Working Class, Intelligentsia and the“spirit of GENERALIZATION”
Bronislaw Czarnocha
Hostos Community College, CUNY, USA
ABSTRACT
Algebra constitutes here a background against which thinking and activity of the left are examined. The search for whereabouts of “the spirit of generalization” among the working class whose absence was observed by Marx in 1870 leads us to algebra as, on one hand, a generalization of arithmetic, and on the other, as in the metaphor: “dialectics - the algebra of revolution”. These two metaphors together open a new point of view with the help of which we can throw some light upon the confusion and, ultimately helplessness of the left in the contemporary world urgently needing a revolutionary boost, in our opinion.The work here approaches the critical math education methodology (Scovsmose and Borba,2004) in reviewing the state of affairs (CS) and, through the explorative reasoning, leads to the imagined situation (IS) of the design of the program for Organic Intellectuals of the Working Class.
THE STATE OF AFFAIRS
I was struck by the Marx’s words of 1870: The English have all the material requisites necessary for a social revolution. What they lack is the spirit of generalization and revolutionary ardour. (Marx,1870)
As a professor of mathematics in a community college in the South Bronx, that is in the working-class institution of higher learning, I know something about the absence of the “spirit of generalization” among students of arithmetic and algebra and, I have been breaking my head as a mathematics teacher-researcher how to re-kindle it. Generalization has been one of the two principles on which I designed the integrated course Arithmetic/Algebra for the working class remedial students at my community college recently.
What exactly is the spirit of generalization? What is generalization? What does it mean that algebra, the same algebra Alexander Herzen used in the metaphorical phrase: “Dialectics – the Algebra of Revolution” is generalization of arithmetic? One could also ask, what would be the Arithmetic of Revolution? Or, pushing the analogy farther, we could ask, what is the dialectics generalization of?
Some of it’s simple. It means that (1) the algebraic symbol of the variable X, the essential concept of Algebra, includes in itself (or means) all real numbers at once, that is all numbers we have on the real number line, and (2) that XY or X+Y, or X symbolize (or mean) multiplication, addition or division of any two real numbers. Thus, writing the symbol X means writing infinite number of reals in one stroke! Writing X+Ymeans writing infinite number of binary additions in one stroke. Quite an economy of thought. In terms of dialectics, it’s the movement from ManyOne, from particular to general. Its need at the present stage of development of the revolutionary movement is tremendous. Let’s look at the examples:
Harvey (2010) argues in his address to the World Social Forum that “the central problem is that in aggregate there is no resolute and sufficiently unified anti-capitalist movement that can adequately challenge the reproduction of the capitalist class and the perpetuation of its power on the world stage (Harvey,2010).”
The “central problem” hides a generalization. Generalization here is necessary in the process of transition between the “aggregate” that is the total collection of social movements in the world together with their ideological positions to the “unified anti-capitalist movement”. To make that mental, and therefore organizational fundamental transition within the practice of the social movements, its participants should discern or formulate the “common denominator” of different struggles, separate it from their particular conditions, focus their attention on the commonness together with the network of relationships that surrounds or incorporates it and formulate a new, general theoretical/practical point of view based in contemporary praxis. It will lead to the new view about how to “wrench out the cancerous tumor of class relations” (Harvey, 2012) from the society. Maybe if within each struggle, we identify how exactly the particular movement, contributes to “wrenching out the class relations”, we will see where we are, what aspects of the struggle need to be strategically and tactically emphasized.
Crowther and Lucio-Villegas (2012) mention that “Educators working in neighbourhoods have to connect analysis of social change and awareness of the wider context, but at the same time beginwith people in the communities “where they are” (pp.59). The process of connecting analysis of social change with “people in the communities where they are” is the process of generalization, and, its reciprocal, particularization.
