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- Genre: Doctoral Dissertation
- All Subjects: Mathematics Education
- Creators: Castillo-Chavez, Carlos
- Member of: Theses and Dissertations
The theoretical lens of developmental psychologists Lev Vygotsky (1978, 1987) and Lois Holzman (2010) that sees learning and development as a social process is used. From this view student development in MTBI is attributed to the collaborative and creative way students co-create the process of becoming scientists. This results in building a continuing network of academic and professional relationships among peers and mentors, in which around three quarters of MTBI PhD graduates come from underrepresented groups.
The extent to which MTBI creates a Vygotskian learning environment is explored from the perspectives of participants who earned doctoral degrees. Previously hypothesized factors (Castillo-Garsow, Castillo-Chavez and Woodley, 2013) that affect participants’ educational and professional development are expanded on.
Factors identified by participants are a passion for the mathematical sciences; desire to grow; enriching collaborative and peer-like interactions; and discovering career options. The self-recognition that they had the ability to be successful, key element of the Vygotskian-Holzman theoretical framework, was a commonly identified theme for their educational development and professional growth.
Participants characterize the collaborative and creative aspects of MTBI. They reported that collaborative dynamics with peers were strengthened as they co-created a learning environment that facilitated and accelerated their understanding of the mathematics needed to address their research. The dynamics of collaboration allowed them to complete complex homework assignments, and helped them formulate and complete their projects. Participants identified the creative environments of their research projects as where creativity emerged in the dynamics of the program.
These data-driven findings characterize for the first time a summer program in the mathematical sciences as a Vygotskian-Holzman environment, that is, a `place’ where participants are seen as capable applied mathematicians, where the dynamics of collaboration and creativity are fundamental components.
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.