 |
 |
|||||||||||
 |
||||||||||||
 |
||||||||||||
 |
|
|
||||||||||
| Download the rtf version of this file. The rationale The companion is a reminder to integrate numeracy ideas into everyday learning experiences and to draw on a numerical analysis of situations when developing argument, communicating ideas and hypothesising. It is like a consciousness, gently reminding project designers and teachers of means for enhancing numeracy skills and knowledge. A definition of Numeracy To be numerate is to use mathematics effectively to meet the general demands of life at home, in paid work, and for participation in community and civic life. In school education, numeracy is a fundamental component of learning, discourse and critique across all areas of the curriculum. It involves the disposition to use, in context, a combination of:
AAMT, 1998, p.1. The definition implies that although Mathematics is one way for students to develop numeracy concepts and the ability to use them wisely and strategically, the contexts of non-mathematics curriculum provide other essential ways for students to develop their numeracy skills. The definition focuses on the value of context and contextual knowledge and how recognising an opportunity to use a numeracy-informed approach, and then having ability to capitalise on this, is essential as a life and work skill. The numeracy companion is a concept to be embedded in online curriculum project designs to help teachers recognise and develop numeracy-oriented learning experiences and to develop numeracy strategies within other learning experiences. Students' application of numeracy skills in a curriculum project in the health or Arts area, for example, will not be for the sake of their numeracy, but rather for the purposes of their Health or Arts (or whatever) learning and understanding. Through such learning experiences, students numeracy - their ability to use mathematics effectively to meet the demands of their lives - will be enhanced, and recognised as valuable by the students themselves. Benefits of including numeracy perspectives into online curriculum projects’ designs. Student curriculum projects provide a timely opportunity to put into practice some curriculum design principles which relate to numeracy development being a responsibility of all teachers. This emphasis on ‘numeracy across the curriculum’ mirrors the acceptance in Australian education of the notion that all teachers are ‘teachers of literacy’, and associated curriculum developments. Numeracy across the curriculum represents more recent thinking, however. Three broad areas of benefit can be identified in the approach being taken: Resources Information and communication technologies make it possible to overcome one of the barriers to implementing ‘numeracy across the curriculum’ approaches. Resources for teachers and students which may have been developed for other purposes, but which will enable numeracy capable approaches, are easily adapted and delivered according to need. In other words, small amounts of effort will create a rich and accessible base of resource base. This has not been possible until the widespread use by educators of information and communication technologies. Leading edge research and development While Australia has seen an emphasis on policy in recent years, there have been few practically oriented numeracy across the curriculum projects and programs. The availability of resources has been one factor — another has been awareness and willingness of those whose main teaching focus is not numeracy/mathematics to see the numeracy implications and be prepared to work on them. The Natcom consortium is a powerful alliance of committed educators who have taken on the issue and are prepared to undertake practical curriculum development and teaching/learning which shows the way. The implementation of the numeracy companion in student curriculum projects represents a significant commitment to research and development on the part of Australia’s peak professional teacher bodies. Their work will inform a major policy thrust across the country. Integration rather than ‘adding-on’ Ensuring that attention to numeracy aspects is included from the beginning of project development means that they will be integral to the whole design rather than an add-on. Experience in the development of literacy enhancing curriculum has shown that this is the best way of ensuring effective and substantial literacy learning. A numeracy companion A numeracy companion creates awareness of numeracy demands and opportunities as designers build online experiences and teachers undertake online activities. The environments and learning activities likely in the context of online student curriculum projects will provide opportunities for students to use and develop their numeracy skills in the following ways, inter alia:
Actual measurements, displays of statistical information and summary statistics (mean, spread etc) are often essential to efficient and informative representation of aspects of our social and physical worlds.
Understanding change is often central to understanding social and physical processes and phenomena—information is enhanced by sensible quantification of such change.
