Teaching numeracy with adults

The internationalisation of perspectives on adult numeracy has been a feature of the last two decades. The OECD has picked up on the significance of numeracy from economic, social and personal perspectives. In late 2013 it will release the report on the first survey in its Programme for International Assessment of Adult Competencies, PIAAC. This data will provide evidence on where 26 countries, including Australia, stand in relation to their LLN skills and capacities.

There is now more consensus on what is meant by adult numeracy. In PIAAC, ‘Numeracy is the ability to access, use, interpret, and communicate mathematical information and ideas, in order to engage in and manage the mathematical demands of a range of situations in adult life.’

Closer to home, in the Australian Core Skills Framework (ACSF), ‘Numeracy is about using mathematics to make sense of the world and applying mathematics in a context for a social purpose.’

There is also consensus on describing and understanding how a numerate person tackles a problem that includes some mathematical information. The OECD Programme for International Student Assessment survey of 15-year-old students identifies three processes that pertain to the use of mathematics in context:

• Formulating mathematics involves identifying opportunities to apply and use mathematics.
• Employing mathematics involves applying mathematical reasoning and using mathematical concepts, procedures, facts and tools.
• Interpreting mathematics involves reflecting upon mathematical solutions or results and interpreting them in the context of a problem or challenge.

The ACSF describes three indicators of numeracy:

• .09  Identifying mathematical information and meaning in activities and texts.
• .10  Using and applying mathematical knowledge and problem solving processes
• .11  Communicating and representing mathematics.

We are looking at how numeracy applies across the life cycle of a problem:

Throughout this process, of course, there is a strong interaction with literacy skills in being able to read and interpret a numeracy problem and describe its solution. The Newman Error analysis method recognises that as much as 50 per cent of errors occur before the learner even starts to apply a standard mathematical method or algorithm.

Anne Newman’s work arose from research into language issues in mathematics in the 1970s. It influenced teaching programs such as ‘Counting On’ in NSW schools. It provides a structured model for numeracy study.

She proposed an ‘interview’ model as a means of addressing the literacy issues that affect numeracy performance. The trainer asks a series of prompts that help the learner to understand the problem.

• Please read the question to me. If you don’t know a word, leave it out.
• Tell me what the question is asking you to do.
• Tell me how you are going to find the answer.
• Show me what to do to get the answer. Talk aloud as you do it, so that I can understand how you are thinking.
• Now, write down your answer to the question.

The point is to be patient with a problem and take time to understand it, rather than rushing to apply rules haphazardly. Practical problem solving is not something that occurs in isolation or in the abstract. Actively engaging the Ls leads to better performance in N.