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The Programme

The Mathematical Literacy Topic Study Group 23 at ICME-13 was organized around three key themes that drew from emerging findings in the literature related to discussions about the Mathematical Literacy field:

  • Conceptual maps and gaps: What topics, conceptual models, or theories should/could be considered in teaching about or for mathematical literacy? Why? When, for whom, and how should we promote mathematical literacy? What needs exist that notions of mathematical literacy might address?

  • The ‘place’ of mathematical literacy: How are notions of mathematical literacy figured into curricula, and in teachers’ identities, beliefs, attitudes and practices, in teacher education, in learning materials, in local/national assessments, etc.? What tensions and challenges emerge? What dis/continuities exist between teaching of mathematical literacy in school—and in tertiary and adult contexts?

  • What can large and smaller-scale studies tell us about mathematical literacy?: How do empirical results from studies with differing scales and foci (e.g., on skill transfer, teachers, literacy/language aspects of applied math tasks, inter/national surveys) inform our thinking about the conceptualization, teaching, learning, or assessment of mathematical literacy? Given such results, should mathematical literacy be directly taught, or be integrated across curriculum subjects, and how? Or can it emerge as a by-product of teaching “regular” mathematics? What evidence do we have about possible (re)solutions?

Papers and discussions related to these themes were intended to stimulate discussion about key directions for future research related to mathematical literacy. Overall, our TSG included two invited plenary presentations followed by two discussant reactions, eight regular (invited) papers and six short oral communications, nine posters, and extended general discussions during all sessions which were moderated by the team members.

Invited plenary papers were presented across the first two sessions. The first plenary, presented by Geiger, Goos & Forgasz, followed from their (Geiger, Goos, & Forgasz, 2015) editing of a ZDM Journal issue focused on mathematical literacy. This plenary provided a historical overview of the range of terminology and the capabilities and facets commonly associated with these terms. As such, this provided participants with an introduction related to the first theme, and an anchor for a range of submissions related to this theme. Among these related papers, North used Dowling’s theorizing of ‘gaze’ to consider what a mathematical literacy gaze might be comprised by, and linked his theoretical development to a discussion of possibilities and critiques related to the Mathematical Literacy curriculum in use in the South African post-compulsory phase. Vohns discussed possibilities and avenues for the development of reflective knowledge within mathematical learning, and arguing that this would be important to fulfilling requirements for a mathematically literate orientation. Developing notions of particular topics within the broader notion of mathematical literacy were seen in Engel, Gal & Ridgway’s incorporation of citizenship into earlier work focused on statistical literacy with attention to ‘civic statistics, and also in Chen’s attention to spatial literacy. Askew, in his discussant response to Geiger et al’s plenary presentation, presented a range of alternatives for thinking about the relationship between mathematics and mathematical literacy, and raised attention to how tasks and how responses to tasks were evaluated often embodied different conceptualizations of this relationship. His presentations also raised questions about whose responsibility it is to develop some aspects seen as central to conceptualizations of mathematical literacy (e.g., interpretation, critical reflection) that seem to fall outside some conceptualizations of mathematics.

In Session 2, Klieme presented a plenary input drawing from his experience within the PISA Mathematical Literacy international assessment analysis team. He focused particularly on the somewhat under-emphasised aspect of comparisons of learning environments across participating nations. In his presentation he shared both the ways in which learning environments were conceptualized within the PISA data gathering process (based on ‘Opportunity to Learn’, ‘Teaching Practices’ and ‘Teaching Quality’), and cross-cultural comparisons that were possible to draw from their dataset. Of particular interest in his presentation was evidence of the culturally situated clustering of several factors that made a difference but in particular geographic regions, contrasting with the underpinning view in PISA of the ‘universality’ of the items selected for international assessments. Jablonka, in her discussant response to Klieme’s plenary presentation, emphasized this disjuncture, while focusing also on the nature of the PISA items and the largely mathematical conceptualizations underlying their formulation. Klieme encouraged discussion, in the multi-national participation within the TSG, of whether participants viewed the items he had shared as fitting with national understandings of mathematical literacy and/or mathematics, as well as asking participants to reflect on his learning environment findings with reference to different national contexts. His talk was related to Theme 3, but the focus on learning environments within the presentation allowed for links with Theme 2’s attention to teaching practices as well.

