Increasingly research is showing that life and work in in the 21st century is requiring higher levels of mathematics and numeracy of its citizens. This paper looks at the implications of this for the skills we want our students to develop and leave school with, and how we can better address these in our teaching and learning.
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Critical connections between Numeracy and Mathematics
Why connections between Numeracy and Mathematics is an important issue in mathematics teaching and learning in the 21st century
Increasingly research is showing that life and work in in the 21st century is requiring higher levels of mathematics and numeracy of its citizens. Numeracy and mathematics are intrinsically connected and BOTH are needed in our ever changing, globalised and technological world. This paper looks at the implications of this for the skills we want our students to develop and leave school with, and how we can better address these in our teaching and learning.
Research about 21st century skills
Research is showing that the skills and knowledge now needed to succeed in work, life and citizenship have significantly changed in the 21st century, often driven by technological advances and an ever-increasing use of numerical and quantitative information and data. This also connects with the transforming nature of the workforce associated with Industry 4.0 and the Gig economy, with increasing demands for science, technology, engineering and mathematics (STEM) skills (e.g. see AAMT and AiGroup 2014; Binkley et al. 2012; FYA 2017; Gravemeijer et al 2017; Griffin et al. 2012; Hoyles et al. 2010; NCTM, 2017; P21 2016; Pellegrino et al. 2012; Wake 2015).
In their 2017 review of mathematics education for the 21st century, the National Council of Teachers of Mathematics (NCTM) in the USA (2017) argued that mathematics is at the heart of most innovations in the information economy. They saw mathematical and statistical literacy as needed more than ever to filter, understand, and act on the enormous amount of data and information that we encounter every day.
What numeracy and maths skills?
One of the key outcomes of such research is that the mathematics, or numeracy, related tasks that people undertake involve much more than basic arithmetic skills and straightforward procedural competence. For example, in an Australian project undertaken by practising maths teachers for the Australian Association of Mathematics Teachers (AAMT) and funded by the Office of the Chief Scientist, Quantitative Skills in 21st Century Workplaces, the research identified and analysed the gaps between young peoples' numeracy skills and the expectations of 21st century workplaces. Mathematics was considered extremely important in all of the companies involved, and changing work practices were found to be generating new demands for mathematical skills, particularly in areas such as efficiency, innovation and Quality & Continuous Improvement.
The application of mathematics in the workplace is not straightforward and goes well beyond a command of ‘core’ mathematical content. Workers perform sophisticated functions which require them to be confident to use mathematical skills in problem-solving situations and to see the consequences of the mathematics related procedures. (AAMT & AiGroup, 2014)
The project found that workers needed a blend of the following key skills:
- ability to recognise and identify how and when mathematics is used in the workplace
- an understanding of mathematical concepts, procedures and skills
- an understanding of the kinds of practical tasks they need to perform
- the strategic processes they should be able to use in using and applying mathematics.
Although the skills observed appeared to be fundamental, it is their use and application in work contexts that is not straightforward (AAMT & AiGroup, 2014).
The critical connections between numeracy and mathematics
What is meant by the term numeracy, and what is its relationship to terms such as quantitative or mathematical literacy, and how does it connect to the world of (school) mathematics?
The term numeracy is used in some countries, like in Australia, however, other expressions are used as well, for example, mathematical literacy or quantitative literacy. This is further complicated by the lack of an equivalent term in some languages. Moreover, what is meant by numeracy also varies between countries, and can vary between how it is understood when applied to school education compared to within adult education. However, increasingly numeracy now refers to the capability to use a range of mathematical and statistical knowledge and skills to solve problems in the real world for a purpose.
Numeracy is not the same as mathematics, nor is it an alternative to mathematics. Today's students need both mathematics and numeracy. Whereas mathematics asks students to rise above context, quantitative literacy is anchored in real data that reflect engagement with life's diverse contexts and situations. (Steen, 2001, p.10)
One underpinning connection and difference that needs to be acknowledged and highlighted is between numeracy and mathematics as a domain of knowledge. The meaning of numeracy used here encompasses the need for individuals to be able to understand, use and apply mathematical (and statistical) skills and knowledge.
Thus, to be considered numerate, it is expected that people will need to know some mathematics, and be able to apply that mathematics within a real-world context.
Why this matters
With 21st-century life and workplaces requiring more critical, reflective mathematical reasoning skills and the ability to interpret and understand a broader range of data and processes, our school leavers need better numeracy and maths skills than ever before.
Hence schools need to teach both numeracy and mathematics well—within maths classes by maths teachers and also as part of numeracy across the curriculum.
Critical element to numeracy
The issue of the need to be critical, and use reflective mathematical reasoning skills is now identified as a key skill and is routinely included in many numeracy frameworks as will be shown below. An emphasis on critical reflection or interpretation has mainly arisen out of adult numeracy research and development, where, for example, Johnston (1994) argued that
To be numerate is more than being able to manipulate numbers, or even being able to 'succeed' in school or university mathematics. Numeracy is a critical awareness which builds bridges between mathematics and the real-world, with all its diversity (p. 34).
Key terms and definitions
The above views about the need for numeracy and maths skills is recognised in Australian curriculum. For example, the Australian Curriculum: Mathematics (V 8.4) includes numeracy as one of the General Capabilities that must be observed while teaching and learning mathematics stating:
… students become numerate as they develop the knowledge and skills to use mathematics confidently across other learning areas at school and in their lives more broadly. Numeracy encompasses the knowledge, skills, behaviours and dispositions that students need to use mathematics in a wide range of situations. It involves students recognising and understanding the role of mathematics in the world and having the dispositions and capacities to use mathematical knowledge and skills purposefully.
Similarly, the Victorian Curriculum and Assessment Authority defines numeracy as:
Numeracy is the knowledge, skills, behaviours and dispositions that students need in order to use mathematics in a wide range of situations.
Internationally, the related term mathematical literacy is used in the OECD's Programme for International Student Assessment (PISA). It is defined as:
… an individual's capacity to formulate, employ, and interpret mathematics in a variety of contexts. It includes reasoning mathematically and using mathematical concepts, procedures, facts, and tools to describe, explain, and predict phenomena. It assists individuals to recognise the role that mathematics plays in the world and to make the well-founded judgments and decisions needed by constructive, engaged and reflective citizens. (OECD, 2019, p. 75)
It should be noted that at the conceptual and implementation level, numeracy and mathematical literacy are very closely related constructs in terms of their core, underlying ideas (e.g., see Gal & Tout, 2014).
As with the above definitions, most 21st century descriptions and definitions of numeracy now refer to the need to use and apply a range of mathematical knowledge.
It is important to note therefore that numeracy is not seen as synonymous with a minimal or low level of mathematical knowledge and skills—but covers a broad spectrum of skills and knowledge. Sometimes numeracy can be viewed as a lower level skill, simply being about numbers and arithmetical operations.