Mathematical language in the political discourse: epistemological and
educational reflections emerged from Dimitris Chassapis' conference plenary
Fragkiskos Kalavasis
Aegean University, Greece.
The use of statistics is both "act of authority" and "authorized act"
Pierre Bourdieu
Abstract
Mathematical language in political discourse (including numbers, ratios, geometrical
figures, tables, function graphs or logical symbols) might help to understand the
complexity of the situation or to describe aspects related to an interactive process of
decision making. Unfortunately, the political and journalistic abuse of mathematical
language transforms the modeling function of mathematics. In fact, it disarms reality
from her mathematized connections and conduces to a superficial formulation of a
deterministic political representation. Mathematisation for a better access to complex
information seems to have been replaced by de-mathematisation and misinformation.
This dangerously false instrumentalisation of mathematics results in reducing any
democratic sense of politics, thus transforming mathematical language to a
communication agent that manipulates public opinion. In the face of this crucial
phenomenon, what is our responsibility as mathematicians, researchers, teachers,
learners, and citizens? These are emerging epistemological and ethical questions
that, in consequence, are closely related directly with processes of educational
decisions concerning mathematics education and didactics. I will try to present some
reflections upon the thoughtful lecture delivered by Dimitris Chassapis.
1.
Politicians and opinion makers often use and abuse scientific knowledge in the
enunciation of their rhetoric to support and serve the argumentative dimension of their
intentions. A kind of disjunction exists between designers and consumers of
mathematics and statistics; a disjunction that characterises the forming of public
discourse, in both local and global levels. The presumed inevitability of this
phenomenon is not independent of the content of mathematics in the school curricula,
neither of the pedagogic practices or the stereotypic beliefs concerning the relation
among mathematics and reality. As Dimitris notes, the mathematical figures are
implicitly and explicitly presumed to be neutral, accurate and objective and are thus
characterised as ‘distant’ and ‘cool’. These properties serve the purposes of rhetorical,
argumentative and polemic political discourses. Mathematical symbols, already
related to the image and status of mathematics in the epistemological, social and
educational context, they now obtain political-value. Their use creates a new –
unhuman, but unfortunately legally unhuman thanks to the scientific construction–
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narrative, inversing the meaning of fundamental political concepts, including national
sovereignty, citizen responsibility, social justice and democratic awareness.
The aforementioned situation is highly complex and the danger for the mathematics
education transcends the frontiers of mathematics education. How, could we then
confront this situation? It seems that we need to turn towards cultivating very early in
the schools an interdisciplinary approach of mathematics –an approach deeply related
to the understanding and acceptance of complexity. We have to coordinate our
teaching in close relation with other disciplines about a variety of concepts that
surpasses the over-simplistic manipulative descriptions and manoeuvres enacted by
both politicians and media-groups.
2.
Making use of numbers places the speaker on the side of the power, as numbers
signify certainty in relation not only of knowledge, but also of ability and agency. The
use of numbers in our local political context, is closely linked to managerial concepts,
the epistemological context of which we must also consider. Three terms characterise
this situation, because they bear clear links with their inner numerical structure,
modelled with finite, measurable indicators: effectiveness (a method of reasoning that
translates into actions), efficiency (the return of capacity, of performance), and
efficacity (a quality that produces the expected effect). Thus, it is posited that we have
to study both the transformation of the meaning of numbers through the bridges of
specific interdisciplinary connections and the impact of our contemporary highly
complex virtually expanded society to the public discourse, in order to gain deeper
understanding of the effects of the (ab)use of mathematics in politics.
Dimitris Chassapis has the privilege to be not only a researcher, but also an acting
person in the most difficult period of the crisis, by participating as the National
Secretary of Education in the first Greek administration which, inspired by
progressive and humanitarian ideas, tried to deconstruct the official image of the
crisis. He had to re-orient education system from an elitist ideology and practice
towards an inclusive and inquiry based perspective. I think that we can easily see
mathematics education as the more fragile field in the contrast between the elitist
point of view and the inclusive one. The school learning or teaching practices of both
teachers and students must be measurable performances. To minimise the role of the
social conditions, we choose the lesson of the mathematics. It is the perfect choice, if
of course we decide to ignore all the didactical mathematical literacy and we assume
that learning mathematics is a neutral game where we can measure general cognitive
performances. They had added in the theory of the standards in mathematics
education the practice of the so called bank of topics, a list of more sophisticated
exercises.
