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The notion of lifelong learning has been adopted in the rhetoric of governments in many countries around the world (e.g., DfEE, 1999), as well as by supranational bodies such as UNESCO (e.g., Delors, 1996), the OECD (e.g., 1996) and the EU (e.g., EU, 2000). However, Australian National Training Authority [ANTA] efforts have largely been focused upon a social marketing strategy (e.g., ANTA, 1999, 2000a) ¾ conducting research at the macro level of policy and planning, but failing to problematise the meso- and micro-levels of knowledge recontextualisation and pedagogical evaluation (Bernstein, 1996).
The changing nature of work is a multifaceted issue of enormous concern and relevance as globalisation and new technologies impact on the individual and collective lives of adults. These require “increased competences, the development of new skills and the capacity to adapt productively to the continuously changing demands of employment throughout working life” (UNESCO, 1997, p. 8). There is a swell of voices calling for Australia to become a knowledge economy, to make the most of its human capital. One significant area to emerge in recent years is research into literacy and numeracy practices in restructuring workplaces, especially in relation to automation, emerging communications technologies, and new approaches to workplace organisation and management (FitzSimons, 2000). Accordingly, the Federal Government is committed to a policy of encouraging adult numeracy, as well as technological and other literacies, in adult/vocational education.
Internationally, studies have researched workplace mathematics (or numeracy) — that is, how mathematical ideas and techniques are used practice, as distinct from in the school classroom (e.g., AAMT, 1997; Buckingham, 1997; Noss, Hoyles, & Pozzi, 1998). These studies show that mathematical elements in workplace settings are subsumed into routines and tools, and are highly context-dependent. The mathematics used is intertwined with professional expertise (at all occupational levels), and judgements are based on qualitative as well as quantitative aspects. In Australia , prior to the introduction of the National Training Framework, accredited mathematics curricula for vocational students showed little evidence of reflecting actual work practice; rather, they reflected school mathematics curricula garnished with pseudo-contextualised examples (FitzSimons, 2000). In recent years, with the introduction of Training Packages, mathematics has become almost invisible (e.g., ANTA, 2000b), taught only as and when it is perceived by literacy tutors or workplace trainers — who themselves may have no post-school mathematics or teaching qualifications, and are likely only to see the most basic skills rather than the ‘big picture’ as grasped by the highly skilled researchers in the projects listed above.
Key international theoretical debates about the nature and function of generic skills have been influential in Australia ( Kearns , 2001). However, in recent reviews of numeracy published by ANTA’s research arm, the National Centre for Vocational Education Research [NCVER], there are no clear definitions of what is meant by numeracy, except as a subset of literacy skills: “literacy includes the recognition of numbers and basic mathematical signs and symbols within text” (Falk & Millar, 2001, p. 9). Watson, Nicholson, & Sharplin (2001) declare that attempts at a single definition are relatively futile, and ANTA is quoted to define numeracy merely as calculations needed in the workplace (Sanguinetti & Hartley, 2000). In the Kearns review, which stresses an increasing demand for generic skills, the word numeracy occurs several times, but the concept is neither defined nor problematised. Numeracy, in relation to basic skills, is assumed to be an important pre-requisite for employability. However it may be defined, it cannot be assumed that (potential) workers enrolled in VET courses have high levels of numeracy ¾ often due to reasons beyond their control — so there is an urgent need to continue their education.
These ANTA review documents, premised upon literacy and numeracy being taught together and integrated into workplace training, mean that literacy and numeracy are treated as a single entity throughout; also in a related guide for practitioners (ANTA, 2000b). Sanguinetti and Hartley (2000) have identified a range of problems which arise from this situation, including:
- Implicit numeracy competencies in industry standards require a high degree of analytical sophistication and educational expertise … not all Enterprise-Based trainers nor workplace trainers have such expertise. Often buried in training packages, literacy and numeracy competencies need to be made more explicit. (p. 33).
- The assessment-driven model minimises need for teaching or support; there are limited opportunities for development of underpinning skills. More holistic and structured approaches are required. (p. 34)
By contrast, this view of numeracy as imbricated with literacy, where the word ‘mathematics’ is never used at all, is not supported by the international mathematics education research community which distinguishes between mathematics and numeracy, yet maintains that numeracy must be underpinned by mathematical knowledge of an appropriate kind (e.g., Evans, 2000; Steen (Ed.) 2001). The OECD Programme for International Student Assessment (PISA) [http://www.pisa.oecd.org/ math/mathm.htm] is firmly committed to mathematical literacy as a scale independent of reading literacy and scientific literacy for school students; the international Adult Literacy and Lifeskills project’s numeracy document [available from http://www.alm-online.org/], likewise. In these studies, numeracy is taken to be much broader than facility with numbers or basic arithmetic, and includes spatial and quantitative (statistical) literacy. Klein (2000) considers numeracy not as a thing to be possessed, but as a capacity for action. Thus, in relation to numeracy, democratic participation depends upon access to mathematical knowledge — information selectively derived from a range of possibilities and which is capable of being interpreted and understood. Klein argues that “numerate behaviour reflects a certain agency with mathematics and comprises intellectual and social aspects of knowing mathematics” (p. 76). Problem solving, systems thinking, and analytic skills (generic numeracies) are stressed throughout the Kearns (2000) report. These are essentially mathematical cognitive skills, and cannot develop into agentic behaviours unless there is strong underpinning disciplinary knowledge to support them (FitzSimons, 2000, 2001).
