On Aspects of Mathematical Reasoning : Affect and Gender

This thesis explores two aspects of mathematical reasoning: affect and gender. I started by looking at the reasoning of upper secondary students when solving tasks. This work revealed that when not guided by an interviewer, algorithmic reasoning, based on memorising algorithms which may or may not be appropriate for the task, was predominant in the students reasoning. Given this lack of mathematical grounding in students reasoning I looked in a second study at what grounds they had for different strategy choices and conclusions. This qualitative study suggested that beliefs about safety, expectation and motivation were important in the central decisions made during task solving.  But are reasoning and beliefs gendered? The third study explored upper secondary school teachers conceptions about gender and students mathematical reasoning. In this study I found that upper secondary school teachers attributed gender symbols including insecurity, use of standard methods and imitative reasoning to girls and symbols such as multiple strategies especially on the calculator, guessing and chance-taking were assigned to boys. In the fourth and final study I found that students, both male and female, shared their teachers view of rather traditional feminities and masculinities. Remarkably however, this result did not repeat itself when students were asked to reflect on their own behaviour: there were some discrepancies between the traits the students ascribed as gender different and the traits they ascribed to themselves. Taken together the thesis suggests that, contrary to conceptions, girls and boys share many of the same core beliefs about mathematics, but much work is still needed if we should create learning environments that provide better opportunities for students to develop beliefs that guide them towards well-grounded mathematical reasoning. 

Teachers' conceptions about students' mathematical reasoning : Gendered or not?

This study looks at how upper secondary school teachers gender stereotype aspects of students' mathematical reasoning. Girls were attributed gender symbols including insecurity, use of standard methods and imitative reasoning. Boys were assigned the symbols such as multiple strategies especially on the calculator, guessing and chance-taking. 

On the EA-style integrated processing of self-contained mathematical texts

A sound and complete first-order goal-oriented sequent-type calculus is developed with ``large-block'' inference rules. In particular, the calculus contains formal analogues of such natural proof-search techniques as handling definitions and applying auxiliary propositions.

Evidence Algorithm and Processing Formalized Mathematical Texts

The goal of a research programme Evidence Algorithm is a development of an open system of automated proving that is able to accumulate mathematical knowledge and to prove theorems in a context of a self-contained mathematical text. By now, the first version of such a system called a System for Automated Deduction, SAD, is implemented in software. The system SAD possesses the following main features: mathematical texts are formalized using a specific formal language that is close to a natural language of mathematical publications; a proof search is based on special sequent-type calculi formalizing natural reasoning style, such as application of definitions and auxiliary propositions. These calculi also admit a separation of equality handling from deduction that gives an opportunity to integrate logical reasoning with symbolic calculation.

Insuring cleaner oceans: the economics of oil pollution prevention

The current system of controlling oil spills involves a complex relationship of international, federal and state law, which has not proven to be very effective. The multiple layers of regulation often leave shipowners unsure of the laws facing them. Furthemore, nations have had difficulty enforcing these legal requirements. This thesis deals with the role marine insurance can play within the existing system of legislation to provide a strong preventative influence that is simple and cost-effective to enforce. In principle, insurance has two ways of enforcing higher safety standards and limiting the risk of an accident occurring. The first is through the use of insurance premiums that are based on the level of care taken by the insured. This means that a person engaging in riskier behavior faces a higher insurance premium, because their actions increase the probability of an accident occurring. The second method, available to the insurer, is collectively known as cancellation provisions or underwriting clauses. These are clauses written into an insurance contract that invalidates the agreement when certain conditions are not met by the insured The problem has been that obtaining information about the behavior of an insured party requires monitoring and that incurs a cost to the insurer. The application of these principles proves to be a more complicated matter. The modern marine insurance industry is a complicated system of multiple contracts, through different insurers, that covers the many facets of oil transportation. Their business practices have resulted in policy packages that cross the neat bounds of individual, specific insurance coverage. This paper shows that insurance can improve safety standards in three general areas -crew training, hull and equipment construction and maintenance, and routing schemes and exclusionary zones. With crew, hull and equipment, underwriting clauses can be used to ensure that minimum standards are met by the insured. Premiums can then be structured to reflect the additional care taken by the insured above and beyond these minimum standards. Routing schemes are traffic flow systems applied to congested waterways, such as the entrance to New York harbor. Using natural obstacles or manmade dividers, ships are separated into two lanes of opposing traffic, similar to a road. Exclusionary zones are marine areas designated off limits to tanker traffic either because of a sensitive ecosystem or because local knowledge is required of the region to ensure safe navigation. Underwriting clauses can be used to nullify an insurance contract when a tanker is not in compliance with established exclusionary zones or routing schemes.

