Mathematics

Learning experiences should enable students to observe and practise the actual processes, products, skills and values that are expected of them.

Students should have the opportunity to engage fully with the concepts they are expected to develop; observe people engaged in the processes which they are to learn; and encounter examples of high-quality products of those processes, so they can see what it is they are aiming to achieve. For example, students are more likely to understand and make sense of mathematical, scientific or social science ideas if the information and experiences they engage with are inherently meaningful. They are more likely to write, perform or design well if they see the writing, performing or designing processes modelled and encounter examples of 'good' writing, 'good' performance or 'good' design. They are more likely to learn to respect and value the views of others if the school environment models such behaviours.

Students should have the opportunity to engage as fully as possible in the processes they are expected to learn about or through. For example, if they are expected to learn to plan, investigate and make choices, then they must practise these skills, rather than carry out the plans, investigations and choices of others. Where skills need to be developed to a high level of proficiency, appropriate practice of the actual skill is needed in settings that approximate those in which the skill is to be used.

Learning experiences should connect with students' existing knowledge, skills and values while extending and challenging their current ways of thinking and acting.

Learning should endeavour to ensure fresh challenges to students' existing knowledge, skills and understanding and new ideas are realistic. Sometimes existing conceptual frameworks and capabilities can be readily extended to incorporate new learning; at other times they need to be exposed (and possibly discarded) in order for new learning to occur. Either way, learners need to be able to connect new experiences to what they already know and can do, while at the same time reconstructing what they know and can do to take account of the challenge provided by their new experience.

Learning experiences should encourage both action and reflection on the part of the student.

Learning is likely to be enhanced when students engage actively with the task at hand. They should be encouraged to think of learning as an active process on their part, involving a conscious intention to make sense of new ideas or experiences and improve their own knowledge and capabilities, rather than simply to reproduce or remember. This means that learning experiences should be meaningful and involve students in both doing and reflecting. Students should learn to carry out relevant actions (do, imitate, plan, experiment, test, create, rehearse, make, choose, try alternatives) and reflect upon and make sense of the results of those actions (What does this mean? Why did that happen? Am I surprised by this answer? Does it make sense? How is this problem like others I have seen before? What worked? Why? How does this connect with other learning? Are these ideas related?). Language plays a major role in connecting doing and reflecting, and students need to learn to use language as a tool for their own learning.

As part of the reflective process, students should be helped to make connections between apparently unrelated ideas and experiences and different areas of knowledge. Teachers should emphasise the interconnectedness of knowledge, skills and values, both within and across different learning areas. Schools should provide an environment in which knowledge, skills and values are seen as an integrated whole, and their development as a lifelong endeavour.

Learning experiences should be motivating and their purpose clear to the student.

Students should be provided with purposeful and relevant activities that stimulate thought, inquiry and enjoyment. They may regard such activities as purposeful and relevant if they have an immediate practical goal (I need to know what happened in the story, we need to reduce harassment at school, we need to work out how much money we have collected) or if they relate to some longer-term goal which the student values (I need to practise my serve so my overall game will improve). Activities should be consistent with students' maturity and should endeavour to engage both their interest and challenge them to succeed. Students should be clear about what is expected of them, what they are trying to learn and why. Teachers can enhance motivation and purposeful learning by making clear to students the long-term outcomes expected from their learning.

Learning experiences should respect and accommodate differences between learners.

Students have a variety of past experiences shaped by their language, culture, health, location, values, abilities and disabilities, and previous education. Thus, teaching must be highly adaptive, acknowledging, respecting and accommodating the diverse background experiences students bring to the classroom. The extent to which a student can benefit from an experience will depend on the extent to which it connects and challenges that student's knowledge.

Students develop at different rates and also learn new ideas more or less quickly. They should be provided with the time, conditions and encouragement they need to learn in stimulating ways, and be discouraged from superficial learning that gives the impression of keeping pace at the expense of long-term and sustained learning. Students may differ in the extent to which they prefer to work independently or collaboratively, through pictures or words, orally or in writing, laterally or in a linear fashion, cautiously or adventurously. The same student may successfully use certain approaches in one learning situation and other approaches in a different learning situation.

Students should be provided with a rich variety of learning opportunities that enable them to build on their existing experiences and personal strengths and work in preferred ways. Ideally, the experiences should also broaden students' horizons by extending the range of contexts in which they can function and the learning strategies that are available to them as individuals.

Learning experiences should encourage students to learn both independently and from and with others.

If students are to become autonomous learners, they need to experience regular opportunities for both individual and collaborative learning. Working individually is necessary and can help to ensure a personal grasp of concepts, processes and skills. Working with peers enables students to be challenged by the views of others, clarify ideas and interpret and use appropriate language. Often discussion will involve students in explaining ideas to others and, in doing so, clarifying these ideas for themselves.

Learning experiences should be structured so that students can learn not only from their immediate peers and teachers but also from family and community members and people from other parts of the world. This will help them to appreciate that all people can contribute to learning and that life experiences are to be valued, together with books and other sources of information. It will also enable them to see things from different perspectives, to stand outside their own culture and their own society, to value and respect diversity, and to be critical of and able to analyse different points of view.

Teachers should plan learning experiences that enable students, whether working individually or in groups, to become increasingly autonomous. Students should be assisted to reflect on their own learning, thinking about how they learn and the conditions that help them to learn. Classroom processes should give students some flexibility in choosing ways of working and encourage them to take responsibility for their own learning.

The school and classroom setting should be safe and conducive to effective learning.

A supportive learning environment provides the intellectual, social and physical conditions in which effective learning can occur. School and classroom policies and practices should be designed to foster in students the knowledge that they can be successful autonomous learners. They should support the development of a confident approach to learning and a desire to achieve well. For example, this means that students should feel challenged and able to take sensible risks in their learning in the knowledge that the errors that may result will be regarded as a necessary, acceptable and often a helpful part of learning.

Further, the school and classroom should provide a cooperative atmosphere, free from harassment such as teasing, sarcasm or remarks that stereotype or denigrate students or their efforts. Difference and diversity should be respected and sensitivity shown to matters of gender, cultural difference, social class, ability and disability, family circumstance and individual difference. A supportive learning environment also provides sufficient, fair, safe and ethical access to a suitable and varied range of resources, including space and equipment, print and other materials and useful technology. This does not imply a need for the same environment for all. Indeed, special provision may often be necessary to ensure that all students are given the opportunity to learn.