to present her work on the introduction of entrepreneurship in the Swedish school but also to do ”my” presentation about the Ritual fabrication of mathematical knowledge. We have prepared a prezi together that can be found
The ritual fabrication of mathematical knowledge
Handout for presentation at ECER 2014
Sverker Lundin (email@example.com)
Ditte Storck Christiensen (firstname.lastname@example.org)
The presentation starts with an attempt to describe, in a way that everybody can agree on, some central aspects of mathematics education as part of the modern education system.
To the left we have the process that gives mathematics education its purpose: learning, that leads to (mathematical) knowledge, that can then be ”used” – whatever is put into that word – outside the education system, in everyday life and professional life.
To the right we have a formal process that we should all be able to agree exists in the education system as well. We have here assessment, grades and regulations for admittance – to further education and also to professions.
We then make some observations concerning these two processes that can be said to run in parallel in mathematics education as part of the education system.
First, we observe that the practice of learning is more or less the same as the practice of knowledge assessment. This observation is important because of the meaning that is ascribed to the results of such assessment. The purpose is to certify that pupils have knowledge that can then, by definition, be ”used” – in a the most general sense possible of that word – outside school. But the assessment takes place in school, in a practice almost indistinguishable from the practice of learning. This observation, of on the one hand the strong similarity of the practices of learning and assessment, and on the other the interpretation of such assessment as a certification of the presence of knowledge, the purpose of which is “use” in some other practice, is intended to raise questions, as to the reasonableness of the logic and rationality of this system.
Secondly, we observe that both the left and the right processes of education contain, as their last step, an attribute that endows their bearers with a certain “power” or a certain set of benefits. Knowledge can be “used” to solve problems and to comprehend – in whatever ways this use is envisioned. Grades can be “used” to get admitted to further education and to professions. We observe that these two kinds of “use” if thoroughly different, but still closely related in the education system. Furthermore, we can note here, that while the left kind of “use” is surely possible, we have very uncertain information about how, when and where it takes place. For the right kind of use, to the contrary, we know exactly how, when and where it functions.
Thirdly, we observe that the sameness between the practice of learning and the practice of use is a contentious question. From one perspective, the two practices are “the same”, so that for instance the problem solving in school can be seen as “use” of knowledge in the same way as problem solving outside school can be seen as “use” of knowledge. On the other hand, critical voices claim that the school practice is in fact not at all like life outside school, that it is “unrealistic”.
Generally, in this first slide, all but the bottom left part of the picture – “use” – is located inside the education system. It is the “use” that puts everything else into purposeful contact with, so to speak, the outside world. If this connection turns out to be a chimera, the whole business of education must seem misdirected. The only connection with the outside world that remains is the administrative system where grades is used as a means for segregation.
In this first slide, we note that the “things”, “entities” or “processes” to the left are, invisible, immaterial and crucial for the purpose of the education system. Furthermore they are what one might call precarious, in the sense that it is non-trivial not only to bring them about but also to confirm their presence. The processes and entities on the right, to the contrary, are what one might call concrete and profane. There is never any doubt when an assessment has taken place, a grading mark is unambiguous and systems for admittance are, if not transparent, so at least concretely there in their “mechanical” functioning.
Given this distinction, we want to say that the entities and processes on the left constitute a framework for interpretation that lends sense and purpose to the education system. With this description, we want to insert a wedge between what is obviously there in the education system, and this framework. We will then talk about the “making” of this framework. We do this by introducing another framework for interpretation, brought in from anthropology. We thus end up with another understanding of what takes place in mathematics education.
This slide presents the alternative framework for interpretation, that is, the framework that does not employ learning, knowledge and knowledge-use as tools for interpretation. The main point of this alternative framework is that it shows how frameworks-for-interpretation are brought into existence. Thus, what we want to focus upon is how it comes that mathematics education (and education in general) is interpreted in the way that it is. What we will say is basically that the education system in itself, because of its relationship between what is done and said, produces its own framework for interpretation. The education system determines, if not completely by itself so still largely, the conditions for its own interpretation. This, furthermore, should be seen as typical for the function of ritual in culture.
In the left of the slide we present what Roy Rappaport calls the ritual form. It is a set of properties of a certain type of activity. With Rappaport we claim that, if an activity has these properties, certain effects can be expected to ensue. These effects can furthermore be quite directly connected to the properties of activity.
To the right we have two such effects, that Rappaport calls the canonical and the self-referential messages, respectively.
The canonical message is the framework for interpretation. It is the set of entities and processes that “exists”, in the sense that they are present at hand for people who want to make sense of the world. They function as interpretive resources, as ways of talking about practice and experience. Thus, one can understand what takes place in a classroom as “learning”, or, possibly, a failed attempt to make learning happen.
The self-referential message connects these general “forms” of the world with particular people and particular situations. One can thus say that pupil A, since he scored well on a test, has knowledge, this then becoming an attribute of this person that sticks, after the test situation and in many cases even after school.
Three things are to be noted here. Firstly, that the general mechanism for the production of these two messages is action “as if”. This is a concept that is elaborated in psychoanalytic theory, and in anthropology, most comprehensively, we think, by the Austrian philosopher Robert Pfaller. The point is that if people act as if something is the case, this something becomes, in a specific sense that cannot be elaborated here, present and real. Secondly, it is to be noted that these two messages – the canonical and the self-referential – tend to support each other, so that discourse on particularities such as how much pupil X can be said to know based on her test score, contributes to the “realization” and “presentation” of the framework that is used in this discourse. The framework is thus not brought into existence by being talked about, but by being used for talking about and interpreting the world. Thirdly, that which is brought into existence, and made real and present by ritual activity is not rightly understood as “beliefs”. The question of what a “belief” is, is complicated, and the concept of “belief” has a problematic place in the history of modernity (see e.g. the work of Talal Asad or Ivan Illich). In particular, early modern anthropologists (e.g. 18th and 19th century) tended to interpret non-modern cultures in terms of a concept of “belief” modelled on protestant faith, where inner conviction is essential. Thus, it was assumed that the entities and processes brought into existence in ritual activity were “believed in” in this so to speak convictional way. To the contrary however, meaning produced in ritual activity is rather made “real and present” in the same way as we moderns relate to such things as love, history and blue. We do not usually find it interesting to ask about the “existence” of these things, nor do we “believe” in them – they are just parts of the world that we can identify, talk about and use as means for understanding. This, hence, is how the “world” of mathematics education should be understood – as present and real, rather than in any particular sense of the world existing.
Slide for explains how the framework of slide 3 can be “applied” as interpretive framework for mathematics education as presented in slide 1.
We present the activity of mathematics education as a ritual, fitting the definition of the ritual form. It is action “as if” a number of things were the case in the world. In particular, mathematics education takes place as if mathematical knowledge was crucial for understanding and managing life in modern society. It takes place as if the activity of problem solving in school was a necessary prerequisite for a problem solving is that supposedly prevalent outside school.
As we do this – and it should be noted how the presence and logic of this activity is ensured “mechanically” through conventions in a number of ways – we bring forth this mathematical and problematic world. One can say that the world inside school is designed to fit the interpretive framework of mathematics, learning and knowing. This framework is the only way to make sense of what takes place in school, and it is virtually impossible not to use it. We thus all contribute to the “making” of our modern world, as we participate in schooling.