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Communicating, thinking, and tools: Exploring two of the key competencies

Jane McChesney and Bronwen Cowie
Abstract: 

Jane McChesney and Bronwen Cowie explore the key competencies of thinking and using language, symbols, and text in terms of Mathematics and Statistics, Science, and Technology. What do these competencies mean in this context, and how do they relate to each other?

Communicating, thinking, and tools:
Exploring two of the key competencies

Jane McChesney and Bronwen Cowie

Abstract

Of all the key competencies, thinking and using language, symbols, and texts are the most closely connected to the learning areas of The New Zealand Curriculum (Ministry of Education, 2007). In this paper we explore these competencies from different perspectives, with a focus on three of the learning areas: Mathematics and Statistics, Science, and Technology. We explore the competency of thinking within the context of disciplinary knowledge, and discuss using language, symbols, and texts from a “cultural tools” perspective. We end by bringing these two competencies together as we attempt to address issues relating to what counts as knowledge and knowing in these disciplines.

Introduction

As a policy document, a curriculum signals learning that educators consider important and worthwhile. The introduction of a new curriculum document is an opportunity not only for teachers to revisit current priorities, practices, and curriculum materials, but also to consider future directions within their educational contexts. Although this process typically contributes to changes in current practices, it can also bring new terminology and meanings, and present different perspectives on learning.

One of the more significant shifts in emphasis signalled in The New Zealand Curriculum (Ministry of Education, 2007) is the inclusion of five key competencies. These are underpinned by an emphasis on lifelong learning and posited as being “crucial to sustained learning and effective participation in society” (p. 4). In the section detailing the key competencies, the ministry notes that while the competencies are key to learning in each “learning area”, they are not in themselves separate or stand-alone (p. 12).

This article presents possible relationships between the key competencies of thinking and using language, symbols, and texts and the learning areas of mathematics (now Mathematics and Statistics), Science, and Technology. We use these two key competencies as a means to reflect on and re-examine some issues associated with the teaching and learning of these three school subjects. The question we are interested in is this: What might these two key competencies mean in terms of the subject learning areas of Mathematics and Statistics, Science, and Technology? Our intention is to suggest potential tensions or dilemmas, and to raise further questions as contributions to ongoing discussions of the New Zealand curriculum.

Beginnings: Engaging with the competencies

It seems reasonable that teachers will initially engage with the competencies in terms of their past and current experiences as they seek to develop localised interpretations and enactments of them (Ministry of Education, 2007). Using language, symbols, and texts in their broadest manifestation is likely to be the competency least familiar to teachers (Hipkins, 2006). This key competency “is about working with and making meaning of the codes in which knowledge is expressed” (Ministry of Education, 2007, p. 12), and involves language, symbols, and texts that are:

systems for representing and communicating information, experiences and ideas. People use language and symbols to produce texts of all kinds: written, oral/aural, and visual; informative and imaginative; informal and formal; mathematical, scientific, and technological. (p. 12)

Aspects of this competency fall within a definition of literacy in an information- and technology-rich world, as discussed by Gee (2003). He defines literacy as “any set of practices that recruits one or more modalities (e.g., oral or written language, images, equations, symbols, sounds, gestures, graphs, artefacts etc.) to communicate distinctive types of meanings” (p. 18). Such a focus can, however, set up a tension between an emphasis on subject content and an emphasis on the learning processes, thinking tools, and social practices of the disciplines that will help students construct and evaluate knowledge in an information-rich world. This concern aligns with Gilbert’s (2005) contention that the “world outside education is increasingly valuing the ability to learn, knowing how to learn, how to keep learning, how to learn with others [italics original], over the ability to master specific bits of knowledge” (p. 67). The debate over the relative merits and value of content compared with learning processes is a long-standing one. It therefore seems timely to ask if, and how, a focus on key competencies might offer something new to this debate.

