Numeracy as Social Practice

Global and Local Perspectives

Keiko Yasukawa, Alan Rogers, Kara Jackson, Brian V. Street, Keiko Yasukawa, Alan Rogers, Kara Jackson, Brian V. Street

• Publisher: Routledge
• Year: 2018
• eBook ISBN: 9781351979177
• Topic: Education
• Subtopic: Adult Education

Learning takes place both inside and outside of the classroom, embedded in local practices, traditions and interactions. But whereas the importance of social practice is increasingly recognised in literacy education, Numeracy as Social Practice: Global and Local Perspectives is the first book to fully explore these principles in the context of numeracy. The book brings together a wide range of accounts and studies from around the world to build a picture of the challenges and benefits of seeing numeracy as social practice ? that is, as mathematical activities embedded in the social, cultural, historical and political contexts in which these activities take place.

Drawing on workplace, community and classroom contexts, Numeracy as Social Practice shows how everyday numeracy practices can be used in formal and non-formal maths teaching and how, in turn, classroom teaching can help to validate and strengthen local numeracy practices. At a time when an increasingly transnational approach is taken to education policy making, this book will appeal to development practitioners and researchers, and adult education, mathematics and numeracy teachers, researchers and policy makers around the world.

PART I
Using case studies to expose the significance of what ‘surrounds’ mathematics in numeracy practices

Alan Rogers and Brian V. Street

Numeracy as social practice (NSP) understands numeracy always and only to be practised in a specific context on a specific occasion. The first Part of this collection of studies includes four research projects – ‘stories from the field’ – which examine different activities, exploring what surrounds the numeracy practices, what it is that gives them meaning. They come from very different parts of the world. All reveal how numeracy practices are used in combination with other social and cultural practices to achieve specific goals.

In Chapter 2, Kane discusses two examples, how waste collection vehicle drivers work out each day the most effective ways to deliver their services and how the managers and workers on a fruit orchard in New Zealand determine the practices they need throughout the season to maximize the yield of the orchard. His examples point to the way that a fine balance between more or less precise measurements and estimations was used in the everyday numeracy practices. An ‘audit’ of the mathematical skills involved would show, for example, that the orchard managers needed to be able to measure accurately the distance between the residual canes of the kiwifruit vines, and to read temperature measurements to know when to commence pest monitoring. For the waste collectors, there were measurements of weight (the weight of the bins) and time (when they can start collecting, when they can get a smooth run, etc). They also needed to have a developed spatial awareness? – of angles and distances to effectively manoeuvre the hydraulic arm to pick up the bins. However, these work practices also called for judgements to be made on the basis of long experience and local knowledge, for example, the weather patterns, and local streetscape and traffic patterns which interact with the mathematics embedded in these tasks.

In Chapter 3, Alangui admires the efficiency of those who build and repair stable and lasting stone walls to support their rice farming terraces in the Philippines. The mathematical knowledge concerns space and shapes, selecting the stones which best corresponded in weight and shape to the spaces which needed filling, ordering or classifying them according to size and shape, and rotating and positioning them. Wisdom from long experience and community tradition joined with (largely unconscious) mathematical practices to form the numeracy practices which helped them to achieve their purposes. They did not always get it right – some walls fell; but repairs reinforced the practices.

In Chapter 4, Kalman and Solares join Mexican workers checking their wages and ensuring they are not exploited by the traders they deal with. Power relations springing from long historical currents help format the numeracy practices involved – number recognition, counting and calculations, not just numerical but also of value, calling for quick decisions.

In Chapter 5, Boistrup and her colleagues analyse the way in which students in Sweden engaged in building a garden as part of the practical work for their courses use different numeracy practices and relate these to the mathematics they are learning in their formal education courses. More or less accurate measurements, more formal formulae (such as Pythagorean triangles) and symmetry in the patterning of the tiles being laid, and calculations of building material needed were made in the light of the available resources.

Within each of these examples, mathematical knowledge and skills joined with local knowledge and skills formed the practices that enabled goals to be achieved.

2
ESTIMATION BY KIWIFRUIT ORCHARD MANAGERS AND URBAN REFUSE/RECYCLING OPERATORS WITHIN THEIR SITUATED HORTICULTURAL OR CIVIC WORKPLACE PRACTICES

Case studies from New Zealand

Phil Kane

Introduction

Researchers have investigated people’s workplace mathematics in occupations such as telecommunications technicians (Triantafillou and Potari 2010), taxi-drivers (Chase 1983), and boat-builders (Zevenbergen and Zevenbergen 2004). Each study explores how people make sense of quantities and workspaces in their roles, although the mathematics used is usually within a wider set of situated (Lave 1993) everyday practices. According to Lave (1996), as people make sense of their circumstances, they are constructing their own in situ identities. Situated learning cannot therefore be passive (Stein 1998); rather action and learning take place connecting people, locations, processes, contexts and situations.

In this chapter I draw from a social practices framework (Street 1995, Baker 1998), specifically from a new literacy studies (NLS) perspective (Gee 1996), to characterize practices entailing numeracy in which orchard managers and refuse/recycling operators engaged. This is counter to the traditional autonomous model of literacy (Street 2012) where reading and writing are valued over oracy and traditional forms of communication. A social practices model of literacy is not reliant on discrete skills but focuses instead on ‘social, cultural, historical, and institutional contexts’ (Gee 2010, 5). Barton (2006, 22) defines ‘what people do with literacy’ as ‘literacy practices … However, practices are not observable units of behaviour since they also involve values, attitudes, feelings, and social relationships’. The social practices model is perhaps a closer fit to literacy than to numeracy. When viewing an incorrect decimal point in a bank transfer, or an erroneous ratio of raw materials in an industrial process, the implications of such errors have greater significance (Cockcroft 1982).

