What does "technology" mean
in educational research on
workplace mathematics?
Tine Wedege
2013
Adults´ mathematics/Vuxnas matematik: Working papers, 3
FACULTY OF EDUCATION AND SOCIETY
What does "technology" mean in educational research on workplace
mathematics?
Adults´mathematics/Vuxnas lärande: Working papers, 3
This paper is written as a part of the research project Adults’ mathematics: From work to school
funded by the Swedish Research Council and Malmö University.
www.mah.se/ls/asm
© Tine Wedege, Faculty of Education and Society
Publisher
Faculty of Education and Society
Malmö University
20506 Malmö
Editorial secretaries:
Catarina Christiansson, [email protected]
Marie Jacobson, [email protected]
http://www.mah.se/ls/eng
What does “technology” mean in educational research on workplace
mathematics?
Tine Wedege, Faculty of Education and Society, Malmö University, Sweden
Abstract. “Technology” is a key term in the educational research field of mathematics in the
workplace. However, the notion of technology is constructed differently in the workplace
studies according to the researchers’ purpose and theoretical frameworks of reference. The
objective of this paper is to analyse discourses on mathematics and technology in selected
literature from Austria, France, Sweden, and UK. The analytical frame is a broad, albeit
specific, understanding of workplace technology with four dynamically inter-related
dimensions: (a) technique and machinery, (b) work organisation, and (c) vocational
qualifications, and (d) workers’ competences. Researchers agree that mathematics in the
workplace is integrated in technology. However, in the four dimensions, mathematics is
integrated (1) explicity as academic mathematics, school mathematics and vocational
mathematics, or (2) implicitly as vocational mathematics and ethnomathematics. The analysis,
with respect to this framework, shows that the construction of mathematics containing
technology also varies with the values and rationales of the stakeholders (e.g. politicians, trade
organisations or researchers in different cultural and societal contexts).
Key words. Discourse, Workplace mathematics, Mathematics containing technology,
Theory, Vocational qualification, Workers’ competences.
Technological and economic development of society is one of the reasons given for
mathematics education (Niss, 1996). Thus, it is important to have a critical look at the interfaces
between education and technology. However, in mathematics education, as in everyday
language, the term “technology” is mostly associated with information and communication
technology (ICT), and research is mainly directed towards ICT in the mathematics classroom
(Artique, 2006). In this paper, the main focus is explicit and implicit mathematics in the
workplace not school mathematics. Thus, the understanding of “technology” has to be broader.
The aim is to analyse discourses on technology and mathematics within the educational research
field of workplace mathematics. Here, the term discourse is used in the general meaning of
written or spoken communication within specific historical, cultural or societal contexts. By
theoretical frameworks of reference (Artique, 2006), I mean the theory, conceptual framework
etc., used and referred to by the researchers.
Within the focussed research field, there is – as mentioned above – a common
understanding that workplace mathematics is integrated with technology (technique, work
organisation, qualifications and competences). However, modern computer techniques hide the
use of mathematics in the software, and mathematics as a visible tool disappears in many
workplace routines (Strässer, 2003). But apart from this objective invisibility there also exists a
subjective invisibility. People do not recognise the mathematics in their daily practice. They just
do not connect the everyday activity with mathematics that most of them associate to the school
subject or the discipline (Wedege & Evans, 2006).
1
The main interest, behind the analysis presented in this paper, is mathematics in the
workplace (see below). I include four types of mathematics which is developed, practiced and
learned in different educational and vocational practices:
 academic mathematics in universities
 school mathematics in general and vocational schools,
 vocational mathematics in vocational schools, and in workplaces and labor market
organizations,
 ethnomathematics in communities of work (wage work, domestic work etc.).
For the analysis, I have selected literature from Austria (Jungwirt, Maasz, & Schlöglmann,
1995), France (Bessot, 2000), Sweden (Gustafsson & Mouwitz, 2010), and UK (Hoyles et al.,
2010, Noss et al., 2007). Criteria for selection of literature have been diversity in focus and
understanding of mathematics and in language (mother tongue of the researchers), but also
national and/or international importance of the authors within the field of workplace
mathematics.
Mathematics containing technologyi
In order to investigate the relationship between mathematics education and technology in the
workplace, it is necessary to have a broad conception of mathematical knowledge and of
technology as well. Technology is a central theme in Gail FitzSimons’ (2002) study on adult
and vocational education where it “provides a nexus between mathematical and industrial
practice, as well as their related educational subfields” (p. 8). She calls attention to the histories
of development of technology and mathematics. They indicate that they operate in a dialogical
relationship which is often invisible for the members of the communities, even those with a
substantial background in mathematics. In the Discussion Document for the ICMI/ICIAM study
on “Educational Interfaces between Mathematics and Industry” (EIMI), it is stated that
“‘Technology’ is understood in the broadest sense, including traditional machinery, modern
information technology, and workplace organisation” (ICMI/ICIAM, 2009, p. 100).
