Learning numeracy on the job: A case study of chemical handling and spraying

This research illustrates the challenges faced by industries using chemical handling and spraying as they attempt to ensure that workers have the appropriate numeracy skills.

• The 'numeracy' task of preparing and applying chemicals requires that the person responsible takes a complex set of variables into account. Although chemical sprayers and handlers may have undergone specific training and/or learned the required mathematical skills at school, they still require further on-the-job mentoring and support.

• The worksite influences both the type of numeracy skills needed, as well as how they are deployed. In other words, the task, the history of the task (for example, how previous records were taken), and the equipment used determine the sorts of calculations people must be able to make. Once these are learned, they have to be embedded through practice.

• Workplace numeracy education cannot be approached from a traditional 'school mathematics' mentality.

• Workplace numeracy requires training that reflects workplace practices and incorporates authentic problem-solving in real or simulated tasks in small groups with shared responsibilities. It also needs to incorporate the development of metacognitive skills, such critical thinking, learning to learn, planning and problem-solving.

The processes of preparation, application, handling, storage and transport of chemicals are key elements of a range of economically significant industries, and place high demands on workers' literacy, and especially numeracy skills. Many of these skills are acquired during employment on the job or in associated off-the-job training.

It is important to gain an understanding of how these skills are developed and maintained in workplaces where there are significant risks to personnel, production and the environment, if these critical tasks are undertaken incorrectly. This understanding is important, not just for numeracy practitioners, but also for policy-makers who frequently view numeracy as a generic skill whose application may be easily transferred from a formal learning context to the workplace, or from one work context to another.

In fact, a substantial body of research evidence demonstrates that such skill transfer is achieved only with difficulty, and that numeracy skills are highly context-dependent. This research therefore sought to investigate actual tasks demanding numeracy skills at a range of worksites in a number of industries.

The research involved a literature review and documentary analysis in relation to legislation, training package common units and the National Reporting System. Empirical work involved 13 case studies of enterprises in New South Wales and Victoria, all of which used chemicals extensively. Industries selected included rural production, amenity horticulture, local government, outdoor recreation and warehousing.

Definitions

The international research literature distinguishes between numeracy and mathematics, yet maintains that mathematical skill underpins, but does not equate to numeracy. Steen (2001) makes a distinction, arguing that mathematics requires a distancing from context. Numeracy ('quantitative literacy' in his terms), on the other hand, is anchored in real data which reflect engagement with life's diverse contexts and situations. Numeracy offers solutions to problems about real situations.

There is a growing understanding of how mathematical knowledge is used in real situations of life and work, to which the present research is a contribution. Following Bernstein (2000), it is argued that the use of common sense-of relatively little value in formal mathematics-is essential in numeracy.

Observations of workplace numeracy practices indicate that knowledge is embedded in ongoing practices. Such knowledge is 'directed towards specific, immediate goals, highly relevant to the acquirer in the context of his/her life' (Bernstein 2000, p.159), and is usually learned face to face and, if necessary, repeated until the particular competence is fully acquired.

Just as there are fundamental differences between mathematics and numeracy, workplace numeracy education requires a fundamentally different curriculum and teaching/learning strategies from those required for teaching school mathematics. However, these would need to encompass underpinning mathematical knowledge and skills in ways that enable the generation of 'new' knowledge in order to solve problems which cannot always be known in advance.

Findings

The tasks of preparing, applying and handling chemicals require that a complex set of numeracy variables-much more complex than the simple application of mathematical skills learned in school or vocational education-must be taken into account by the person responsible. Critical tasks include the calculation and measurement of chemicals, taking note of:

• space (areas to be sprayed), time of day (night, early morning) time of year (for example, not too close to harvest), carrying capacity of particular tanks

• weather conditions (humidity, wind speed and temperature)

• economic and legal contingencies

• the calibration of equipment (with associated calculations)

• the need for accurate record-keeping and consultation with previous records

• efficient location of chemicals in warehouse situations.

