In the Mathematics learning area, students learn about mathematics, what it is and how it is used in making decisions and solving problems. Mathematics involves observing, representing and investigating patterns and
relationships in social and physical phenomena and between mathematical objects themselves:
Mathematics is often defined as the science of space and number … [but] a more apt definition [is that] mathematics is the science of patterns. The mathematician seeks patterns in number, in space, in science, in computers, and in imagination. Mathematical theories explain the relations among patterns … Applications of mathematics use these patterns to ‘explain’ and predict natural phenomena … (Steen, L.A. (1988), “The science of patterns”, Science, 240, 29, 616.)
Mathematics can enhance our understanding of the world and the quality of our participation in society. Since it is valuable to us individually and collectively, it should be an integral part of the general education of every young person.
This statement is based on three premises:
• All students are capable of learning the mathematical ideas and skills that underpin a wide range of everyday uses and can benefit from doing so.
• All students have a right to learn mathematics in a way that enables them to see that mathematics itself makes sense, that they can make sense of mathematics, and that working mathematically can help them make sense of their world.
• For students to become confident and capable users and learners of mathematics we will need common high standards and flexible curricula which respond to students’ non-standard learning needs.
Students’ future personal and occupational needs will vary, as will the demands of the times. Students should, however, learn to deal readily and efficiently with commonly occurring situations that can benefit from the use of mathematics: for example, everyday decision making often involves asking questions about the ‘cheapest’, ‘best’, ‘biggest’, ‘furthest along’, ‘quickest’, ‘most reliable’ or ‘most likely’, and answering such
questions requires facility with number, measurement and chance. Planning, planting and maintaining a garden, making garden furniture, and sewing covers for chairs all make considerable demands of spatial and measurement skills.
Students also need to be able to use their mathematics in tackling new or unfamiliar tasks. A student nurse trying to understand how the amount of medication in the bloodstream is related to the time since administration began may need to find a previously unseen formula, read symbolic expressions, ensure that the measurements to be used are in the right units, and rearrange the computation needed to enter it
efficiently into a calculator. Activities such as making sense of a magazine article that uses the terms ‘fertility’ and ‘mortality’ to describe birth and death rates, rather than states, also call for mathematical thinking, albeit less obviously so.
Being numerate is about having the disposition and competence to use mathematics to solve practical problems outside mathematics and as a tool for learning beyond the mathematics classroom. The Mathematics Learning Area takes a major, although not sole, responsibility for the development of students’ numeracy. Students should learn to read, write and speak mathematics in a variety of contexts and forms so that they can interpret and convey mathematical ideas, interpret prose containing mathematical forms, and continue to use and learn mathematics autonomously. Whether dealing with familiar or unfamiliar tasks, they need to:
• recognise when mathematics might help;
• choose appropriate mathematics;
• decide on levels of precision and accuracy;
• do the mathematics;
• interpret the results; and
• judge the reasonableness of results and appropriateness of the methods used.
Informed numeracy involves knowing what mathematics is and isn’t, and what it can and cannot do, in order to judge and question the appropriateness of its use in particular situations. Students need to learn to ask about and question the assumptions underpinning particular uses of mathematics: for example, upon reading an advertisement that claims a bank had ‘10 million happy customers’ in the previous three months, the critical reader would say: ‘That figure does not make sense. It’s half the people in Australia. Upon what assumptions were the numbers based?’ Importantly, students should also learn that mathematics cannot determine what we should or should not do in any particular circumstance. Thus, it may assist us to predict the effect on groups of individuals of introducing a new tax, but not whether we should introduce the tax – the latter is a matter for ethical and other considerations.
