Ogata, H. et al. (Eds.) (2015). Proceedings of the 23 rd International Conference on Computers in Education. China: Asia-Pacific Society for Computers in Education Non Numerical Aspects of School Mathematics Khalid KHAN * & Jon MASON International Graduate Centre of Education, Charles Darwin University, Australia *khalid.khan@cdu.edu.au Abstract: In this short paper, we describe issues resulting from a lack of clarity in understanding the nomenclature of numeracy in mathematics education at the school level and consider some of the underlying foundational structures of mathematical thinking. The purpose of the paper is to open a conversation about shifting the focus from the narrower conceptual boundaries concerning numeracy by considering theoretical perspectives that describe mathematical thinking as a form of intelligence on the one hand, and as a skill within the paradigm of 21 st century skills, on the other. We identify a number of questions to be considered in teaching mathematics and specifically in contexts where digital technology is utilised. Keywords: STEM, mathematics, digital technology, sense-making, 21CC 1. Introduction When instructions for a task are too directive, then it may be possible to carry them out without actually encountering the intended ideas behind the task. (Mason & Johnston-Wilder, 2006, p. 29) As opposed to solving an issue or problem using rules, a key purpose of mathematics education is to enhance student cognitive ability to connect the non-numerical aspects of the process and enable application of this learning in other situations. It is this aspect of mathematics, however, that is often not effectively conveyed, either explicitly or implicitly, at the school level of the discipline. The purpose of this paper is to provoke discussion that could assist in shifting focus from numeracy – a term given far too much emphasis as a proxy for basic mathematical ability – to other aspects of cognitive facility associated with mathematics at the school level. Intended learning may fail to be achieved for many reasons and if the purpose of the mathematical tasks is confined or limited to ‘solving’, rather than ‘learning from solving’, it is likely that learners may neither learn nor enjoy engaging with the problem. Focusing merely on the numerical aspects of mathematics and problems does not create opportunities for students to generalize the situation in order to apply the mathematical learning in other contexts. Differences in perceptions between teachers and students regarding the purpose of a task may also exacerbate non-effectiveness in the performance of the tasks. As Stein (1987) has famously pointed out, the intention to ‘teach thinking’ can easily turn into a set of instructions so that learners do not have to think. The main purpose of the paper is to provide an overview of issues resulting from an over emphasis upon numeracy in school mathematics education and to consider some of the underlying foundational structures of mathematical thinking. Conveying a sense of the range of thought processes available when working within a problem can help children engage with the logic and ideas which is arguably more at core of mathematics teaching. Doing so could bring the focus back from the algorithmic processes, numerical memorization, and rote learning aspects to a richer palette of sense-making, abstraction, and inquiry. In the words of Anderson (2001): “In trying to connect mathematics with what is learnable, we have disconnected school mathematics from what is genuinely useful.” Now that we are mid-way through the second decade of the 21 st century it is also timely to consider how numeracy and mathematics education relate to the discourse on 21 st century skills or 21 st century competencies (21CC). This discourse has arisen largely as a consequence of ongoing innovation in digital technology and the proliferation of networks (global and local) as an organizing 477