A case study research design was used in each workplace since ‘the variables were so embedded in [each] situation as to be impossible to identify ahead of time’ (Merriam 2009, 45). A single-case study approach was employed since participants’ efforts typically model their real-time everyday jobs (Yin 2009). In the first case, orchard managers occupy a major link in the production chain, growing export-quality kiwifruit in each site they oversee. Their efforts are ultimately judged on post-harvest appearance, freshness and consumer taste of the fruit, and returns for grower/owners, or ‘orchard gate returns’ (NZKGI 2016). In the second case, refuse/recycling operators work individually in mobile settings and are responsible for emptying every bin in their territory. Operators must comply with the rules of their organizations and the regulations of the destination depots where they unload. They are regulated also by a national road transport authority and the local territorial council authority with its occasionally disgruntled residents. The perspective of numeracy as situated social practices is appropriate since the participants’ numeracy in each context is not a set of isolated skills, rather an authentic, complex, varied and meaningful part in an organization’s milieu. Each participant contends with commercial and/or civic interests and authority.

The following section begins with a discussion of estimation. Backgrounds of the two workplaces and the participants are then described (all names are pseudonyms), before their respective work practices and instances where estimation is used are given.

Estimation

Estimation practices are of interest for two reasons. First, there are many instances of estimation by orchard managers and refuse/recycling operators that align with the key mathematical competences across many workplaces (Hodgen and Marks 2013). Second, estimation traverses other mathematical themes in workplaces (Sowder 1992) such as number sense, measurement and spatial reasoning. Estimation is pervasive and probably extends beyond other fundamental quantitative abilities (Siegler and Booth 2005). Adept estimators know when to estimate, when to ‘trade-off between simplification and proximity’ (LeFevre, Greenham and Waheed 1993, 120), and they can detect an incorrect quantity or reading, then take remedial action. But it is impractical and time-consuming to measure or count everything, so at times estimators will ‘sacrifice precision for convenience’ (Gal 1999, 11). Over time estimates evolve to become benchmarks or landmarks, although some are more precise depending on the context (Hogan and Morony 2000).

Siegler and Booth (2005) define two categories of estimation. Numerical estimation is when an amount does not need to be exact, rather it is close to the correct magnitude. Sowder (1992, 373) describes ‘clos[ing] in on a target value’ as an approximation. Approximating enables decision-making but does not require more time spent calculating. LeFevre, Greenham and Waheed (1993) suggest time is better spent deciding on when to estimate, and on the concepts around number sense to provide a sound base for estimation. Non-numerical estimation (Siegler and Booth 2005) involves spatial and relevant geometrical reasoning other than calculating. Non-numerical estimations may be influenced by natural phenomena (e.g. temperature) or by idiosyncratic strategies. For instance, Adams and Harrell (2010, 12) describe a strategy about estimating tyre tread depths, where an American penny is placed in a tyre tread and if one saw ‘all of Lincoln’s head [then there was] less than 3/32 of an inch [so] your tire is worn out’. Smith (1999) adds that work teams train newcomers to industry standards, so practices (like estimation) take time to develop, especially as newcomers must become familiar with the quality ranges and, perhaps, any statistical process controls.

The workplaces and their participants

Kiwifruit orchard managers

After viewing horticultural students inspect kiwifruit vines at a polytechnic orchard, a case study of orchard managers was initiated. In view of the breadth of the New Zealand kiwifruit industry, the numeracy practices in the pivotal position of orchard managers only were explored. Three managers completing a horticultural qualification at the polytechnic were invited to participate and two, Gary and Dave, volunteered. Interviews revealed that orchard work was essentially seasonal, so this guided the coding of their stories. FitzSimons (2000) notes that with people’s often complex workspaces, the mathematics they engage in is not always definitive. Accordingly, this case study focused on the numeracy practices drawn on by managers during their seasonal workplace practices.

An easily grown ‘backyard fruit’, the ‘chinese gooseberry’ (from 1959 ‘kiwifruit’) has been grown commercially since the early 1940s. By 2007, over 2500 kiwifruit growers contributed 29 per cent of New Zealand’s total horticultural exports (Mainland and Fisk 2006, Campbell and Haggerty 2008, HortResearch Rangahau Ahumara 2007), twice the volume of apples, the next largest export. The Bay of Plenty (eastern North Island) with its favourable climate and soils has become the prime commercial growing region in the country.

The managers had contrasting levels of experience: Gary had worked in the region since the 1980s at first in dairy farming. Following a serious accident, a chance encounter led him and his partner to kiwifruit. Thirty years on, the couple now manage orchards and teams of workers for several owner-growers in the Eastern Bay. The younger manager, Dave, was a recent arrival although like Gary he had first worked elsewhere; his cadetship with a packing company acquainted him with every facet of the industry. During his orchard initiation, Dave was mentored by a senior manager, Rod, who had over twenty years’ experience growing kiwifruit.

Recycling and refuse operators

Following a pilot investigation (Chana and Kane 2010), the second case study investigated collection operators of two South Auckland refuse and recyclables collection companies. Company X employed refuse/recyclables operators while Company Y contracted recyclables operators only. During the study, Company Y ended its Auckland operations owing to unrelated concerns offshore, and Company X successfully tendered for the vacant territories and absorbed Company Y’s thirteen operators. These contractors joined the team of operators but each employment structure remained. By the end of the study, Company X had a combined...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• List of illustrations
• List of contributors
• Foreword
• Introduction
• Part I Using case studies to expose the significance of what ‘surrounds’ mathematics in numeracy practices
• Part II Mathematics education and everyday numeracies: theoretical resources for analysis
• Part III Numeracy and power: facilitating learning of numeracy as social practice
• Conclusion
• Index