Occupy Wall Street (OWS) movement showing the injustice of the ratio 1:99 in terms of the national wealth distribution. The slogan “we are 99%” engaged the process of proportional thinking - the very first step in the transition between arithmetic and algebra; the very first step in generalization. While un-doubtfully that first step had imprinted itself very deeply in American imagination, it has been no more than that – it could not produce the full-fledged generalization, because the education of participants has not emphasized the process of generalization in their school and college preparation. While generalization is a natural process of thinking, its full development requires systematic learning environment focused on the process. However, the steady focus of educational policy (Hacker, 2012) is to eliminate such learning environment by eliminating elementary algebra from college requirements. Participating members of the General Assembly at the Zuccottipark were profoundly democratic but could not move beyond the listing of the relevant issue and their particular causes, later categorized into working groups themes.
The theoretical importance of the spirit of generalization can be easily grasped paying attention to another interesting quote of Marx, who, wanting to bring his dialectics closer to the natural science, offered the following analogy: “The Sun is the object for a plant – an indispensable object to it confirming its life – just as the plant is object for the Sun, being an expression of the life awakening power of the Sun…”(Ollman,2003). A similar relationship, indicated italic, exists between a variable (the Sun) and a number (the plant). The variable is an object for a number because the variable helps the number transcend its specificity. The number is an object for the variable, because the number helps the variable to become specific.Algebraic processes of generalization and particularization are essential for grasping Marxian dialectics in a nutshell. In similar vein the dialectical relationship between a number and a variable carries a name in mathematics education, the “process-object duality”, whose mastery is the criterion for understanding and mastery of algebra itself. Therefore an expression of the type 2x + 1 can be understood as the object, an algebraic expression with its own algebraic operations, and it can also be understood as a process during which the meaning of the expression 2x + 1 is attained by substituting a number instead of the variable x to calculate its numerical value with the help of arithmetic operations. Thus the mathematical object 2x + 1 can also be understood as an abstraction from the pattern of the series of arithmetic expressions: 2*3 + 1, 2*4 + 1, 2*(-5)+1, etc. Therefore the “process/object duality” is similar to Marx’s type of abstraction, which joins the process with the result “…for Marx, as for Hegel before him, “abstraction functions as a noun [the result of abstraction] and as a verb [the process of abstracting].”(Ollman, 2003)
How critical is the presence of the spirit of generalization for the praxis of the actual struggle has been brought to strong relief by the Polish Revolution of Solidarity of 1980/1981, where that spirit was clearly missing from the rank-and-file Solidarity members of the rising. The fascinating chapter Dynamics of the Working Class: Consciousness of Staniszkis (1984) written almost simultaneously with the event itself informs that: “The workers could only keep referring to their isolated, concrete experiences (and thus gain only local concessions), or else they could remain silent. It was precisely this silence when they realized that Gierek’s diagnosis was incompatible with their own but could not express it made the workers realize that differences in linguistic competence indicate not only dissimilarity but also a hierarchy”[both political and conceptual] (p.120)[1]. It is precisely that constant reference to concrete isolated experiences without the ability to draw and express more general conclusions applicable to wider environment than their own factory that tells us about the absence of the spirit of generalization. Here the absence of the spirit of generalization was the explicit cause for defeats in the Solidarity struggles.
Mastering that hierarchy means to develop the two-way linguistic bridge between workers’ language and that of intelligentsia (together of course with the underlying conceptual frameworks). Properly designed present education system has no major problems in facilitating this process. Instead, however, Polish dissident intellectuals “monopolized nearly all expressive roles in Solidarity movement” (p.121) eliminating working class from participating in the decisions concerning future Poland.
Staniszkis’ description sounds very much like a description of the situation in our arithmetic/algebra classes in the Bronx with missing spirit of generalization where students are locked into concrete arithmetical procedural thinking The algebraic rules that is the syntax of algebra as generalization of arithmetic operations do not fare well with students because they are not based on the developmental process from those operations – that is they do not arise out of understanding their arithmetic roots or manifestations. Instead they are handed down as rules not connected with student arithmetic experience. Because of this “banking” (Freire, 1971) pedagogical approach students get bogged down in concreteness of arithmetic thinking, do not see algebraic relationships and, therefore, have tremendous difficulties with algebra and its spirit of generalization.
