Links between mathematics education and democracy

Werner Blum and Mogens Niss (1989) and Niss (1987) list five groups of arguments for introducing modelling and applications into the mathematics curriculum. Though not mutually exclusive, they reflect very different goals for education, obviously involving socio-cultural ideological values (Ernest, 1991; Niss, 1987: 6). The two goals most directly linked to democracy appear to be:

􀂾 Promote and qualify a critical orientation in students towards the use (and misuse) of mathematics in extra-mathematical contexts.

􀂾 Prepare students to be able to practice applications and modelling – in other teaching subjects; as private individuals or as citizens, at present or in the future; or in their future professions.

The first goal is relevant because of the wide range of contexts in which mathematics is applied, where the purpose of the modelling may vary (descriptive, predictive or prescriptive, cf. (Davis & Hersh, 1986/88: 115-121)) or the nature of the foundation of the model may vary (from theoretically very strong to consisting of a collection of rather ad hoc assumptions, cf. (Emerik, Gottschau, Karpatschof, Møller, & Nørgård, 1981; Jensen, 1980)). The identity of methods and procedures masks the total diversity of situations and encourages the indiscriminate use of certain non validated mathematical methods in totally unacceptable contexts as well as in acceptable, productive contexts. (Booß-Bavnbek & Pate, 1989: 168) 

For an in-depth discussion of types of models, the necessary types of critique and its relevance to mathematics discussion, see (Christiansen, 1996). Included in the second option may be the use of mathematics to create awareness of what for some would be considered problematic societal situations, as probably most strongly demonstrated in the activities for adult learners discussed by Marilyn Frankenstein (Frankenstein, 1981, 1983, 1990). A third obvious link between mathematics education and democracy is the development of a democratic and egalitarian culture in the classroom (cf. Ellsworth, 1989; Young, 1989). As Povey (2003) states it:

To harness mathematical learning for social justice involves rethinking and reframing mathematics classrooms so that both the relationship between participants and the relationship of the participants to mathematics (as well as the mathematics itself) is changed (p. 56).

First Narrative: Mathematical Competencies in Critique of Models

A month before Christmas 1999, the summaries of the  news contained the following:

CITIZENS CHEATED OF 43 BILLIONS?

A 74 year old pensioner, Hans Peter , today summoned the Ministry of Finance, demanding payment of an amount which the state wrongfully has withheld from him – and in his opinion from all other citizens . He has meticulously studied the financial models which the Ministry of Finance uses in calculating the key numbers from which pensions, social security, and unemployment benefits are calculated – as well as the different taxation limits. His claim is that the Ministry of Finance since 1996 systematically has used misleading numbers for the average salaries . Instead of looking at all salary earners and their salaries as a basis for calculating the average salary, the Ministry of Finance has – in collaboration with the employers’ association which provides the salary information – chosen to disregard IT companies. Also, they do not make corrections to make up for that several employees go from being appointed on a group contract basis to being officials. The lower average implies that the pensions, social security, and unemployment benefits, which according to the law must follow the average, are too low. Hans Peter thinks that it is an amount around 3 billion . At the same time, the limits for top and bottom taxation have been set too low – and that implies that the tax payers have paid app. 40 billions too much! Hans Peter is not some arbitrary pensioner – he has done it before! In 1996 he obtained judgement that the Ministry of Finance had calculated the pensions incorrectly and paid out 1.5 billion  too much. That lead to a reprimand to the Minister of Finance and to the reduction of pensions for the following years.

There are many examples that mathematics plays a part in decision processes; cases where it requires a good deal of mathematical competencies to reflect critically on the situation (Blomhøj, 1999). In this case, however, one could claim that it is not what we usually understand as mathematical competencies which make it possible for Hans Peter to criticise the existing financial models. He ‘simply’ considered if all information had been utilised ‘correctly’. However, that investigation required the use of numerical values and

models, and it required a knowledge that information does not exist in and by itself but is constructed as part of the modelling process – choice of variables, formulation of connections and relations, the determination of constants, etc. It is the same kind of understanding of the choices underlying a modelling process involved in challenging the classification of research with military purposes as ‘research’ rather than as ‘military spending’ (Frankenstein, 1983).

Should we expand our understanding of ‘mathematics’ to include these core modelling competencies and the ability to relate in a critical fashion to models which involve mathematics? In the end, technology has to a large extent made it superfluous to learn the methods and techniques which for so long have dominated most mathematics instruction. But it still takes people to formulate and develop mathematical models and to interpret these as well as to apply and criticise the interpretations. As suggested by , the Ministry of Finance’s application of mathematics may well influence who feels competent criticising the decisions from the Ministry – even if it is not the mathematics which makes a difference but the modelling process and its underlying assumptions. In other words, the use of mathematics may exclude someone from (feeling confident) taking part in the discussion. It may also change what we (believe) count(s) as arguments (Christiansen, 1996, 1998; Skovsmose, 1990). It remains an open question what the links between mathematical competencies, a general understanding of the limitations of the modelling process derived from specific experiences, and self-confidence are in determining a person’s competencies and willingness to challenge political decisions as Hans Peter did.

In society, the use of mathematical models and scientific investigations play a role in legitimising certain political decisions – discussed by among others Morten Blomhøj (1999) and Peter Kemp (1980). The ‘expert ideology’ makes language games which focus on ‘correct versus wrong’ and ‘efficient versus ineffecient’ more acceptable than language games which focus on ‘ethical versus unethical’ or ‘esthetically pleasing versus esthetically offensive’. This also applies when mathematics is applied to realistic situations in the classroom (Christiansen, 1996, 1997, 1998). But as Paola Valero has pointed out, this is far from the case in many other countries, such as Colombia:

[...] decisions are made based [...] also on personal loyalty [...], political convenience, power of conviction through the use of language or violent, physical imposition. In this political scenario and ‘rationality’, mathematics does not necessarily constitute a formatting power that greatly influences decision making. (Valero, 1999)

Is a focus on giving students competencies with which to critically consider mathematical models and their use really that relevant in the rest of the world? Is this focus relevant  – or is it more about becoming aware of and critical towards which discourse is the dominating one? Could and should mathematics education contribute to the development of this competency, simply because mathematics often is a tool in the ideology

which relies on expert statements?