Session Information
24 SES 08, The Role of Mathematical Knowledge in the 21st Century
Paper Session
Contribution
This paper discusses the challenges and boundaries of numeracy in the field of adults learning mathematics. We draw on a research project funded by the European Commission, under the Erasmus + Program. The main aim is to explore the concept of numeracy, discussing what the new challenges that numeracy has to face nowadays are. The potential impact of this study is to contribute to updating the contents of mathematics included in the curriculum of courses addressed to adult learners.
During the last decades, numeracy has been one major concern for countries. In 2016 the OECD reported that two in five adults have limited reading and numeracy skills on average, in the 24 countries participating in the first cycle of PIAAC (OECD, 2016). According to this report, "nearly one in two adults is proficient only at or below Level 1 in problem-solving in technology-rich environments." (OECD, 2016, p. 17)
In this survey, numeracy was defined as "the ability to access, use, interpret and communicate mathematical information and ideas to engage in and manage the mathematical demands of a range of situations in adult life." (OECD, 2016, p. 48)
The first cycle of the PIAAC survey explored numeracy in four different contexts: everyday life, work-related, societal or community and further learning (Tout et al. 2017). This classification is consistent with previous definitions of numeracy. Groenestijn(2002), for instance, defined it as: “the knowledge and skills required to effectively manage mathematical demands in personal, societal and work situations, in combination with the ability to accommodate and adjust flexibly to new demands in a continuously rapidly changing society that is highly dominated by quantitative information and technology.” (Groenestijn, 2002, p. 37)
When we explore scientific literature on numeracy, the most prominent body of studies belong to the work-related context (Coben & Weeks, 2014; FitzSimons, 2004; Keogh, Maguire, & O’Donoghue, 2014; Straesser, 2000; Wedege, 2004; Williams & Wake, 2007). Geometry, algebra, calculus and a deep understanding of basic arithmetic (including number sense and proportional reasoning) are the most common mathematical contents reported throughout the different contexts analyzed in the literature. FitzSimons (2004) observed that numeracy in different workplaces involve: "(a) collecting, analyzing and organizing information, (b) communicating ideas and information, (c) planning and organising activities, (d) working with others and in teams, (e) using mathematical ideas and techniques, (f) solving problems, and (g) using technology.
Therefore, numeracy exceeds workplace settings. In the first PIAAC cycle, the Numeracy Expert Group stated that numeracy is "the ability to access, use, interpret and communicate mathematical information and ideas, to engage in and manage the mathematical demands of a range of situations in adult life." (Gal et al., 2009, p. 21)They added the concept "numerate behavior", trying to cover not only what numeracy is, but also its use in a wide range of situations.
In our current world, in which technologies and big data are gaining prominence, knowledge about new branches of mathematics are the more and more necessary, including statistics and probabilities (Evans et al., 2017), applied mathematics (van der Wal, Bakker, & Drijvers, 2017)and discrete mathematics (Gravemeijer et al., 2017). OECD has described the need for different types of mathematics: statistics and probability, complex systems, and computational mathematics. The Royal Society ACME adds mathematical modeling to that list. In this paper, we discuss these new demands drawing on a meta-analysis of previous studies in the field.
Method
This paper is a discussion based on a literature review. We conducted a systematic meta-analysis of articles, book chapters, books and proceedings related to numeracy. As Hart (2018) states, a literature review is “the selection of available documents (both published and unpublished) on the topic, which contain information, ideas, data and evidence written from a particular standpoint to fulfil certain aims or express certain views on the nature of the topic and how it is to be investigated, and the effective evaluation of these documents in relation to the research being proposed.” (Hart, 2018, p. 13) In order to identify relevant documents, we used scientific databases (Web of Science, Journal Citations Reports and Scopus), as well as pertinent repositories of the field (the Adults Learning Mathematics organisation, which is an international scientific organisation devoted to the study of adults who learn mathematics, the journal Adults Learning Mathematics: An International Journal, one of the primary sources to get access to newly and outstanding research in the field), as well as reports and technical reports from the international surveys in adults’ learning mathematics (OECD surveys, such PIAAC). We organized the documents found using Hart's (2018) suggestions on how to classify and read the selected research. We distinguished among basic and applied research, with emphasis on the type of data sources and methods used. In order to analyze the research studies found, we used argumentation analysis using inductive logic (as in the grounded theory -Glaser & Strauss, 2017-) to identify the main components related to numeracy present in the documents. Atlas.ti (8.3.1) was used to organize the information.