How come Polish workers in communist Poland of 1980, thirty six years after the communist takeover, had a problem with generalization, and at the same time, as a class, they reached the high level of their consciousness manifested in the demand of the independent union, followed by the vision of new Poland with the factory workers’ councils as one of its foundations?
The answer is quite complex and it reaches the very beginnings of the left movement and starting, possibly, at the Marx’s note of 1870 whose part 2 states
Only the General Council can provide them with this, and thus accelerate a truly revolutionary movement here and, in consequence, everywhere. The only way of bringing about this change is to do what the General Council of the International Association is doing. As the General Council, we are able to initiate measures (for example, the founding of the Land and Labor) which later, after their execution, appear to the public as spontaneous movements of the English working class.
It seems that Marx here is advocating manipulation using working class rather than facilitation of the spirit of generalization within working class. Similar attitudes became institutionalized first by Kautsky (1901), a leader of German Socialdemocracy at the turn of 19 and 20 centuries who asserts:
Modern socialist consciousness can arise only on the basis of profound scientific knowledge. Indeed modern economic is as much a condition of socialist production as, say modern technology, and the proletariat can create neither one nor the other, no matter how much it may desire to do so. The vehicles of science are not the proletariat, but the bourgeois intelligentsia. Thus the socialist is something introduced into the proletarian struggle from without and not something that arose from it spontaneously.
and soon later by Lenin in What’s to be done?where he follows Kautsky train of thought condemning the intellectual possibilities of proletariat and reinforcing disbelief in proletariat’s own strength and power:“This consciousness can be brought to them [to workers] from without. The history of all countries shows that the working class, exclusively by its own effort, is able to develop only trade union consciousness.”
The definiteness of this dismissal of workers as intellectuals is surprisingly like the contemporaneous dismissal of teachers of mathematics as independent creators of “research” knowledge within the mathematics education profession. A colleague, Whittmann (1999), who wants to convince the profession to undertake the research investigation of “teaching units” that is a sequence of classes devoted to the development of a concept asserts that till recently, the design of teaching units was considered a mediocre task normally done by teachers and textbook authors. He asks, why would anyone anxious for academic respectability stoop to designing teaching and put him-or herself on one level with teachers (p.94) While he acknowledges that “many of the best units were published in teacher journals”, at the same time he asserts that “by no means it [the design] can be left to the teachers, though teachers can certainly make important contribution within the framework of design provided by experts”. We see here the process of disenfranchisement of teachers from their own didactic tools with the simultaneous characterization of their work as below standard, resulting of course in the familiar divide between the theory and practice, exactly the same divide created by the Marx, Kautsky, and Lenin in their dismissal of workers as intellectuals in favour of “bourgeois intelligentsia”.
The book Polish Workers (Malachowski, 1981) appeared more or less the same time as Staniszkis analysis, and it represents the knowledge about working class seen from the perspective of sociological research conducted during the communist experiment. He informs that young workers in Poland (15-29 years of age) constituted 51% of the young Polish generation. Among those, approximately 49% had no more education than the grammar school (p.97), and around 45% of those that went beyond the grammar school (~1% of the total of young workers) were the students of vocational schools which in the word of the author “is the type of education that doesn’t open, in practice, opportunity for further studies nor it does it create the general knowledge needed to function in the contemporary world. Instead, it gives them the knowledge necessary to become skilled worker (craft knowledgeable).”