The discipline of mathematics has evolved historically through a dialogical relationship with technology. Mathematics education, understood here to include statistics education and the underpinning knowledge required for numeracy, has the possibility of interacting with technology in a complex set of arrangements. For example, applications programmed into the technological artefacts of calculators and computers may be used to enhance understanding of mathematical concepts or to explore hypothetical situations through simulations. Other applications of these technologies may be used to manipulate data of various kinds, as a form of labour-saving device, allowing richer interpretations of the data to be made by the user. Mastery of certain applications of these technologies may be another end in itself. Finally, technology may be the object of study — for example., the impact on society of computerisation of many job functions which allow greater control over the social, economic, and ecological environment. The complex relationship between mathematics and technology has been little problematised (e.g., FitzSimons, 2000).
The Kearns (2000) report stressed the need for workers to be competent in working with new technologies. Internationally, there is a burgeoning interest in the integration of technology as a pedagogical tool for mathematics learning; much has been written about the use of scientific and graphic calculators; computer graph and geometry programmes, and so forth. However, while much is known about principles of pedagogy and exemplary practice of integrating technology in the mathematics classroom (e.g., Alexander & McKenzie, 1998; Forster & Taylor, 1999; Galbraith & Haines, 1998; Lagrange, 2000; Noss & Hoyles, 1996; Trouche, 2000; TWIN, 1999), there is a dearth of research in the Australian adult and vocational education literature on such integration for pedagogical purposes, let alone as a goal — such as the use of spreadsheets for mathematical purposes (Wake, Williams, & Haighton, 2000). In fact, Lagrange et al. (2000) identify that within the large corpus of research literature the issues are most complex. Recent studies indicate the evolution towards dialectic relationships between perception and conceptualisation, as well as contextualisation of knowledge with implications for teaching and learning. Technology-based learning is unlikely to be enacted in classrooms or training sites where the teacher or trainer has little or no competence or confidence in using these mathematical tools.
In an era of globalisation, the delivery of education is becoming technologised (e.g., EU, 1996), as adults study at diverse locations and times, oftentimes outside of recognised institutions. There is a burgeoning interest in the production of distance education materials, especially electronically distributed forms. Herremans (1995) outlines a comprehensive range of perspectives on what he terms new training technologies, designed to support delivery mechanisms of classroom and distance education as well as individual learning. However, while much is known about principles of andragogy and of exemplary practice in mathematics education, in Australia there is a dearth of research-based knowledge about how to transform these principles into high-quality technologised educational products. Few researchers (e.g., Pickard & Cock, 1997; Vanhille & D’Halluin, 1997) have considered the impact of new teaching technologies as a medium for teaching mathematics in situations comparable to distance education, where the learner is (or may be) remote from the teacher in space and/or time. Lifelong education in mathematics needs to consider relationships with the affective domain of adults as well as the cognitive domain (FitzSimons, Coben, & O’Donoghue, in press; FitzSimons & Godden, 2000). ANTA is supporting research into the development of online technologies (e.g., Brennan, McFadden, & Law, 2001; Harper, Hedberg, Bennett, & Lockyer, 2000). In Australian adult education, students may be working with a numeracy tutor who is qualified only as a literacy tutor or a workplace trainer with no pedagogical background in mathematics at all. Observation of one TAFE online mathematics programme reveals little evidence of any well-founded theoretical basis in mathematics pedagogy. There is an even greater need for research into CD-ROMS (Lagrange et al., 2001).