The key competency of thinking, the second focus of this paper, is likely to be the one most familiar to teachers. Previously, the Ministry of Education established it as an aspect of the essential skill of problem solving (Ministry of Education, 1993), and has also explored it in discussions relating to thinking strategies and metacognition in various ministry documents focusing on quality teaching (see, for example, Alton-Lee, 2003; Hipkins et al., 2002). Hipkins (2006) notes that thinking has a role that cuts across all competencies and is intimately linked with knowledge generation. Within The New Zealand Curriculum, thinking is described as an act that involves creative, critical, and metacognitive processes necessary to make sense of information, experiences, and ideas. The ministry not only contends that these processes can be applied to purposes such as developing understanding, making decisions, shaping actions, and/or constructing knowledge, but also asserts that “intellectual curiosity is at the heart of this competency” (Ministry of Education, 2007, p. 12).

In regard to mathematics, science, and technology, the ministry regards creative, critical, and metacognitive thinking as essential to learning these subjects, as is the development of a high level of awareness of the nature of thinking underpinning any decisions. Being able to step back from a situation and answer questions such as “What is happening?”, “Why is it happening?”, “Should it be happening?”, and “How could it be done differently?” relies on sophisticated thinking skills. For example, within a technology context such thinking is essential for making informed decisions that are based on both ethical and functional grounds, thereby allowing for an understanding of fitness for purpose, as well as explorations of the fitness of any stated purpose.

In interpreting this competency, teachers and schools in New Zealand are likely to be influenced by programmes for thinking already evident in the country’s classrooms (Cowie, 1995).1 These approaches to thinking, however, could be described as general rather than subject specific, and raise questions about the similarities and differences between general and subject-specific thinking strategies. Also, the different learning area descriptions indicate that intellectual curiosity can be exercised in diverse ways, with different kinds of focus and distinct purposes within the different learning areas. These concerns point to another important issue for discussion and debate: What might it involve to think mathematically or statistically, or to think scientifically, or to think technologically?

Linking to the learning areas

On first impressions the achievement objectives of the learning areas of Mathematics and Statistics, Science, and Technology might be taken as a reduction and re-assembling of familiar curricular disciplinary content, but with a greater emphasis on the nature of the disciplines. This shift in emphasis is not inconsequential because it is likely to put long-held perceptions of the nature of different disciplinary practices under close scrutiny. One of the current tensions relating to how the disciplines are conceptualised centres on whether they comprise a situated set of purposeful practices or a body of stable knowledge that might be transmitted (Kelly, Luke, & Green, 2008; Sfard, 1998). Recent studies of the ways mathematicians, scientists, and technologists work have found that these professionals work together to generate and validate knowledge through a range of agreed practices. They use not only discipline-specific technical verbal languages, but also a range of mathematical, graphical, diagrammatic, pictorial, and a host of other modalities of representation (Lemke, 2000). These disciplinary studies support a shift in focus from student cognition to student ability to communicate in the language of a particular community, and to act according to its norms.

Lemke also points out, in regard to science and mathematics, that being proficient in the discipline involves the ability to move across the different modalities used to generate and represent ideas:

… scientific concepts are articulated across these media of representation. What it means to be able to use a scientific concept, and therefore to understand it in the way that a scientist does, is to be able to fluently juggle with its verbal, mathematical, and visual-graphical aspects, applying whichever is most appropriate in the moment and freely translating back and forth among them. (Lemke, 2000, p. 248)

We would propose that a similar statement applies to technology: learning and knowing, whether an individual or social act, necessarily invokes the use of those representations and modes to which a student has access, and with which they are familiar. When seen this way, as Vygotsky (1978) has proposed, learning and knowing within a discipline involve developing proficiency with the representational means used within the subject. Students become increasingly familiar with and proficient at selecting and using representations that are the most apt in a particular circumstance for signifying their meanings (Kress, 2000). Embedded within this work on the disciplines are two questions: “What is the most apt resource, and why?” and “How does this choice vary across contexts and purposes?”