The frame for my analysis is an even broader and, at the same time, dynamic understanding
of workplace technology where mathematics is integrated in four dynamically inter-related
dimensions: (a) technique/machinery, (b) work organisation, and (c) vocational qualifications,
and (d) workers’ competences (Wedege, 2000). The term technique is used in a broad sense to
include not only tools, machines and technical equipment, but also cultural techniques (e.g.,
communication & time management), and techniques for deliberate structuring of the working
process (e.g., Taylor’s scientific management, the ISO 9000 quality management system).
Mathematics is applied and embedded in technique as well as in machinery. Work organization
is used to designate the way in which tasks, functions, responsibility, and competence are
structured in the workplace in order to achieve a specific goal. Mathematics is applied and
embedded in work organization. Vocational qualifications are the knowledge, skills, and
personal qualities required to handle technique and work organization in a work function; for
example, formal mathematical ideas and techniques. Mathematics is integrated in vocational
qualifications as respectively academic, school and vocational mathematics. Human
competences are workers’ capacities (cognitive, affective, & social) for acting effectively,
critically and constructively in the workplace. Mathematics is incorporated and embodied in
human competences as respectively vocational mathematics and ethnomathematics. In table 1,
2
notions of explicit mathematics and of implicit mathematics in workplace technology are
developed. Explicit mathematics is applied in techniques (e.g. folding rule and mechanical
weighing and pricing) and in work organization (e.g. scientific management and Just in Time);
integrated in workers’ vocational qualifications as functional mathematical skills and
knowledge (e.g. numeracy and techno-mathematical literacy) and incorporated in workers’
competences (e.g. mathematics containing technological competence and techno-mathematical
literacy). Implicit mathematics is embedded in technique (e.g. hammer and digital weighing and
pricing), work organization (e.g. shifting cultivation) and embodied in workers’ competences
(e.g. personal time managing and pattern weaving). Per definition there is no implicit
mathematics in vocational qualifications, which are explicitly communicated in curricula,
course plans etc.
Table 1. Mathematics in workplace technology
(a)
Technique/
machinery
(b)
Work organization
(c)
Vocational
qualifications
(1) Explicit
use and
integration of
mathematical
tools
Applied
mathematics
(academic and school
mathematics)
Applied
mathematics
(academic and school
mathematics)
Functional
mathematical
skills and
knowledge
(academic, school
and vocational
mathematics)
(2) Implicit
integration of
mathematical
tools or
mathematics
developed in
practice
Embedded
mathematics
(vocational
mathematics/
ethnomathematics)
Embedded
mathematics
(vocational
mathematics/
ethnomathematics)
Technology
(d)
Workers’
competences
Mathematics
----
Incorporated
mathematics
(vocational
mathematics)
Embodied
mathematics
(ethnomathematics)
This understanding of mathematics containing technology presupposes that new information
and communication techniques [ICT] – or any techniques – do not bring about change or
development by itself. Competent workers are needed who are qualified to handle the particular
ICT as well as appropriate work organization (Wedege, 2004).
Strässer (2003) has used the development from mechanical to digital weighing and pricing as
an example of “disappearance of mathematics from societal perception” (p. 30). Keitel,
Kotzmann and Skovsmose (1993) (Keitel, Kotzmann, & Skovmose, 1993) point out two
contrary processes:
The most important concepts of implicit mathematics (…) are time, space, and money. We
areacting in a highly mathematical space-time-money system without knowing (or even
3
having to know) the underlying mathematical abstraction processes explicitly. This results
in the paradox that a “demathematisation” process takes place parallel to the
mathematisation of our world. (…) More and more mathematics (learnt in school) only
exists implicitly, i.e. one needs only a certain operative ability (e.g. using a pocket
calculator or a computer doing the calculations by programs) and a certain attitude and
belief (e.g. the conviction that decisions based on mathematical methods are more reliable
than by other arguments).(p.251)
Mathematics is always integrated in workplace technology, i.e. applied, incorporated or
embedded. In practice at work one does not solve mathematical problems like in the school.
One solves practical problems like washing a car, controlling the quality, cutting the hair,
dosing the medicine etc. In the mathematics classroom (Gellert, 2008) or in surveys like PISA
(OECD, 2003), the students often have to forget what they might know about the context and
only use logic and school mathematical knowledge to produce the correct answer (Wedege,
2010).The so-called invisibility of mathematics in technology or that mathematics generally is
hidden in todays’ technology is agreed among researcher (ICMI/ICIAM, 2009).
