Adaptation of a questionnaire to assess the epistemological beliefs of mathematics in secondary school teachers

The objective of the study is to determine the psychometric properties of the Epistemological Beliefs Questionnaire on Mathematics. 171 Secondary School Mathematics Teachers of the Central Region of Cuba participated. The results show acceptable internal consistency. The factorial structure of the scale revealed three major factors, consistent with the Model of the Three Constructs: beliefs about knowledge, about learning and teaching. Irregular levels in the development of the epistemological belief system about mathematics of these teachers were shown, with a tendency among naivety and sophistication poles. In conclusion, the questionnaire is useful for evaluating teacher’s beliefs about mathematics.

Internalities and the Foundations of Corporate Governance

This paper considers the potential contained in an 'internalities' approach to corporate governance. Rather than viewing the company as a ‘black box’ that can only be regulated through state action, we argue that corporate governance holds in tension the relationship between investors, managers and the corporate board. It is from that tension that a change in corporate culture will emerge. We argue that a state focus on promoting and managing the dialogical character of corporate governance will limit the negative effects of corporate power

Nana, Prostitution and the Textual Foundations of Zola’s 'Au Bonheur des Dames'

This article considers the textual forces operating in Au Bonheur des Dames, Zola's 1883 novel on modern commerce. It proposes that, with its echoes of the disorderly impulses that governed the infamous prostitute Nana earlier in the Rougon-Macquart cycle, coupled with its appreciation of the benefits of regulation, the dynamics of controlled and contained prostitution constitute the energy which fuels an efficient and successful business model in Au Bonheur des Dames. By closely analyzing both texts as well as Zola's preparatory documents, and borrowing from Genette's theories of intertextuality, this study reads Nana as a pre-historic hypotext, buried in the textual chantier from which the structure of Au Bonheur des Dames emerges.

On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

Ontological constructivism : Negri and the philosophical foundations of a future communism

As we find in Empire and Multitude, Antonio Negri's political project IS a thoroughly Marxist analysis and critique of global or late capitalism. By modifying and updating Marx's conceptual tools, he is able to provide a clear account of capitalism's processes, its expanding reach, and the revolutionary potential that functions as its motor. By turning to Negri's philosophical works, however, we find that this political analysis is founded on a series of concepts and theoretical positions. This paper attempts to clarify this theoretical foundation, highlighting in particular what I term "ontological constructivism" - Negri's radical reworking of traditional ontology. Opposing the long history of transcendence in epistemology and metaphysics (one that stretches from Plato to Kant), this reworked ontological perspective positions individuals - not god or some other transcendent source - as the primary agents responsible for molding the ontological landscape. Combined with his understanding of kairos (subjective, immeasurable time), ontological constructivism lays the groundwork for opposing transcendence and rethinking contemporary politics.