Bringing together thinking and using language, symbols, and text

For us, the word thinking evokes the sculpture of Rodin’s The Thinker— a person sitting alone, gazing into space, presumably contemplating images in his (or her) head. But thinking also evokes for us our experiences of vigorous discussion and debate supplemented by drawings, reference to research papers, and model making. This latter view fits with Sfard’s (2001) notion of thinking-as-communicating. She draws on Vygotsky’s work to argue that thinking is nothing but our communicating with ourselves. She argues that thinking is not necessarily inner or verbal communication, but a social process and an active part of generating and validating knowledge, in which a range of representations serve as communication-mediating tools. The exceptional reliance that mathematical discourse has on symbolic artefacts as communication-mediating tools is central to her case for regarding communication not simply as an aid to thinking, but equivalent to thinking itself. This notion collapses together the two key competencies because thinking-as-communicating is thinking-using-tools; that is, thinking using language, symbols, and texts.

Over time, disciplines have “created specialized discourse, signs and symbols, ways of representing knowledge, and ways of thinking and inquiring that come to count as knowledge” (Kelly et al., 2008, p. viii). Disciplines therefore have different focuses, different relational structures, and different means of generating and validating knowledge; that is, different ways of thinking. Sfard (2001) also suggests that thinking-as-communication is regulated by the “meta-rules” of the discipline, where meta-rules define what counts as authoritative knowledge and how this knowledge is validated. Coming to know about the “rules of the game” is therefore a critical element of authentic learning in subject disciplines (Gilbert, 2005). The rules of the game are aspects of disciplinary knowledge, often not explicitly set out for learners in school but rather embedded within valued classroom practices and ways of working. The issue for teachers, students, and researchers is how to make these disciplinary rules of the game explicit in meaningful ways.

Conjecturing about the generative potential of thinking-as-using-tools

Within a thinking-as-using-tools perspective, aspects of subjects such as symbols and texts can be reconceptualised as cognitive tools. In mathematics, for example, (cognitive) tools include symbols such as the decimal notation of numbers, and texts such as equations and expressions, graphs, tables, and diagrams. Symbols and texts are recognisable as representations of mathematical artefacts, with numbers representing quantities, equations and graphs representing mathematical relations, and so on. Similarly, language in the form of mathematical terminology such as decimal, triangle, or volume, represents specific meanings for (mathematical) entities. Language, symbols, and texts are therefore tools that encompass a range of representations; that is, multiple modalities.

Identifying subject artefacts as tools is only one aspect of the potential contribution of a tools perspective. The metaphor of a tool implies “making things easier”, because physical tools such as a spoon, spade, or scissors offload effort in human activity and offer greater precision and efficiency. Similarly, a cognitive tool is a representation that offloads mental effort (Pea, 1993). The offloading of effort relates to the properties of a tool, and these are known as “affordances”. According to Pea (1993), an affordance refers to “the perceived and actual properties of a thing, primarily those functional properties that determine just how the thing could possibly be used” (p. 51). For instance, a chair affords sitting and a pen affords writing. In a similar way, mathematical notation, such as numbers and symbols, involves visual representations that afford specific information about mathematical entities. The affordances of numerical representations have been noted by Hipkins (2006), who discusses place value notation as an example of how a symbol “encodes several separate symbols and symbol systems” (p. 24). In other words, a representation re-presents and reorganises symbolic information, thereby affording resources for reasoning in further mathematical activity (McChesney, 2004).

It is important that we not overlook the verb “using” in the key competency because it implicates “language, symbols, and texts” as tools-in-activity. The phrase “tools-in-activity” suggests that using a tool involves recognising and activating a tool’s affordances that are suitable for the activity context. In the case of mathematics, for example, symbols and texts afford the knowledgeable user a choice of representations that are more or less useful for different contexts. Recognising the affordances of a tool plays an important role for anyone adapting the design of a tool for a particular purpose or context, as required in technological practice. Similarly, coming to know about the affordances of a cognitive tool involves knowing about the properties of the tool, recognising these properties of the tool-in-context, and activating the properties as affordances of the tool within activity (Greeno, 1991).

