The purpose of this study was to attempt to enhance performance in the Australian Mathematics Competition of a group of Western Australian Year 9 students, to a level beyond that which they might have been expected to attain, through the use of a heuristic-based intervention technique using Vygotsky's zone of proximal development principle.Since 1978, students of mathematics in Australian high schools have been meeting the challenge of the Australian Mathematics Competition. This national competition aims to provide students with a sense of achievement in mathematics and to emphasise the importance of this subject in the high school curriculum.Vygotsky's zone of proximal development refers to the difference between a student's actual developmental level and the student's potential developmental level given adult assistance. In effect, this means that while students may achieve to a plane commensurate with their actual developmental level, they will progress into their zone of proximal development with assistance and their level of achievement will rise. Vygotsky's concept of Intervention coupled with Siegler's concept of heuristic-based strategy learning provided a methodology suitable for enhancing and maximising developmental effects in this study.The study involved three distinct stages: the preparatory phase, the treatment phase and the concluding phase.In the preparatory phase, student's actual developmental levels were determined based on their performance in the 1979 Junior level Australian Mathematics Competition paper. This data facilitated identifying the paths that learning should follow in order that students' problem solving skills should improve. During this phase, students also attempted an Australian Council for Educational Research (ACER) test entitled 'Test's of Reasoning in Mathematics' (TRIM). This measure was used to monitor expected development ++ / in mathematics reasoning ability for students over the period of the study.The treatment phase involved the students in over 35 hours of instruction which exposed them to a heuristic-based intervention technique designed to enhance their performance in problem solving. Students practised various problem solving techniques and the Australian Mathematics Competition ittself became the focus for improved performance.An index of improvement was provided in the concluding phase of the study by scores obtained from the treatment group on the 1982 Intermediate level Australian Mathematics Competition paper. Scores were significantly higher than the national average of either the Year 9 or Year 10 groups. The second ACER 'TRIM' test verified that the students achieved their expected development in mathematics reasoning ability during the study.The implication of this result is that the practice of restricting students to year groups or courses on the basis of age should be examined in the light of the Vygotskian principle.

abstract: The Mathematical and Theoretical Biology Institute (MTBI) is a summer research program for undergraduate students, largely from underrepresented minority groups. Founded in 1996, it serves as a 'life-long' mentorship program, providing continuous support for its students and alumni. This study investigates how MTBI supports student development in applied mathematical research. This includes identifying of motivational factors to pursue and develop capacity to complete higher education. 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. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics for the Life and Social Sciences 2015