Expected Outcomes
Nowadays, the concept of numeracy incorporates not only "basic computation skills", referring to the ability of using arithmetic algorithms for calculating, but also other components (in terms of mathematical objects, representations, and processes such as communicating, reasoning or modelling), involving algebraic thinking, geometric reasoning, logic, measurement, and interpretation of (big) data (Geiger et al., 2015; Kaye, 2018). The international surveys on numeracy (i.e., PIAAC) are making a great effort to update the current framework to assess numeracy all over the World. In Europe also, a team of experts is redefining the Numeracy framework in Europe, to cope with the challenges of our current society (Hoogland et al., 2019). Well into de 21st Century, the new social phenomena of "big data" are colonizing everyday life, work-related, societal or community contexts. "Expert systems” (Giddens, 2013) make mechanical calculations and routinize actions that used to be performed by individuals (i.e., calculating the tip, finding an address in a map, etc.). Now, apps do this work for us. However, new demands emerge, such as dealing with significant amounts of data (read statistics, tables, indicators, etc.), designing logic algorithms to solve problems (i.e., using discrete mathematics). For this reason, numeracy needs to be re-defined, accordingly. Failing in doing that may lead adult people to risk (Beck, 1992) in being able to respond to the 21st century requirements. Redefining numeracy also has the potential to encourage the practical discussion of how to update the mathematics curriculum addressed to adults who are taking courses to develop, reinforce, upgrade their numeracy and literacy skills. The envisioned impact of this literature review, which is also part of the research project mentioned below, is to provide guidelines to the educational authorities to address the challenges and opportunities for numeracy in our current time.
References
Beck, U. (1992). Risk society: Towards a new modernity. Sage. Coben, D., & Weeks, K. (2014). Meeting the mathematical demands of the safety-critical workplace: Medication dosage calculation problem-solving for nursing. Educational Studies in Mathematics, 86(2), 253–270. Evans J. et al. (2017). Numeracy skills and the numerate environment: affordances and demands. Adults Learning Mathematics: An International Journal, 12(1), 17–26. FitzSimons, G. E. (2004). Adult numeracy/mathematics in Australian workplaces. In L. Lindberg (Ed.), Adults Learning Mathematics. Bilding and /or training (pp. 79–85). Göteborg University. Gal, I. et al. (2009). PIAAC Numeracy: A Conceptual Framework. OECD. Geiger et al. (2015). A rich interpretation of numeracy for the 21st century: A survey of the state of the field. ZDM, 47(4), 531–548. Giddens, A. (2013). The consequences of modernity. John Wiley & Sons. Glaser, B. G., & Strauss, A. L. (2017). Discovery of grounded theory: Strategies for qualitative research. Routledge. Gravemeijer, K. et al. (2017). What Mathematics Education May Prepare Students for the Society of the Future? International Journal of Science and Mathematics Education, 15(1), 105–123. Hart, C. (2018). Doing a Literature Review: Releasing the Research Imagination. Sage. Kaye, D. (2018). Defining Adult and Numeracy: An Academic and Political Investigation. In Contemporary Research in Adult and Lifelong Learning of Mathematics (pp. 11–37). Springer. Keogh, J. J., Maguire, T., & O’Donoghue, J. (2014). A Workplace Contextualisation of Mathematics: Measuring Workplace Context Complexity. Adults Learning Mathematics, 9(1), 85–99. OECD. (2016). Skills matter: Further results from the survey of adults skills. OECD. Straesser, R. (2000). Mathematical means and models from vocational contexts. In Education for mathematics in the workplace (pp. 65–80). Springer. Tout, D. et al. (2017). Review of the PIAAC numeracy assessment framework: Final report. Camberwell, Victoria: Australian Council for Educational Research and OECD. van der Wal, N. J., Bakker, A., & Drijvers, P. (2017). Which Techno-mathematical Literacies Are Essential for Future Engineers? International Journal of Science and Mathematics Education, 15(1), 87–104. Van Groenestijn, M. (2002). A gateway to numeracy. A study of numeracy in adult basic education. Utrecht: Utrecht CD-B Pres. Wake, G. (2007). Considering workplace activity from a mathematical modelling perspective. In Modelling and applications in mathematics education (pp. 395–402). Springer. Wedege, T. (2004). Sociomathematics: Researching adults mathematics in work. Universitätsverlag Rudolf Trauner. Williams, J., & Wake, G. (2007). Black boxes in workplace mathematics. Educational Studies in Mathematics, 64(3), 317–343. This work was supported under the EC Erasmus + Research Program (Project number 2018-1-NL01-KA204-03913).
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