Two Essays on the economics of Education

We develop a job-market signaling model where signals may convey two pieces of information. This model is employed to study the GED exam and countersignaling (signals non-monotonic in ability). A result of the model is that countersignaling is more expected to occur in jobs that require a combination of skills that differs from the combination used in the schooling process. The model also produces testable implications consistent with evidence on the GED: (i) it signals both high cognitive and low non-cognitive skills and (ii) it does not affect wages. Additionally, it suggests modifications that would make the GED a more effective signal.

Inflation and income inequality: a shopping-time aproach: (Forthcoming, Journal of Development Economics)

Our work is based on a simpliÖed heterogenous-agent shoppingtime economy in which economic agents present distinct productivities in the production of the consumption good, and di§erentiated access to transacting assets. The purpose of the model is to investigate whether, by focusing the analysis solely on endogenously determined shopping times, one can generate a positive correlation between ináation and income inequality. Our main result is to show that, provided the productivity of the interest-bearing asset in the transacting technology is high enough, it is true true that a positive link between ináation and income inequality is generated. Our next step is to show, through analysis of the steady-state equations, that our approach can be interpreted as a mirror image of the usual ináation-tax argument for income concentration. An example is o§ered to illustrate the mechanism.

The diversity of diversity: further methodological considerations on the use of the concept in cultural economics

The implications of diversity still raise confusion in the cultural debate. We address them from both a formal and conceptual viewpoints, putting in check the validity of some arguments. We conclude that: measuring diversity demands key decisions and careful statistical procedures; ignorance on optimal diversity levels and on ways to generate them is widespread in the cultural field; there is no support for cultural diversity as something associated to fair economic and political systems; restriction to sheer economics requires the establishment of links between diversity and measurable properties – something rather incipient. Diversity, as a social choice, should be distinguished from it as an economic value.

Essays on international economics

This study in International Economics has three main goals. First, to indicate, among seven price indices, the one with the highest purchasing power parity (PPP) evidence; second, to suggest that the international trade theory explains to satisfaction the real exchange rate parity among countries with similar relative-factor-endowment; and third, to study the impact of the Brazilian trade openness on labor demand elasticity.

The two methods of economics

A Teoria Econômica Emprega Dois Métodos: o Método Hipotético-Dedutivo, Utilizado Principalmente Pelos Economistas Neoclássicos, e o Método Histórico-Dedutivo, Adotado Pelos Economistas Clássicos e Keynesianos. Ambos são Legítimos, Mas, Desde que a Economia é Substantiva, não uma Ciência Metodológica, Onde o Objeto é o Sistema Econômico, o Método Histórico-Dedutivo é o Mais Apropriado. o Método Hipotético-Dedutivo Permite que o Economista Desenvolva Ferramentas para Analisar o Sistema Econômico, Mas Falha ao Analisar o Sistema como um Todo. em Contrapartida, o Método Histórico-Dedutivo Parte da Observação Empírica da Realidade e da Busca por Regularidades e Tendências. é um Método Empírico, Apropriado para as Ciências Substantivas que Tratam de Sistemas Abertos, como é o Caso da Economia.

The insurance function of contracts

One of the central problems in contract law is to define the frontier between legal and illegal breaches of promises. The distinction between good and bad faith is perhaps the conceptual tool most commonly used to tell one from the other. Lawyers spend a lot of energy trying to frame better definitions of the concepts of good and bad faith based on principles of ethics or justice, but often pay much less attention to theories dealing with the incentives that can engender good faith behavior in contractual relationships. By describing the economics of what Stiglitz defined as “explicit” and “implicit” insurance, I highlight the “insurance function” hidden in any promise with basically no mathematical notation. My aim is to render the subject intelligible and useful to lawyers with little familiarity with economics.