In the Critical Connections between Numeracy and Mathematics monograph that is part of a series produced by the Victorian Department of Education and Training, I have described how critical it is for students in the 21st Century to have both numeracy and mathematics knowledge and skills.
I believe that numeracy and mathematics are intrinsically connected and both are needed in our ever-changing, globalised and technological world. This has been exaggerated by the current environment of COVID-19 and its dependence on understanding and interpreting quite sophisticated statistics and data, amongst a range of other mathematical information.
Different but mutually beneficial and critical
My monograph 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. Evidence shows that investing in the numeracy skills of young people has significant benefits – for the individual, for society and for the economy.
However, the reality is, many children (and adults) who have studied mathematics education in school are unable to easily transfer formal mathematical skills and apply them to tasks that are embedded in authentic tasks or resemble real-world contexts. In parallel with this, increasingly research is showing that life and work in the 21st Century is requiring higher levels of mathematics and numeracy of its citizens. Our school leavers need better numeracy and maths skills than ever before.
After many years working in numeracy and mathematics education locally, regionally, nationally and internationally, I have often been surprised how some maths educators believe that numeracy doesn't count, especially in comparison to the views about the value and importance of mathematics. However, evidence shows that both young people and adults need to have both sets of skills and knowledge – numeracy and mathematics are different, but mutually beneficial and critical. Hence the critical need to connect the two, and not ignore either. To quote one of my favourite authors:
...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)
In the monograph, I reflect on what we mean by numeracy, and what its relationship is with 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. Increasingly, numeracy now refers to the capability to use and apply a range of mathematical and statistical knowledge and skills to solve problems in the real world for a purpose.
Thus, to be considered numerate, it is expected that people will need to know some mathematics, and be able to use and apply it within a real-world context. One key element about viewing mathematics and numeracy as critical partners is that numeracy therefore involves much more than just basic arithmetic skills and straightforward procedural competence.
There are many models and definitions now that reflect this view of numeracy, such as in the Australian Curriculum and by the Victorian Curriculum and Assessment Authority (VCAA). One such comprehensive description is illustrated in Figure 1. This model incorporates four dimensions of settings/contexts, mathematical knowledge, tools, and dispositions that are embedded in a critical orientation to using mathematics. These dimensions are described more fully in other publications (e.g., Goos et al., 2014; Geiger et al., 2015).
Figure 1: Numeracy in the 21st Century (Goos et al., 2014; Geiger et al., 2015)
The model views numeracy as having the capacity to use mathematical knowledge in a range of contexts, both within schools and beyond school settings; to have positive dispositions to maths and the confidence, willingness and preparedness to flexibly use mathematical approaches and knowledge to engage with life-related tasks; to use physical materials and tools (models, measuring instruments), representations (symbol systems, graphs, maps, diagrams, drawings, tables) and digital tools (computers, software, calculators, internet) to mediate and shape the mathematical actions and thinking. And the model suggests there is a need for a critical orientation that enables the use of mathematical information to make decisions and judgements, and to argue and challenge.
So numeracy is the skill to be able to use and apply mathematics within a context and for a purpose. Schools need to teach both numeracy and mathematics well. Numeracy needs to be explicitly addressed and taught within maths classes by maths teachers and also as part of numeracy across the curriculum.
Strategies to address the challenges
So, how do we go about addressing this challenge of teaching numeracy well? The importance of numeracy across the curriculum is being addressed, as with the numeracy General Capability in the Australian Curriculum, and in related work and research about the training of all teachers in numeracy. However, there is the need for more work, and to extend this approach.
In the monograph I have named three specific challenges, and hopefully provided some ideas and activities for schools and teachers to reflect on and address each. This issue of improving student's numeracy skills overlaps with many of the other topics covered in the monograph series, such as maths anxiety, engaging families in maths education, gender issues, highlighting the M in STEM, and Big ideas in Mathematics.
The three specific challenges I name are:
- the disconnect between school maths and the real world, including the world of work;
- a lack of awareness and knowledge about the way to teach numeracy; and,
- the issue of word problems in maths.
The first challenge is about teachers implementing approaches whereby they engage their students in real-world, authentic numeracy tasks and activities. A key to being numerate is to be able to start from a real-world problem or situation and excavate the maths and formulate it as a mathematical problem to solve. This implies we need to take the students out into the real world to do some mathematical investigations, or, alternatively, at least bring the real world into the maths classroom.
Second, and related to the above, because of a disconnect between school maths and the real world, including the world of work, the challenge for school teachers of maths is about how to see and incorporate numeracy as an integral part of their teaching. Numeracy needs to be explicitly taught – leaving it to providence will not guarantee success. And because of the critical connections between numeracy and mathematics, it cannot be solely left to non-mathematics trained teachers to teach numeracy.
The third challenge I pose concerns the use of traditional school-based mathematical word problems, which often disregard and challenge students' sense making and only help serve to distance students from the real world, and the usefulness and value of mathematics. It is critical in the teaching of numeracy and mathematics that a key value in mathematics is about its relationship with real world things – whereas word problems often do the opposite.
In the monograph I suggest two key ways that schools can support the improvement of the numeracy outcomes for their students. One relates to better supporting all teachers in the school about how to enhance numeracy across the curriculum. The second relates to how teachers of mathematics can better engage with the world of numeracy and support their students to become numerate in their lives at school, out of school and be better prepared for the world of work when they do graduate from school.
The latter approach recommended is to integrate the actions below into classroom teaching and learning:
- use a problem solving, investigative, open-ended approach – use real texts and real situations – make connections between maths and the real world;
- start from the real world – teach students how to identify and extract the maths from the messy, real-life situations that they are likely to face;
- and a key part of this is to make the maths explicit, and then, when the need arises, or gaps in knowledge appear, teach the maths knowledge that is required: ‘just in time, not just in case'.
I hope that the engagement activities I have suggested in the monograph, along with the associated resources and readings, will support you and your school community to better address the numeracy (and mathematics) needs of all your students.
The Critical Connections between Numeracy and Mathematics monograph, written by ACER Senior Research Fellow Dave Tout, is due to be published later this month. This monograph, and all the others in the series, will be available to access on the Victorian education department's website, via this link.
Dave Tout has written a 10-part series for Teacher on real-world maths. You can access all the articles in this series by visiting his author page.
Geiger, V., Goos, M., & Forgasz, H. (2015). A rich interpretation of numeracy for the 21st century: A survey of the state of the field. ZDM Mathematics Education, 47(4), 531–548.
Goos, M., Geiger, V., & Dole, S. (2014). Transforming professional practice in numeracy teaching. In Y. Li, E. Silver, & S. Li. (Eds.), Transforming Mathematics Instruction: Multiple approaches and practices (pp. 81-102). Springer. https://doi.org/10.1007/978-3-319-04993-9_6
Steen, L. (2001). Mathematics and Numeracy: Two Literacies, One Language. The Mathematics Educator, 6(1), 10-16.
Thinking about your own context: What are your school priorities for numeracy and mathematics? How are you connecting maths and the real world in your classrooms? Do you use problems that reflect the real-life situations that your students are likely to face?