School mathematics word problems framed in real world contexts play a mediating role between mathematics per se and real world situations, suggesting and in most cases creating templates for “reading” mathematically the objects and events of the world. In such a context the role and function of mathematics word problems may be understood from the viewpoint of what Goffman (1986) calls the “frame” of a (social) situation. Frame is primarily a psychological concept that refers to the cognitive process wherein people bring to bear background knowledge to interpret an event or circumstance and to locate it in a large system of meaning (Oliver & Johnston, 2000). In Goffman’s perspective, the concept “frame” implies that there is a definition of a situation which the participants share and most of them take for granted. A frame can be seen as the participants’ shared response to the question “what is going on here” (Goffman, 1986, p. 18), which means that they have construed events, actions or utterances in line with the frame which they perceive as relevant.
Frames are basic, individual, cognitive structures, which guide the perception and representation of reality or, put in other words, frames structure which parts of reality become noticed. Frames select and organise information drawn from real experiences and about people and objects and which are actually in the world, therefore they orient and guide interpretation of individual experience, that is "enable individuals to locate, perceive, identify and label occurrences" (Snow et al. 1986, p. 464). A distinction between the concepts “frame” and “framing” is rather helpful. “Frame” is a mental structure. “Framing” is a behaviour by which people make sense of both daily life and the grievances that confront them. Frame theory, therefore, as developed after Goffman’s founding contribution, embraces both cognitive structures whose contents can be elicited, inferred, and plotted in a rough approximation of the algorithms by which people come to decisions about how to act and what to say and the interactive processes of talk, persuasion, arguing, contestation, interpersonal influence, subtle rhetorical posturing, outright marketing that modify—indeed, continually modify—the contents of interpretative frames (Oliver & Johnston, 2000).
Conveying frames for reading the real world mathematically, textbook word problems infuse in children a practical relationship with mathematical knowledge, a relationship of usage. Such a relationship of usage without doubt contributes to the construction of mathematics knowledge. This knowledge however is primarily a practical knowledge of using mathematics and alongside it is a scientific knowledge of the mathematics subject matter. This fact may, in my view, be considered as the essential meaning of the concept of “mathematical enculturation”; a mathematical knowledge invested in a practical knowledge of its usage. For this reason among others, mathematics traditionally constitutes a fundamental component of the socio-cultural indoctrination of children. Mathematics trains children towards “the correct” modes of thinking, “the correct” modes of deducing, “the correct” modes of decision making. A relation of this type between school mathematics and its subject matter may not in any case be considered as an exclusively learning relation.
Rather, it is a relation of ideological indoctrination of children, which, by using mathematics – a subject matter commonly agreed to be valuable - habituates them in particular standpoints and specific patterns of behaviour and directs them through mathematics towards the prevailing social values (Althusser, 1970). In conclusion, school mathematics - as well as the teaching of many other school subjects - incorporates a double relation with its subject matter: a scientific relation as a means for theoretical knowledge of mathematics concepts and tools and an ideological relation as a vehicle for practical knowledge about the use of mathematics. This practical knowledge concerns particular patterns of behaviour towards the theoretical and social function of mathematics. In this sense, the teaching of mathematics aims both at learning mathematics concepts and tools and at appropriating an ideology for mathematical activities and their outcomes, that is, an ideology concerning mathematics, based on a specific conception of place and function of mathematical activity, its outcomes and applications in the present-day dominant social reality.
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