematics, with the power born of its structure, beauty, connections and usefulness. . They enable students to develop new mathematical understandings that build on and enrich their knowledge and appreciation of mathematics. A variety of appropriate teaching strategies is incorporated in the intended learning experiences, enhanced by available technologiesThere is wide range of technologies available for the teaching and learning of mathematics. In particular, there is an increasing array of electronic technologies -- devices and software -- from which teachers can choose. Excellent teachers of mathematics plan the use of technologies in their work based on their assessment of their suitability and effectiveness in relation to the mathematics being learnt. Within an overall framework of ensuring that, during their schooling, students encounter the ways in which mathematics is done in the modern world, these teachers ask and answer the fundamental question of 'How would using this technology and other resourcesThe resources for the teaching and learning of mathematics are typically taken to be books, models and other physical material, videos and other technology, and making informed and effective choices from among these is an important aspect of teachers’ planning. A wide range of other resources can also support students’ learning. These can be people and organisations in the community (including the students themselves) and aspects of the natural and human-made environments. Excellent teachers of mathematics make purposeful choices from among the full range, ensuring variety over time as part of their efforts to engage and extend all students. . Students' backgrounds and prior mathematical knowledge are taken into account. Students are provided with opportunities to explore and apply mathematics across key learning areas and beyond the school settingOne of the key connections that school mathematics needs to attend to is the connection between mathematics and students’ lives. Their work and learning in other curriculum areas at school provides many contexts in which the mathematics they are learning can be further developed and applied. For primary teachers who most often have responsibility for most or all learning areas, planning in and for mathematics can respond to needs and opportunities in other learning areas on the basis of their own knowledge and involvement. For most secondary teachers, knowing the emphases in the other areas needs to be actively researched, and may require ongoing collaboration with colleagues who teach in other areas. Students’ lives and interests outside of school are much more diverse, but as part of their knowing of their students, excellent teachers of mathematics will have information they can and do draw on in developing their plans for student learning. .
3.3 Teaching in actionExcellent teachers of mathematics ultimately prove themselves worthy of that description through their performance as a teacher -- their actual work with students in their class(es).
Excellent teachers of mathematics arouse curiosity, challenge students’ thinking, and engage them actively in learning. They initiate purposeful mathematical dialogue with and among studentsTalking -- explanation, discussion, argument -- is an important feature in mathematics classrooms. Students’ learning is facilitated, at least in part, by the complex range of types of verbal communication in the classroom. Excellent teachers implement strategies that promote talking that is about the mathematics and its learning (purposeful). Their classrooms are characterised by communication that involves them and their students both speaking carefully and listening carefully (dialogue). . As facilitators of learning, excellent teachers negotiate mathematical meaningStudents who are learning mathematics are on a path of ever increasing sophistication in terms of their knowledge and understanding. New information needs to be built into their framework. This will often involve a challenge to their existing conceptions. Through their practices and interactions with their students, excellent teachers of mathematics seek to help them to make sense of what they are learning, to give it meaning within their framework for mathematics. The negotiation comes in through the teacher’s judgement of what is appropriate for the personal meaning-making by the student, in the light of their knowledge of the mathematics, its potential for development and the risks of establishing particular misconceptions, and their knowledge of the student. and model mathematical thinking and reasoningAn important feature of effective practice in mathematics is explicit attention to developing mathematical thinking and reasoning. Students need to see their teacher ‘doing’ mathematics. This enables teachers to demonstrate (model) to students their approach (ie their thinking and reasoning as well as techniques and skills). More than providing models for the students to draw on, the teacher’s emphasis on thinking and reasoning in their modeling of ‘doing’ mathematics sets the expectation that students will value and be clear about the processes they use to do mathematics. . Their teaching promotes, expects and supports creative thinking, mathematical risk-takingTeaching practices in mathematics need to encourage, allow and enable students to think laterally and to ask and explore 'What if...?' questions. They also need to be rewarded for doing so. Excellent teachers of mathematics create an environment and use learning experiences that support students to work in this way. They expect and encourage students to ‘have a go’ and ensure that students see ‘mistakes’ they might make along the way as opportunities to learn from. Importantly, if teachers are to see these traits in their students, they need to model similar behaviours in their approaches to their teaching -- a case of ‘do as I do’ rather than ‘do as I say’. in finding and explaining solutions, and involves strategic interventionNo matter how careful the planning, nor how ‘good’ the teaching and learning activities may be, students will grasp concepts and take on board new learning at different rates. Excellent teachers of mathematics monitor this progress (see 3.4 Assessment) in order to determine when to take extra action. This may be to further extend and challenge students who need this, or it may be to provide further scaffolding and support for students having difficulties. These interventions are strategic in the sense that the teacher takes actions that are matched to the individual students and their needs, and that are informed by their knowledge of the mathematics and strategies for helping students to learn. and provision of appropriate assistance.