A range of papers attended to issues related to mathematical literacy teaching and learning, with paper presentations occurring in Session 3 and in an adjoining Oral Communication session, and supplemented by the poster presentations. Given space restrictions we can discuss only some illustrative examples: Bennison presented examples of the ways in which mathematical literacy could be seen as a cross-curricular enterprise, while noting too, through a focus on ‘boundary objects’ some of the complexities that needed to be negotiated in taking on mathematical literacy as a multi-disciplinary goal. Winter (2016) echoed some of these complexities in his study of pre-service teachers’ work with contextual tasks. His data pointed to ways in which the notion of mathematization, developed within Realistic Mathematics Education in the context of mathematics, might need extending to take on board the orientations and goals of mathematical literacy. Curriculum development to take on board mathematical literacy orientations were also foregrounded in presentations from Turkey (Gurbuz) and England (Lee).

In Session 4, the emphasis was on discussion within TSG23 on key issues and points of contention that had emerged across the discussions in the earlier sessions. A key discussion related to a focus on ‘mathematical literacy tasks’ and how task selections made either by teachers, assessment designers or researchers can provide an important and under-researched avenue for exploring conceptualizations of mathematical literacy in ‘bottom-up’ ways, rather than the ‘top-down’ ways that have tended to predominate in approaches that work from definitions and curricular specifications. A potentially productive route that was discussed related to whether descriptors and/or criteria could be developed for mathematical literacy tasks that would help to disaggregate the views of mathematical literacy that they operationalized, and then the potential in this approach for evaluating the extent to which assessments either diverged from, or only partially reflected the mathematical literacy goals and definitions that they purported to cover. An initial list of criteria that emerged from the Session 4 discussion across the participants were as follows:

  • Decision making or coming to a judgement/interpretation/understanding the decisions of others/forming an opinion relating to personal, social and political actions or activities (transport/environment/tourism/advertising),

  • Use of evidence as the basis for decision making,

  • Tasks designed to `inform´ the public about an issue, including consumers,

  • Supporting ´literate´ reading of text for improving participation in personal and civic life (local and global issues), at work and in lifelong learning,

  • Should ML support preparation for employment? Can this be taught in a ´generic´ way? (e.g. budgets/allocation of resources),

  • Critique/challenge from a basis in evidence and interpretation, and for influence.

The closing discussion included a focus on whether some contexts or situations would or should be privileged over others if mathematical literacy was conceptualized as a ‘life-orientated’ competence rather than a ‘knowledge-oriented’ subject. Picking up on the learning environments focus, there was broad agreement on the need for more ‘open’ pedagogic relationships if the goals of mathematical literacy were to be realized.

In conclusion, our sense of the progress of the Mathematical Literacy TSG23 was that the discussions around the plenary papers and discussant responses, coupled with the paper and poster presentations, highlighted some key under-represented and under-theorised areas in the ongoing debates around notions related to mathematical literacy. We see a need to increase attention in teaching, teacher preparation and professional development, assessment design, and future research to the unique aspects of mathematical literacy (numeracy). For example, more attention is needed to ‘use, apply and interpret’ situations where some mathematics may be a useful part, but only a part, of the toolkit that can be brought to bear to understand a terrain and/or solve problems within it was central to the discussions. Askew problematized this notion of mathematical literacy with the following diagram and an accompanying question, reproduced below:

This question and the broader discussion around it and around the three key themes that drove the design of our TSG start to get at the most important (http://dictionary.cambridge.org/dictionary/english/important) or basic (http://dictionary.cambridge.org/dictionary/english/basic) aspect of what it might mean to focus on mathematical literacy in ways that are linked to, but not subsumed by, mathematics. Our sense, as co-chairs of TSG23 is that this direction, with the strands related to task design and learning environments noted above, indicates some promise for debates and further development in the coming years. As a professional community we should furnish mathematical literacy with a more distinct identity and a gaze that contains some aspects that are independent of mathematics, while retaining some overlaps, in order to better serve learners as well as the needs of society at large.