Methodological Approach

Summary of Original Objectives of Project (2002)

1. Clearly define adult numeracy in the Australian context in terms congruent with international mathematics education research.
2. Present identifiable examples of adult numeracy in a variety of workplaces and popular media.
3. Identify international examples of high quality mathematics education using technology as a tool and as a medium of delivery.
4. Identify the strategies used by the producers of these programmes which might contribute (or otherwise) towards their success.
5. Research, design, and trial a framework for the evaluation of new learning technologies for adult numeracy along each of three dimensions (mathematics/numeracy, pedagogy, technology), to support learners in (semi)autonomous learning situations, and tutors and trainers in TAFE institutes, community settings, workplaces, and in the home.

Research Questions (2002)

1. How might adult numeracy be understood from a mathematics education research perspective?
2. How can this understanding inform the content development of new learning technologies [new learning technologies] which will assist independent learning as well as support numeracy tutors and workplace trainers?
3. What factors contribute (or otherwise) to high quality mathematics education programmes which use technology as a tool and a medium of delivery?
4. How can understandings synthesised from the fields of mathematics education, lifelong learning, and new learning technologies inform the development of educational artefacts such as online programmes and CD-ROMS which will assist independent learning in adult numeracy?
5. How can understandings synthesised from the fields of mathematics education, lifelong learning, and new learning technologies support numeracy teachers and workplace trainers, who may well lack post-school qualifications in mathematics and mathematics education?
6. How can understandings synthesised from the fields of mathematics education, lifelong learning, and new learning technologies enable potential purchasers and/or users to evaluate these educational artefacts?

Methodology Plan (2002)

1. Update extensive reviews already completed of current international literature on mathematics and numeracy in the workplace. This will enable the empirical research to be informed by recent research observations and interpretations.
2. Validate these workplace findings in an Australian setting, using an ethnographic approach based upon work shadowing (AAMT, 1997) and UK workplace research (Noss, Hoyles, & Pozzi, 1998). Visits to 10 workplaces as case studies in manufacturing and service industries in Victoria . The researcher will follow a sub-professional worker or operator on a ‘typical’ day’s practice, as well as attend a ‘team’ meeting, interview the subject about their work, explore critical incidents, and interview their immediate manager. The written accounts of the researcher will be verified by participants.
3. Data will be analysed and categorised into generic/specific numeracies (Buckingham, 1997). Engeström’s (1999) Expansive Learning framework, building upon Vygotsky’s Activity Theory, encompassing the various knowledge interest groups, their multi-voicedness, historicity, contradictions, and zones of proximal development will provide the framework for analysis of vocational tasks and future pedagogical artefacts. Rich documentation of case studies will allow for interpretations by other researchers and practitioners.
4. Syntheses of international literature on teaching mathematics/numeracy to adults will inform the critique and future development of pedagogical artefacts from the perspective of the broad range of learners, learning styles, and learning situations.
5. Syntheses of reviews of the international literature on mathematics/numeracy and the use of technology as a teaching tool will inform the critique and development of pedagogical artefacts from the perspective of the tutor or trainer, or prospective new learning technologies producer not currently familiar with these aspects of technology.
6. Syntheses of reviews of the international literature on the use of technology as a means of delivery will inform prospective producers of new learning technologies in adult numeracy.

Methodology Review (2006)

1. I have further developed the 2002 review of international literature on mathematics and numeracy in the workplace, and included literature on learning in the workplace, formally and informally. These enabled my empirical research to be informed by research observations and interpretations of others in the field. In addition, I reviewed selections from the literature on the educational uses of technology, with particular reference to mathematics.
2. I validated findings from the workplace research and gained new insights in Australian settings, using an ethnographic approach based upon work shadowing. I visited 14 Victorian workplaces in manufacturing and service industries as well as primary industries involved in chemical handling and spraying. I followed workers on a ‘typical’ day’s practice, interviewed them about their work, explored critical incidents and, where possible, interviewed their immediate managers. My written accounts of the researcher were verified by participants.
3. Using activity theory as a language of description and of analysis enabled me to frame the fieldwork interview questions and observations. I analysed the workplace data using Engeström’s (2001) Expansive Learning framework, which built upon Vygotsky’s Activity Theory, and encompassed the various knowledge interest groups, their multi-voicedness, historicity, contradictions, and zones of proximal development. Rich documentation of case studies allows for interpretations by other researchers and practitioners.
4. Bernstein’s (2000) theorisation of vertical discourses and horizontal discourses enabled me to differentiate between mathematics and numeracy respectively. The synthesis of the international literature on adult numeracy as well as the teaching of mathematics/numeracy to adults and vocational and workplace education informed the critique and development of the Mathematics/Numeracy section of the framework.
5. The synthesis of the international literature encompassing the perspectives of the broad range of learners and learning situations informed the critique and development of the Learner section of the framework.
6. The synthesis of reviews of the international literature on the use of technology as a means of delivery and as a teaching/learning tool informed the critique and development of the Technology section of the framework for prospective producers and users (teachers, tutors, trainers, & learners).
7. I utilised Engeström’s (1987) elaboration of the basic mediational triangle in activity theory to frame these three categories in mathematics/numeracy teaching, whether delivered to adult learners electronically via distance education means (wholly or in part) or in proximal teaching-learning situations. The use of new learning technologies is playing an increasingly important part in both.

References

Bernstein, B. (2000). Pedagogy, symbolic control and identity: Theory, research, critique (Rev. ed.). Lanham , MD : Rowman & Littlefield.

Engeström, Y. (1987). Learning by expanding: An activity-theoretical approach to developmental research. Helsinki : Orienta-Konsultit. Retrieved February 20, 2003 , from the World Wide Web: http://lchc.ucsd.edu/MCA/Paper/Engeström/expanding/toc.htm

Engeström, Y. (2001). Expansive learning at work: Toward an activity-theoretical reconceptualization. Journal of Education and Work, 14(1), 133-156.