That approach of bringing consciousness from without has survived till the times of Solidarity in the form of Solidarity “experts”. Their recent publications show the same technique of organizing consent through intellectual manipulation (Bugaj, Obywatel, 2014):”Us experts! My God, we were really manipulating them! In the best of faiths, but nonetheless, we were, doubtlessly, manipulating them.” On one hand, it was clear during the opposition time that “without the workers’ support, the elimination of the system or even its reform was impossible.” On the other hand, some of us were not very happy that “we are dealing here with people who don’t read books and do not go to the theater.” As a result, he asserts that “although obviously workers played an essential role in Solidarity, they did not become, apart from few exceptions, leaders nor even regular participants of political activities” (Bugaj, 2014).
Polish workers of Solidarity had enough of revolutionary ardour. What they missed solely, was the spirit of generalization!
Thus, workers’ youth in Poland of the seventies was severely underrepresented at the institutions of higher learning; constituting most of young generation, at the end of sixties/beginning of seventies daughters and sons of workers’ origin constituted only 4% of student population at the Warsaw University (240 out of 6000 students at the time; anecdotal evidence). Clearly, the development of the spirit of generalization through public education was not in the interest of the communist rules in post-war Poland.
Nor it is in the interest of American academia. This situation in Poland of the seventies was not very different from our contemporary conditions of working class education in US. Andrew Hacker (NYT, July 22, 2012), a political scientist retiree from CUNY informs us that “Of course, people should learn basic numerical skills: decimals, ratios and estimating, sharpened by a good grounding in arithmetic”. But algebra, the generalization of arithmetic is not necessary for workers, since “a definitive analysis by the Georgetown Center on Education and the Workforce forecasts that in the decade ahead a mere 5 percent of entry-level workers will need to be proficient in algebra or above”. And then he adds “It’s not hard to understand why Caltech and M.I.T. want everyone to be proficient in mathematics” – demonstrating explicitly the hierarchy of knowledge, where the working class of South Bronx occupies the lowest level in that hierarchy characterized by knowledge of rules and skills separated from its subject-natural integral development into a coherent schema of thinking. Aren’t arguments of Hacker in 2012 surprisingly similar to the Malachowski’s reasons, 30 years earlier in communist Poland?!
We see that both, “left” and “right” intelligentsia, proclaim and reinforce, for different reasons, the intellectual limitations of the working class anchored in the absence of the spirit of generalization, disempowering it at the same time.
Considering that first public schools appeared in England around 1874, we see that, while education has made in general a tremendous progress, the degree of absence of spirit of generalization among working class has not changed within last 150 years.
Just to make sure how general is the phenomenon of Achievement Gap between the professionals and working class (called in OECD terminology, elementary professions) we can note its evidence-PISA (2012) report. It shows the difference in achievements of children from different social grouping in every participating country confirming 150 years long absence of the spirit of generalization among children of working people.
Organic Intellectual of the Working Class.
It was Antonio Gramsci who for the first time in the context revolutionary movements, understood and recognized the issue that one can’t separate homo sapiens from homo faber, the man - the thinker from the man – the maker, the worker from the intellectual. He recognized that “In any physical work, even the most degraded and mechanical, there exists a minimum of technical qualifications, a minimum of creative intellectual creativity” p (8). On the basis of this recognition he formulates, in his Prison Notebooks the fundamental new entity that of the organic intellectual of the working class, which is the first, most probably, attempt at the creative synthesis of the worker and the thinker. However, he does not formulate it completely hence interpretation conflict persists. Thus Hoare and Smith, (1971), the editors of the Quaderni, assert “that, ideally, the proletariat should be able to generate its own intellectuals within the class and who remain intellectuals of their class”(p.9), while New York City’s rank and file left intellectual Stanley Aronowitz, (2015) in his chapter on Gramsci defines it as The organic intellectual [of the working class] is one whose work is the expression of the worldview of the proletariat. Aronowitz supports this view by the later statement: “In this context Gramsci’s famous phrase “organic intellectuals” refers not primarily to those who have sprung from the ranks of the workers…”.