Embodied mathematics (table 2, 2d) is implicit mathematics in human competences at work.
I have chosen the term “embodied” with inspiration from (Leplat, 1995), according to who
embodied competences are competences encapsulated into the action, difficult to verbalize, very
connected to the context but easily available and unproblematic. The worker’s feeling for time
and space is an example of embodied mathematics.
Studies of mathematics in and for the workplace
In educational research on workplace mathematics, it is possible to distinguish two kinds of
interest:
 Mathematics for the workplace. The interest guiding the studies is education for
mathematics in the workplace. The research questions concern vocational qualifications
in mathematics and how they can be developed through formal education (e.g. Bessot,
2000, Hoyles, Noss, Kent, & Bakker, 2010, Jungwirth, Maasz, & Schlöglmann).
 Mathematics in the workplace: The interest guiding the studies is to understand
workers’ mathematical competences and practices within the complexity of workplace
technology (e.g. Gustafsson & Mouwitz, 2010, Noss, Bakker, Hoyles, & Kent, 2007).
In the full paper, I will present the analysis, with respect to the framework presented above, of
the discourses on mathematics containing technology in the selected studies.
It is not surprising that technology – just like mathematics – is a contested notion in
mathematics education in and for the workplace. Nor that the notion of technology depends on
the theoretical frame in use. However, the analysis has shown that the discourse on technology
is also depending of the stakeholders’ interest and involvement. In the international research
project Adults’ mathematics: From work to school, the primary focus is the incorporated or
embodied mathematical competences at work. However, we do not intend to validate the
workers mathematical competences in relation to the mathematical qualifications required in
vocational education. The purpose is to establish a scientific ground for developing formal and
non-formal mathematics education in a way that the adult students’ mathematical competences
are recognized and respected.
4
Acknowledgements
This paper is written as part of the research project “Adults’ mathematics: From work to school”
which is supported by the Swedish Research Council in 2011-2014. I thank Gerd Brandell, Per
Jönsson, Tamsin Meany and Troels Lange for constructive comments to an earlier version of
this draft.
References
Artique, M. (2006). Towards a methodological tool for comparing the use of learning theories
in technology enhanced learning in mathematics (TELMA). Paris: Kaleidoscope.
Bessot, A. (2000). Geometry at work: Examples from the building industry. In A. Bessot & J.
Ridgway (Eds.), Education for mathematics in the workplace (143-157). Dordrecht: Kluwer
Academic Publishers.
FitzSimons, G. E. (2002). What counts as mathematics? Technologies of power in adult and
vocational education. Dordrecht: Kluwer Academic Publishers.
Gellert, U. (2008). Validity and relevance: Comparing and combining two sociological
perspectives on mathematics classroom practice. ZDM – the International Journal on
Mathematics Education, 40, 215-224.
Gustafsson, L., & Mouwitz, L. (2010). Validation of adults’ proficiency: Fairness in focus.
Göteborg: Nationellt centrum för matematikutbildning, Göteborgs universitet.
Hoyles, C., Noss, R., Kent, P., & Bakker, A. (2010). Improving mathematics at work: The need
for techno-mathematical literacies. New York: Routledge.
ICMI/ICIAM. (2009). Discussion document of the joint ICMI/ICIAM study on educational
interfaces between mathematics and industry. L’Enseignement Mathématique, 55, 197-209.
Jungwirth, H., Maasz, J., & Schlöglmann, W. (1995). Mathematik in der Weiterbildung.
Abschlussbericht zum Forschungsprojekt. Linz: Johannes Kepler Universität.
Keitel, C., Kotzmann, E., & Skovmose, O. (1993). Beyond the tunnel vision: Analysing the
relationship between mathematics, society and technology. In C. Keitel, & K. Tuthven
(Eds.), Learning from computers: Mathematics educatication technology (pp. 243-279).
Berlin: Springer.
Leplat, J. (1995). À propos des compétences incorporées. Education Permanente, 123(1995-2),
101-114.
Maasz, J. (1998). Technology transfer: A useful metaphor for university level maths courses for
engineers and scientists. In D. Coben, & J. O’Donoghue (Eds.), Proceedings of ALM – 4 the
fourth international conference of adults learning maths – a research forum, university of
limerick, ireland, 4-6 july, 1997 (pp. 58-62). London: Goldsmiths University of London.
Maasz, J., & Schlöglmann, W. (Eds.). (1989). Mathematik als Technologie? Wechselwirkungen
zwischen Mathematik, Neuen Technologien, Aus- und Weiterbildung. Weimheim, Germany:
Deutscher Studien Verlag.