Predictions about the unknown through identification of trends in and features of data are often best done when the data is numerically/visually represented
If mathematical means are used in presented arguments, methods and conclusions, sensible critique of these will rely on understanding and application of these means; if appropriate mathematics has not been used this in itself may be a legitimate source of critical commentary.
Understanding physical and social phenomena and processes often relies on answers to questions like "What is going on here?" — questions which go deeper to find underlying connection and causation — and numeracy informed analysis can contribute powerfully. A numeracy companion supporting a project design would point to the opportunities to focus on or integrate a number of mathematical concepts and skills including numerical, spatial, graphical, statistical and algebraic concepts in these and other general ways. Situating these mathematically-based aspects in the context of the curriculum project will help students learn the value of transferring knowledge into different circumstances and through different domains. In the particular context of online student curriculum project development some examples of foci for a numeracy companion include: Numerical data can be generated in online content. The new opportunities to collect data and generate online context are new strategies and ideas for teachers to address. Streamed data, national collections and providing audience for students' data collections are ideas yet to be explored in numeracy education. Development of tools to collect data from online communities and connected devices requires a new understanding of numeracy by web developers. Further users of such tools need to understand the impact of the collection process on the value of the numerical information, especially in relation to the assumptions inherent in the collection process, Online mathematical models and tools may encourage students to engage in mathematical ideas more often. The programming tools available in online environments may enable students to work with authentic models and contexts. Online services which enable students to input data and develop information to use in problem solving may be attractive to, and valuable experiences for, young Australians. The use of online calculators, loan simulators, stock and shares models (and others yet to be developed) are valuable experiences for modern Australians taking advantage of information economy initiatives. Numerical data can be used to enhance or bias argument. When interpreting or communicating information it is important to use statistical knowledge to support arguments, identify gaps in arguments and draw conclusions. Readers of online information need to be aware of the "tricks" of statisticians for biasing arguments. Developers of online content need to understand how to use numerical arguments powerfully and share this with students. Students need to develop skills in developing and organising data which can be used within the telecommunications curriculum project to support other learners. Often the omission of statistical information from generalisations can bias an argument, so that the one case is seen as applying to all cases. When communicating with people and reading authoritative and non-authoritative content, students and teachers need to understand the significance of omitted statistics and the omission of the numerical context to an argument. There is a difference between data and that which is interpreted into information. In information literacy approaches, the mathematical and statistical value of data is often omitted from the stories told to students. Further, attention needs to be drawn to opportunities to help students develop skills in collecting, organising and manipulating data into information while participating in online activities and events. Hypertext organisation structures may alter how students interpret and communicate numerical data and knowledge. Exploring the potential of hypertext structures to convey relationships between data can be explored in student publishing and when working through the processes of organising and communicating numerical concepts and information. Online publishing and online tools will alter the accessibility of numerical ideas to the community. Students should be given opportunities to identify additional skills required to work with and produce graphical and other representations of number and statistics. Students need also to consider the impact of the medium and its context when interpreting online numerical and graphical representations. The awareness and practical knowledge bases of teachers will grow as they interact with increasing numbers of ideas and participate in online communities where planned, intentional numeracy development as a cross-curricular emphasis is discussed in practical terms. This will enhance their capacity to attend to their students’ numeracy development through their everyday teaching, well beyond the context using online curriculum materials. A numeracy companion may manifest itself as a combination of educational resources to enrich existing ideas and a consultancy/mentoring process to directly remind project managers, teachers and students of the numeracy demands and opportunities. Some examples are included below. Examples of Numeracy companions Numeracy companions will appear differently to different stakeholders in telecommunications curriculum projects at different stages. It is considered essential by the Natcom consortium, however, that thinking about and acting on numeracy issues commence in the initial stages of project design and carry through to implementation and, where applicable, student assessment. Project designers might experience a numeracy companion as:
Teachers who involve their students in particular projects might experience the numeracy companion as
Students — as those expecting to learn within the context of an online curriculum project — will see a numeracy companion as a helper to help them develop new ways of looking at and doing things. It may be:
Reference |
|
 |
||||||||||