Filtering by
- All Subjects: Applied Mathematics
- Creators: Castillo-Chavez, Carlos
Research shows that the subject of mathematics, although revered, remains a source of trepidation for many individuals, as they find it difficult to form a connection between the work they do on paper and their work's practical applications. This research study describes the impact of teaching a challenging introductive applied mathematics course on high school students' skills and attitudes towards mathematics in a college Summer Program. In the analysis of my research data, I identified several emerging changes in skills and attitudes towards mathematics, skills that high-school students needed or developed when taking the mathematical modeling course. Results indicated that the applied mathematics course had a positive impact on several students' attitudes, in general, such as, self-confidence, meanings of what mathematics is, and their perceptions of what solutions are. It also had a positive impact on several skills, such as translating real-life situations to mathematics via flow diagrams, translating the models' solutions back from mathematics to the real world, and interpreting graphs. Students showed positive results when the context of their problems was applied or graphical, and fewer improvement on problems that were not. Research also indicated some negatives outcomes, a decrease in confidence for certain students, and persistent negative ways of thinking about graphs. Based on these findings, I make recommendations for teaching similar mathematical modeling at the pre-university level, to encourage the development of young students through educational, research and similar mentorship activities, to increase their inspiration and interest in mathematics, and possibly consider a variety of sciences, technology, engineering and mathematics-related (STEM) fields and careers.
Chapter 1 carries out a review of the mobility models found in the literature and sets the economic context of this dissertation. Chapter 2 explores a simple model that considers poor and rich classes and the impact that educational success may have on altering mobility patterns. The role of the environment is modeled through the use of a modified version of the invasion/extinction model of Richard Levins. Chapter 3 expands the socio-economic classes to include a large middle class to study the role of social mobility in the presence of higher heterogeneity. Chapter 4 includes demographic growth and explores what would be the time scales needed to accelerate mobility. The dissertation asked how long it will take to increase by 22% the proportion of educated from the poor classes under demographic versus non-demographic growth conditions. Chapter 5 summarizes results and includes a discussion of results. It also explores ways of modeling the influence of nonlinear dynamics of mobility, via exogenous factors. Finally, Chapter 6 presents economic perspectives about the role of environmental influence on college success. The framework can be used to incorporate the impact of economic factors and social changes, such as unemployment, or gap between the haves and have nots. The dissertation shows that peer influence (poor influencing the poor) has a larger effect than class influence (rich influencing the poor). Additionally, more heterogeneity may ease mobility of groups but results depend on initial conditions. Finally, average well-being of the community and income disparities may improve over time. Finally, population growth may extend time scales needed to achieve a specific goal of educated poor.