There is a substantial literature on evaluation in education (e.g., Bennett & Rockewell 1995). Generally, it is concerns programmes, students or teachers; formatively or summatively. In recent years there have been evaluations of online or web-based delivery in higher education (e.g., Felix, 2001). Lim (2000) recommends the adoption of a sociocultural approach, in particular the Activity systems approach of Engeström (1999) and others, to capture the complexities of evaluating the adoption of new learning technologies. Tuovinen (2000) offers a comprehensive framework for the evaluation of multimedia interactions in the distance education mode and further (Tuovinen, in preparation), a taxonomy for discovery learning as a frequently recommended pedagogical practice for flexible learning — all of which will support this proposal. Another strong source of support is in Sims (2000), which presents four comprehensive dimensions of interactivity (learners, content, pedagogy, and context), and which are problematised, suggesting that considerable design effort must attend to the ways learners adopt and adapt to the exchange of ideas and engagement with content in computer-mediated resources. Developmental work has begun in the UK into evaluation methodologies and pedagogical frameworks for new learning technologies, e.g., http://www.unl.ac.uk/tltc//elt/, http://www.icbl.hw.ac.uk/ltdi/cookbook/, & http://iet. open.ac.uk/research/index.cfm. The meta-analysis of Lagrange et al. (2001) [longer version available at http://www.maths.univ-rennes1.fr/~lagrange/cncre.rapport.htm] offers another series of dimensions on the integration of new learning technologies into mathematics teaching which offer potentially fruitful pathways for research: general approach, epistemological and semiotic, cognitive, institutional, and instrumental dimensions. This project is novel and innovative in its intention to use evaluation in an anticipatory manner, in order for prospective consumers (students or teachers) of new learning technologies in adult numeracy to make reasoned choices and to guide developers in the production process. Frechtling and Sharp Westat (1997) offer a useful guide in mixed method evaluations.
Much is at stake in terms of financial and opportunity costs to industry and the Australian community generally. Australia needs to have a numerate population — as a workforce to increase productivity and, more broadly, as a citizenry to participate fully in a democracy. The concept of adult numeracy has been under-theorised because most people, policy makers included, already think they know what it is — merely rote learned ‘basic skills’. On the other hand, a good understanding of the role of mathematics is essential for people to understand their social realities in a technological world and to make responsible decisions as citizens and workers (e.g., Madison , 2002).
Adults returning to study numeracy cannot afford to ‘fail’ again due to poor quality educational technologies. On the production side, good intentions are not sufficient. It cannot be assumed that adult learners will have access to an instructor with any post-school mathematics qualifications. (This also applied to adults in developing countries who may be recipients of AUSAID funding and utilising new learning technologies for adult numeracy.) There is no similar research, combining mathematics and information technology, being undertaken, in English-speaking countries at least, although there are international trends towards technologising adult numeracy. Personal communications with world leaders in adult numeracy strongly support the need for such a framework.
The teaching of adult numeracy, whether onsite in the workplace, in class, or by flexible delivery, has serious and important political, economic, and social implications. For example, poor quality teaching and resources may result in (further) alienation from mathematics in learners (young and old) who lack self-confidence, raising barriers to further study and employment. One of the major recommendations in the Kearns report was to foster a willingness and a capacity to learn. This can only take place where teachers are well-prepared and supported by high quality pedagogical resources. The project will be of potential social and economic benefit to Australian society at large through amelioration of the range of educational products which might enhance lifelong learning in mathematical skills and in thinking processes applied in contexts meaningful for the user.
In order for adult numeracy teaching in Australia to be comparable to world standards the concept of numeracy needs to problematised. There needs to be a clear definition based upon international research into mathematics in the workplace, validated under Australian conditions. In addition, use must be made of research into teaching adults (e.g., Coben, O’Donoghue & FitzSimons, 2000). Only then can world class pedagogical resources be developed to support adult numeracy teachers, trainers and students in their attempts to develop a knowledge-based economy in Australia . Based on the wealth of experience of the researcher, and building on work done in the international Adult Literacy and Lifeskills project on assessment of adult numeracy, this project will address issues of content, pedagogy, and technology.
The project is innovative in that it melds several discrete policy commitments of the Australian government, to synthesise research and forge new territory in a burgeoning area of education. It has the potential to advance the knowledge base of the entire post-compulsory sector in terms of informing and transforming university and other mathematics and statistics courses into high quality technologies of education, using technology as a means of delivery as well as a teaching tool, as well as pursuing the goal of mastery in increasing technologised workplaces.
In summary, this project aims to identify factors which contribute to the effective and efficient utilisation of new learning technologies in mathematics education, primarily from the perspective of technology as an alternative means of delivery. However, the use of technology as a tool for enhancing understanding of concepts, hypothetical thinking, and interpretation of data is an integral part of this research. Accordingly, the project will synthesise research in mathematics education, including adult numeracy, and new technologies of teaching and learning, grounded in the literature of lifelong education. It will iteratively research, design, and trial a framework for the evaluation of new teaching and learning technologies (online, CD-ROMs, etc.) intended as a means of distribution of mathematical knowledge to support mathematics, statistics and numeracy education for learners located in (semi)autonomous situations in relation to time and place of learning. This project will advance, from a critical perspective, current theoretical knowledge in the pedagogical transposition of content for delivery by electronic means in order to inform both the developers (commercial and academic) of these materials and the potential users (lecturers, teachers, tutors, industry trainers, & students).
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