María T. Sanz

A Stochastic Model for Population and Well-Being Dynamics

This article presents a stochastic dynamic model to study the demographic evolution per sexes and the corresponding well-being of a general human population. The main model variables are population per sexes and well-being. The considered well-being variable is the Gender-Related Development Index (GDI), a United Nations index. The models objectives are to improve future well-being and to reach a stable population in a country. The application case consists of adapting, validating, and using the model for Spain in the 2000–2006 period. Some instance strategies have been tested in different scenarios for the 2006–2015 period to meet these objectives by calculating the reliability of the results. The optimal strategy is “government invests more in education and maintains the present health investment tendency.”

A stochastic dynamic model to evaluate the influence of economy and well-being on unemployment control

Abstract This paper presents a stochastic dynamic mathematical model to study the evolution of the unemployment rate and other relevant related variables in a country. This model is composed by three basic interrelated subsystems: demographic, economic and well-being ones. A key aspect of this model is that it considers three UN well-being variables simultaneously: Human Development Index, Gender Empowerment Index and Gender Differentiation Index. These variables involve key concepts for human development, as Health, Education, Economy and Female Labor. With this model, the most outstanding variables found in the literature in relation with unemployment control can be used to design strategies and scenarios to reduce the unemployment rate in the future. The model has been fitted for the case of Spain in the 2002–2014 period, the largest one with information about all the variables involved in the model. Finally, several tentative scenarios and strategies have been tested to reduce the unemployment rate in Spain in the horizon of year 2025, and the corresponding forecast evolution of the Gender Differentiation Index, National income per capita, Public debt and the ratio between Public debt and Gross domestic product are shown.

SIMULATING DEMOGRAPHY AND HUMAN DEVELOPMENT DYNAMICS

A deterministic/stochastic model in which the demographic and the well-being subsystems of a country are involved and related is presented as a way to approach human development. The demographic subsystem is a side-by-side, single-gender, age-structured population dynamic model. The well-being subsystem states the dynamics of the United Nations Hybrid Human Development Index. The model has been validated in the case of Spain and Belgium. Some simulations have been performed with the model for the case of Spain in the 2009–2020 period to determine strategies and scenarios that could increase the life expectancy at birth per gender.

Including an environmental quality index in a demographic model

This paper presents a new well-being index which allows environmental quality to be measured through CO2 emissions, renewable energies and nuclear power. Its formula derives from a geometric mean used to calculate which things in the human production system warm the planet and which do not. This index has been introduced into a gender-defined stochastic population dynamic mathematical model which measures well-being in a country. The main variables in this model are rates of death, birth, emigration and immigration, as well as three UN indices: Human Development Index, Gender Development Index and Gender Empowerment Index. This model has been extended with variables that allow an environmental quality evaluation, and it has been validated for Spain during the 2001-2010 period. Moreover, a sensitivity analysis has been carried on the simulated future trend (2011-2020) to see which environmental quality variables refer more to deaths, births or the Human Development Index.

Missing Curious Fraction Problems

In this paper we present a study of one of the best-known types of descriptive word fraction problems. These problems have disappeared from today’s textbooks but are hugely important for developing arithmetic thinking. The aim of this paper is to examine the historical solution methods for these problems and discuss the analytical readings suggested by the authors. On the basis of this analysis we have conducted a preliminary study of the performance of 35 Spanish students who are highly trained in mathematics. Our results show that these students have a preference for algebraic reasoning, are reluctant to use arithmetic methods, and have reading comprehension difficulties that are reflected in their translations, from literal language to symbolic language, of the relationship between the parts expressed in the problem statement.

A stochastic dynamical social model involving a human happiness index

Abstract This paper presents a new human happiness index built through five dimensions: development, freedom, solidarity, justice and peace. These five dimensions are evaluated through quantitative variables obtained from the Human Development Reports, World Data Bank and Eurostat. The new happiness index has been built following the guidelines set by the Human Development Reports of the UN for the construction of quality indices, and it has been compared on a set of 13 EU countries with the Overall Life Satisfaction Index, which is used by the UN. Moreover, the new index has been included in a dynamic mathematical model through the demographic rates to study the evolution of the population. The obtained model has been calibrated for the period 2004–2009 and validated for the period 2010–2015 for the case of Spain. Finally, the model has been used to maximize the happiness index in Spain for the period 2016–2030, with the conclusion that to achieve this purpose, it is necessary to invest in education, research and development.

Using System Dynamics to Model Student Performance in an Intelligent Tutoring System

One basic adaptation function of an Intelligent Tutoring System (ITS) consists of selecting the most appropriate next task to be offered to the learner. This decision can be based on estimates, such as the expected performance of the student, or the probability that the student successfully solves each particular task. However, the computation of these values is intrinsically difficult, as they may depend on other complex latent variables that also need to be estimated from observable quantities, e.g. the current students ability. In this work, we have used system dynamics to model learning and predict the students performance in a given exercise, in an existing ITS that was developed to teach students solve arithmetic-algebraic word problems. The high correlation between the predicted and real scores outlines the potential of this type of modeling as a prediction tool to support the decision about the next task that should be offered to the learner.