Estimation is always necessary, based on prior experience of the kind of spraying needed. Common sense is essential. Mistakes in the actual process may threaten public safety and also the livelihoods of the workers.

Workplace numeracy tasks are always a social-historical and cultural practice, in the sense that previous experience and historical data play a major role in determining the reasonableness of answers. At the same time, calculations are double-checked, and team and group work are fostered as part of workplace practice. Artefacts (equipment, tables, chemical labels, charts, ready reckoners) are used as resources to aid formal calculations, or in other situations requiring assessment and evaluation.

Implications for policy and practice

In the workplace the priority and intended outcome are to get the job done as effectively and efficiently as possible, assisted by numeracy as but one tool. In a formal education setting the intended outcome is the learning of mathematics. Unlike a formal education setting, the results obtained in the workplace really matter in terms of public and personal safety, the environment, economic costs and maintaining one's job. Solutions to calculations for chemical spraying must necessarily be error-free, but in contrast to formal education, the actual methods used allow some discretion, and more importantly, they involve collaboration with or validation by at least another person.

Numeracy in the workplace involves the practical application of rational numbers and the metric measurement system with contextualised approximations and estimations in critical calculations, often with other workers. It also may incorporate each of the key competencies (for example, planning, organising, cooperating and communicating effectively). This is in marked contrast to the traditional conception of mathematics education as an abstract, rule-bound, individual activity, with one correct answer (usually a number, an algebraic expression, or a standard graph), and where mistakes are temporary setbacks.

Numeracy educators need to ensure that workers have a deep understanding of the metric system within the context of common workplace usage. An understanding of rational numbers (that is, fractions, decimals) will result from carefully chosen practical activities and explicitly made connections, as well as from sophisticated calculator activities. Learners need to be presented with opportunities to become familiar with, and use various artefacts from relevant workplaces, for example, reading and interpreting non-standard graphs, chemical labels, tables, charts, calibration charts for specific equipment, and other ready reckoners. They also need to learn how to complete record sheets and templates for calculations accurately.

Given that learners will need to make sense of activities and ill-defined problems in unfamiliar workplace situations, problem-solving activities are recommended, using case study examples from industry workplaces. Realistic group projects with open-ended solutions and shared responsibilities need to be devised. As workplace activity shapes the process and meaning of the mathematics used, simulations can be applied off the job. In addition, viewing video material relating to specific weather and workplace conditions could also be used to provide contextualisation. Teachers could make links with enterprises for the use of part of their premises, for example, a golf course. Encouraging learners to keep a logbook, or journal about strategies they would adopt in certain situations is also an invaluable exercise and an individual 'living' resource. In order to develop workers' ability to interact with computerised systems, which may hold vital information, authentic data could be obtained (with permission) and a simulation organised.

Although workplace supervisors tend to assume a strong foundation of school mathematics, and the transference of such knowledge, this is not necessarily the case for many workers involved in chemical spraying and handling. Specialised tuition may be needed to enable workers to develop the relevant mathematical skills (or earlier learning reinforced) in relation to the mandatory chemical spraying and handling training required in these industries. Findings from this study indicate that, although most workers have undertaken formal chemical use training, mentoring and support in how numeracy processes operate within the particular enterprise are still required, since each workplace is individual.

Because enterprise numeracy skills are so specific and not every context/situation can be covered in formal training, metacognitive strategies (learning to learn, critical thinking, planning, problem-solving) are crucial and need to be consciously developed.

Questions arise over how competently workers would be taught by teachers or trainers with little or no background in mathematics education, or with little or no knowledge of the social-cultural numeracy context of the workplace. There is an urgent need for mandatory specialised preparation of and/or professional development for teachers and trainers involved in adult numeracy, even if this is not their principal role.

In addition to this report, the study produced an extended literature review and more detailed descriptions of the case study sites. This information can be downloaded as a support document.