But! Reality is much more complex than any of her descriptions! At the same time
mathematics education is a ‘resilient’ field of education, considering the nature of
mathematics as human construction and its development as a scientific philosophy
that is not afraid of antinomies, paradoxes, infinities, irrationality or the inexpressible. Mathematical culture and science are nursed from the resilience. Their
capacity to survive traversing through the paradoxes and to extend in a qualitative
way the theories to include the antinomies of quantification and measurement is
maybe one of the secret of their inexplicable power. The introduction of such
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characteristics in ‘mathematical education for all’, remains the main concern of the
critic researchers-teachers. So, thank you for the opportunity to make some comments
in the conference. I shall try to make some connections with the didactic of
mathematics and in particular with the approach of complexity and interdisciplinary
theories.
3.
The central topic of this plenary is the use and misuse of numbers and numerical
expressions, which appear on the headlines, related to the construction of truth. I think
that each individual and each community feels the necessity of truth and expresses
this necessity by constructing a variety of relationships with the truth. Maybe truth is
contained to its necessity, so each construction of truth is corresponding to the
formulation of this necessity. It is exactly in this formulation of the necessity of truth
that starts, from my point of view, the more difficult and interesting stage of the
consequences of mathematics. It resembles the effort to construct the most accurate
description of the complexity; for example, to construct the best map of a territory:
the perfect identification is impossible, but the need of this (even impossible)
identification conduces to the construction of a variety of models. To compare these
constructions, we need indicators. Indicators have to be measurable, so we need
numbers and then more sophisticated mathematical formulae, tables, figures and
symbols to describe the models. The objective is the communication and the decision
making, in order to persuade others about the representation of the reality, not the
reality per se.
Thus, we measure dimensions and we calculate proportions in order to design a map
upon which we can reflect and make action plans about the mapped territory.
Mathematical objects are now in the first line of the construction. But the only perfect
map of a territory is the territory itself an, even then, such a correspondence
construction is impossible, because τὰ πάντα ῥεῖ (everything flows). Hence, the only
possibility to understand and communicate the description of a complex phenomenon
relies on the conventional agreement about the meaning and the use of language
expressions and symbols.
What kind of number concepts and numerical expressions are used in the headlines?
Do they correspond to cardinal numbers, ordinal numbers, ratios and analogies, limits
of series, rhythms of variation, approximations? Not at all! We observe that the public
opinion makers seem to avoid the use of high-school mathematics symbols and
formulas. It is argued that such a decision prevents the citizens from trying to recall
their mathematic knowledge in order to make sense of the model of the described
situation. Instead, public opinion makers appear to prefer the employment of simple
numerical formulations, usually number comparisons or easily representable
percentages. A situation in which everybody could consider as easily conceivable and
understandable and, consequently, a situation which nobody would try to read deeper
into the presented information.
Let’s try to distant ourselves for a moment from the ‘newspapers’ (in the broad sense,
including both traditional and digital new media) and to ponder about the implications
of mathematics in this kind of modelling. The necessity and expressing ability of
mathematics can be discerned in the necessity to understand the phenomena
corresponding to the formulation or the expression of a critical situation. But what
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mathematics do we need? And how this mathematics has been presented in school?
Has it ever been related to concrete situations?
Dimitris notes that headlines particularly use numbers and numerical expressions and
he becomes more concrete when he talks about “whole numbers, decimal numbers,
fractions, but mainly percentages, ... selected to put forward a “fact”, a decision or a
plan”. Could we say now that we have in front of us a kind of mathematisation of the
complexity? Or, maybe, the inverse? Isn’t it a kind of reductionism to a simplistic
mapping? Chassapis notes that “On such a ground, we are faced with a
numericalization of politics and respectively with a politicalisation of numbers.” I
think that the situation is worse, in the sense that it is a distortion of reality that
produces mathematical symbols empty of mathematical meanings. Such distortion
produces disinformation.