Another consideration is that the tools of a culture carry important aspects of prior collective meaning (Wertsch, 1998). Today’s learners were not privy to the often protracted development of many of the cultural tools of the school curriculum, and they engage with these tools in terms of their contemporary social and cultural contexts. The affordances of any tool are inextricably linked to the social and historical contexts in which it has come to have meaning and value for the user. Consequently, teachers have an important role in sensitising students to the affordances of different tools, and in a crowded, outcomes-based curriculum, teaching about meanings and purposes of the tools can easily be neglected. For their part, today’s learners invent new language and other tools that represent entities of importance in their worlds, such as their rapid, adaptive, and collectivised generation of new tools in ICT environments. Such developments pose a challenge to educators about what might serve as a contemporary curriculum and as effective teaching, a challenge that has yet to be addressed in New Zealand and internationally.2

Challenging our own thinking

The question we set out to consider in this paper was: What might the key competencies thinking and using language, symbols, and texts mean in terms of the subject learning areas of Mathematics and Statistics, Science, and Technology? We were interested in the tensions, dilemmas, and opportunities that emerged when we used these competencies as a lens to look at the disciplines with which we are familiar and to which we are committed, and then used the disciplines as a lens to look back at the competencies. Somewhat to our surprise, we have ended up making a case for thinking-as-using-tools, a position that stresses possible relationships between the two competencies.

In order to make this idea more accessible to teachers and students, we propose that a more useful term than tools might be resources (Newfield, Andrew, Stein, & Maungedzo, 2003). Resources for thinking and communicating are provided by particular properties or affordances of tools. “Being attuned to and activating affordances” can be rephrased as “resourcefulness”; that is, noticing, recognising, recruiting, and adapting the resources of a tool for particular contexts and purposes. In this way, the resources metaphor can encompass the use of language, symbols, and texts for communication and thinking, or thinking-as-communicating.

The disciplines of mathematics and statistics, science, and technology value different kinds of inquiry and different notions of how content domains might be modelled or represented. Within each discipline, representational tools are activated as forms of evidence and as communication devices. Also, although tools are activated in any evaluation of this evidence, this always occurs in relation to the “epistemic commitments” of the disciplines (Lehrer & Schauble, 2006, p. 380). Notions of what are valued representations and representational practices in a discipline may be a useful entry point for re-examining the achievement objectives of the learning areas.

We suggest that the nature of valued disciplinary practices is fertile ground for further discussion and debate, and considering thinking-as-using-tools will be a crucial element in this discussion. In what ways could thinking-as-using-tools contribute to a debate about the nature of the disciplines, and what are the implications for a school curriculum? How might thinking with tools contribute to how teachers and learners engage with the valued positions, practices, and tools of a discipline? Closer examination of valued disciplinary practices will also involve consideration of the nature and roles of the three other key competencies through notions of participation, managing selves, and working with others. This paper is a small contribution to the ongoing discussion of the following questions: What counts as learning? What learning counts? What counts as knowledge? And what knowledge counts?

Notes

1&;&;Hipkins (2006) mentions a range of popular approaches, such as “Habits of mind”, “Three story intellect”, and de Bono’s “Six thinking hats” (p. 17).

2&;&;Review of Research in Education has recently published special issues: Rethinking Learning: What Counts as Learning and What Learning Counts (2006) and What Counts as Disciplinary Knowledge in Educational Settings: Disciplinary Knowledge, Assessment, and Curriculum (2008).

References

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The authors

Jane McChesney teaches in secondary mathematics education, professional studies, and master’s courses at the College of Education, University of Canterbury. She was a secondary teacher of physics, science, and mathematics before her involvement in teacher education. Her research interests include social practices, tools, and classroom interactions in mathematics lessons.

Email: jane.mcchesney@canterbury.ac.nz

Bronwen Cowie is director of the Wilf Malcolm Institute of Educational Research at the University of Waikato. Her research interests include assessment for learning, interaction in science and technology classrooms, and the role of ICT. She was a secondary teacher of physics, science, and mathematics before her involvement in educational research.

Email: bcowie@waikato.ac.nz