Many students develop strong views about mathematics during their schooling: what it is about, who it is for, and what kind of people need it and are good at it. Some are effectively excluded from some of life’s opportunities because they, and others, assume that they cannot do ‘it’. For this reason. it is essential that school mathematics be as rewarding as we can make it, that all students feel, and be, able to learn mathematics, and that students develop a positive attitude to their own continued use of it. Every student needs to develop an awareness of the nature of mathematics, how it is created, used and communicated, for what purposes, and how it both influences and is influenced by the things we believe and the values we hold.
relationships in social and physical phenomena and between mathematical objects themselves:
Mathematics is often defined as the science of space and number … [but] a more apt definition [is that] mathematics is the science of patterns. The mathematician seeks patterns in number, in space, in science, in computers, and in imagination. Mathematical theories explain the relations among patterns … Applications of mathematics use these patterns to ‘explain’ and predict natural phenomena … (Steen, L.A. (1988), “The science of patterns”, Science, 240, 29, 616.)
Mathematics can enhance our understanding of the world and the quality of our participation in society. Since it is valuable to us individually and collectively, it should be an integral part of the general education of every young person.
This statement is based on three premises:
• All students are capable of learning the mathematical ideas and skills that underpin a wide range of everyday uses and can benefit from doing so.
• All students have a right to learn mathematics in a way that enables them to see that mathematics itself makes sense, that they can make sense of mathematics, and that working mathematically can help them make sense of their world.
• For students to become confident and capable users and learners of mathematics we will need common high standards and flexible curricula which respond to students’ non-standard learning needs.
Students’ future personal and occupational needs will vary, as will the demands of the times. Students should, however, learn to deal readily and efficiently with commonly occurring situations that can benefit from the use of mathematics: for example, everyday decision making often involves asking questions about the ‘cheapest’, ‘best’, ‘biggest’, ‘furthest along’, ‘quickest’, ‘most reliable’ or ‘most likely’, and answering such
questions requires facility with number, measurement and chance. Planning, planting and maintaining a garden, making garden furniture, and sewing covers for chairs all make considerable demands of spatial and measurement skills.
Students also need to be able to use their mathematics in tackling new or unfamiliar tasks. A student nurse trying to understand how the amount of medication in the bloodstream is related to the time since administration began may need to find a previously unseen formula, read symbolic expressions, ensure that the measurements to be used are in the right units, and rearrange the computation needed to enter it
efficiently into a calculator. Activities such as making sense of a magazine article that uses the terms ‘fertility’ and ‘mortality’ to describe birth and death rates, rather than states, also call for mathematical thinking, albeit less obviously so.
Being numerate is about having the disposition and competence to use mathematics to solve practical problems outside mathematics and as a tool for learning beyond the mathematics classroom. The Mathematics Learning Area takes a major, although not sole, responsibility for the development of students’ numeracy. Students should learn to read, write and speak mathematics in a variety of contexts and forms so that they can interpret and convey mathematical ideas, interpret prose containing mathematical forms, and continue to use and learn mathematics autonomously. Whether dealing with familiar or unfamiliar tasks, they need to:
• recognise when mathematics might help;
• choose appropriate mathematics;
• decide on levels of precision and accuracy;
• do the mathematics;
• interpret the results; and
• judge the reasonableness of results and appropriateness of the methods used.
Informed numeracy involves knowing what mathematics is and isn’t, and what it can and cannot do, in order to judge and question the appropriateness of its use in particular situations. Students need to learn to ask about and question the assumptions underpinning particular uses of mathematics: for example, upon reading an advertisement that claims a bank had ‘10 million happy customers’ in the previous three months, the critical reader would say: ‘That figure does not make sense. It’s half the people in Australia. Upon what assumptions were the numbers based?’ Importantly, students should also learn that mathematics cannot determine what we should or should not do in any particular circumstance. Thus, it may assist us to predict the effect on groups of individuals of introducing a new tax, but not whether we should introduce the tax – the latter is a matter for ethical and other considerations.
Many students develop strong views about mathematics during their schooling: what it is about, who it is for, and what kind of people need it and are good at it. Some are effectively excluded from some of life’s opportunities because they, and others, assume that they cannot do ‘it’. For this reason. it is essential that school mathematics be as rewarding as we can make it, that all students feel, and be, able to learn mathematics, and that students develop a positive attitude to their own continued use of it. Every student needs to develop an awareness of the nature of mathematics, how it is created, used and communicated, for what purposes, and how it both influences and is influenced by the things we believe and the values we hold.
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