4.
Truth, in the case of construction as described by Dimitris, is linked to fear. Such
seems to be the purpose of this kind of journalism. Truth is obliged not to disturb the
austerity project, otherwise we shall enter in the hell of uncertainty and unpredictable.
Consequently, it may be obvious why the use of mathematical concepts that could
help us to understand uncertainty and complexity is avoided, so that fear would not be
replaced by alternative projects! The necessity of truth, linked to fear,
decontextualizes the concept of its philosophical meaning, detaches it from its
dialectical construction and its social and democratic dimension, thus imprisoning it
in a strictly financial interpretation. A financial interpretation of and into a non
financial modelling, because of the lack of financial mathematics. Such a line of
thinking has already obtained the status of dogmatic truth and is no longer a political
argument.
Thus, considering education, we must ‘make a wink’ to the financial mathematics and
the concepts of the risk and loss functions, a research field that is developing more
and more during the period of the crisis. Risk is the combination of four factors: a
danger, a probability of occurrence, severity and acceptability. Hence, the “danger”
being a dreaded event (by itself and its consequences) is not confused with the “risk”,
which results from the fact that this danger has a certain probability of manifesting
itself and the gravity of its consequences. The criticality of a risk results from the
combination of the impact (or effect or severity) and the probability of a risk. All
these hidden concepts, might be studied in the context of mathematical modelling,
quantifying and understanding the phenomena governing financial transactions and
markets. Within this framework, it is crucial to understand the meaning of the time
factor and estimation tools related with probability theory, stochastic calculus,
statistics and differential calculus. ‘Time’ is unique, different from the other variables;
it is irreversible! As states networks, banks and markets form a high complexity, a
range of instruments for steering and monitoring is proposed for the governance
systems; in particular, a system of indicators measuring the impact, effectiveness,
efficiency and efficacy. These indicators are the main management tool for the pilot
system.
The major difficulty rests on the choice of these indicators. The identification and
choice of criteria that are "evaluable" (i.e. that can be the subject of a measurement)
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appear to be the only way to ensure, ultimately, that the objective of the policy
concerned is reached. However, some of the services offered by the public sector lend
themselves poorly to the establishment of statistical indicators, which appear to be too
narrow in relation to the nature of the objectives sought. So how can we measure the
effectiveness of an education system, a health system, or social assistance? In which
ways is it possible to quantify effects of an essentially qualitative nature?
Another difficulty of the modelling and the interpretation of the use of mathematics in
this framework is related to the expected impact of public activities: Should we try to
measure the immediate outcome of each action, or the medium- and long-term global
involvement in society? The evaluation of performance in the public or nonmarket
sector concerns both the level of output (referring to the results obtained by the
realization of services) and the level of impact (referring to the final results of a
process of production of goods and services) in relation to the society or community
concerned. Following these, taking for example the police action, the level of
production could be the number of thieves arrested, while the level of result would be
the impact on the feeling of security of the population.
Dimitris' plenary invites us to open perspective to include the great image of the
insertion of mathematics in political language, which is linked to the organisation of
the State. Today, the organisation of bureaucracy and of political discourse seems to
be highly internationalised or globalized, whether it refers to the European Union or
the OECD, to the IMF or the International Stock Market. The impact of
communication technologies and of networks is on the linking of the aforementioned
global structure with the construction of a multimodal language in which the
numericalization and the organisational symbolization are the key poles. It is our
responsibility to study this mathematics within its environment in the educational
systems. What is the relationship of our difficulties to understand the role of the
numerical expressions in the case of the headlines with the obstacles presented in the
use of mathematics in other academic disciplines, as sciences (physics, chemistry,
biology, geography), environmental studies or economics and management courses?
Which kinds of epistemological obstacles and didactical difficulties emerge in each of
these interdisciplinary contexts? Such really epistemological and educational
questions are very pragmatic and of great methodological interest.
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