Niss, M. (1996). Goals of mathematics teaching. In Bishop, Alan J. et al. (Ed.), International
handbook of mathematics education (pp. 11-47). Dordrecht: Kluwer Academic Publishers.
Noss, R., Bakker, A., Hoyles, C., & Kent, P. (2007). Situating graphs as workplace knowledge.
Educational Studies in Mathematics, 65, 367-384.
OECD. (2003). Learning for tomorrow's world. First results from PISA 2003. Paris: OECD.
Strässer, R. (2003). Mathematics at work: Adults and artefacts. In J. Maasz, & W. Schlöglmann
(Eds.), Learning mathematics to live and work in our world: ALM10: Proceedings of the
5
10th international conference on adults learning mathematics in Strobl (Austria) 29th june
to 2nd july 2003 (pp. 30-37). Linz, Austria: Universitätsverlag Rudolf Trauner.
Wedege, T. (2000). Technology, competences and mathematics. In D. Coben, G. FitzSimons &
J. O'Donoghue (Eds.), Perspectives on adults learning mathematics: Research and practice.
(pp. 191-207). Dordrecht: Kluwer Academic Publishers.
Wedege, T. (2010). Ethnomathematics and mathematical literacy: People knowing mathematics
in society (Key note speech). In C. Bergsten, E. Jablonka & T. Wedege (Eds.), Mathematics
and mathematics education: Cultural and social dimensions (pp. 31-46). Linköping: Svensk
Förening för Matematikdidaktisk Forskning, Linköping universitet.
Wedege, T., & Evans, J. (2006). Adults' resistance to learn in school versus adults' competences
in work: The case of mathematics. Adults Learning Mathematics - an International Journal,
1(2), 28-43.
In this framework, as in the research project Adults’ mathematics: From work to school, “technology”
means ”workplace technology” (meso and micro level – see FitzSimons, 2002). However, it is possible to
apply the dynamic understanding at the macro level (labor market and society) as well.
i
The author
Tine Wedege
Faculty of Education and Society
Malmö University, Sweden
[email protected]
6
Vuxnas matematik: Arbetsdokument / Adults’ mathematics: Working papers
Dec 2013
Wedege, Tine & Björklund Boistrup, Lisa (2013). Från arbetet till skolan: Ett forskningsprojekt om
vuxnas matematik. Adults’ mathematics: Working papers, 1.
Wedege, Tine (2013). Workers’ mathematical competences as a study object: Implications of general
and subjective approaches. Adults’ mathematics: Working papers, 2.
Wedege, Tine (2013). What does “technology” mean in educational research on workplace
mathematics? Adults’ mathematics: Working papers, 3.
Wedege, Tine (2013). Integrating the notion of foreground in critical mathematics education with the
theory of habitus. Adults’ mathematics: Working papers, 4.
To be published in Ernest, P., & Sriramann, B. (Eds.). Critical mathematics education:
Theory and praxis. Charlotte, NC: Information Age Publishing (IAP).
Björklund Boistrup, L. & Gustavsson, L (2014). Mathematics containing activities in adults´ workplace
competences. Adults’ mathematics: Working papers, 5.
Submitted to ALM International Journal
Adults’ mathematics: In work and for school
Working papers
School knowledge versus everyday knowledge is a fundamental issue in
mathematics education. The objective of this research project is to describe,
analyse and understand adults’ mathematics-containing work competences –
including social, ethnic and gender related aspects – in relation to the demands
made on students’ mathematical qualifications in formal vocational education.
The working model for researching the dynamics of adults’ mathematics in
work and for school combines a general approach – starting with demands from
the labour market and school mathematics – and a subjective approach starting
with the individual’s needs and competences in work. The problem complex is
studied through empirical investigations – quantitative (survey) and qualitative
(observations, interviews and document analysis) – in interplay with theoretical
constructions. Mathematics is integrated within workplace activities and often
hidden in technology: mathematical elements are subsumed into routines,
structured by mediating artefacts (e.g., texts, tools), and are highly contextdependent. As a discourse of education, lifelong learning assumes that learning
takes place in all spheres of life. This project seeks to reverse the one-way
assumption from school knowledge to workplace knowledge and to learn from
workplace activity what might be appropriate for vocational education and
training with implications for general schooling in Sweden.
The research project Adults’ mathematics is initiated by professor Tine
Wedege and is organised as a co-operation between researchers at
Malmö University, Copenhagen University, Melbourne University and
Stockholm University. The leaders of the project are Tine Wedege,
Malmö University, and Lisa Björklund Boistrup, Stockholm University. The
project is funded by the Swedish Research Council and Malmö University.
Working papers are either preliminary or completed papers. Some of the
working papers are not available in any other form. Others are pre-prints that
are to be published elsewhere.