3.4 AssessmentExcellent teachers of mathematics plan and undertake their assessment of students’ learning in ways that effectively and efficiently fulfil the multipl
Excellent teachers of mathematics regularly assess and report student learning outcomes, both cognitive and affectiveIt is only through careful assessment what the students have learnt (cognitive) and how they feel (affective) at teachers can have a sufficiently complete picture of the student, particularly in relation to their further work with the student. Excellent teachers of mathematics employ a purposeful variety of formal and informal assessment strategies to find out ‘where their students are at’ in relation to the range of aspects (knowledge, skills, processes, attitudes and values) they know to be important components in students’ learning of mathematics. , with respect to skills, content, processes, and attitudes. They use a range of assessment strategies that are fair, inclusive and appropriateThe ways in which student learning of mathematics is assessed (i.e. the actual strategy(ies) used) will be determined by a complex set of factors. Some of these, such as mandated tests, are outside of the teacher’s control, but to the extent that the do have control, excellent teachers of mathematics implement strategies that give all students the opportunity to demonstrate what they know and can do, and how they feel about their mathematics (fair). They ensure that the form and substance of their assessment does not disadvantage any student, or group of students (inclusive). For example, assessment that relies on high levels of control of Standard Australian English may disadvantage some students living in traditional Indigenous communities, and not allow them to fully demonstrate the mathematics they know and can do. Overall, these teachers make conscious choices for assessment and can back their choices with a clear articulation of the educational rationale for these. Their actions demonstrate that they ‘know what they are doing’ in relation to the mathematics as well as equity in assessment. to both the students and the learning context. They maintain on-going, informative records of student learningThrough formal and informal assessments of their students, teachers have a wealth of information about students’ learning and progress. There are compelling reasons for maintaining records of that information, including the teacher’s interpretations of the information. Teachers need to be able to draw on assessment information for a variety of purposes -- to monitor students’ progress; to inform their future teaching; for reporting to parents and others, including the student’s future teachers. Excellent teachers of mathematics are comfortable about being accountable for their work, particularly to the students and their parents/care-givers, and use their records to make clear and informative statements. Records may or may not be extensive, depending on the teacher’s ‘style’, with careful and comprehensive coverage of the important aspects of students’ learning in a form that is easily accessed their main purpose (informative). outcomes that are used to map student progress and to plan appropriate future learning experiences. The excellent teacher of mathematics provides constructive, purposeful and timely feedbackAnnotations of students’ work and other feedback to students is most effective when it clearly focuses on the mathematics -- what was done well, where and how improvement might be achieved, prompts for further learning and investigation by the student, and so on. Excellent teachers of mathematics commit the time to do this in ways that are supportive and challenging, in line with the overall ethos for the classroom. Similarly they report to parents carefully and constructively, taking the opportunity to both inform them about, and involve them in, their children’s learning of mathematics. to students and their parents, and to school authorities, as required.
