Matching Items (5)

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Characterization of the Mathematical Theoretical Biology Institute as a Vygotskian-Holzman zone of proximal development

Description

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,

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.

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  • 2015

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Cooperative learning in a community college setting: developmental coursework in mathematics

Description

This action research study, set in a community college in the southwestern United States, was designed to investigate the effects of implementing cooperative learning strategies in a developmental mathematics course.

This action research study, set in a community college in the southwestern United States, was designed to investigate the effects of implementing cooperative learning strategies in a developmental mathematics course. Introductory algebra was formerly taught in a lecture based format, and as such regularly had a low course completion rate. To create a more engaging learning environment, formal and informal cooperative learning activities were integrated into the curriculum. Bandura's self-efficacy theory, Vygotsky's constructivist theory, and Deutsch's social interdependence theory guided this study. Qualitative and quantitative data were collected through pre and post self-efficacy surveys, semi-structured student interviews, student journal entries, class observations, focus groups, and pre and post mathematics assessments. Data were analyzed using a mixed methods approach. As a result of implementing cooperative learning practices as a part of my teaching, there was an increase in student attendance as well as a decrease in student withdrawal rates. Students were also more motivated to work with each other on mathematics homework outside of class sessions. There was a strong sense of community that I had not witnessed in previous courses that I have taught. Use of cooperative learning practices served as a vehicle to motivate students to work on their mathematics coursework with their peers. Keywords: cooperative learning, developmental mathematics, constructivism, social interdependence theory, self-efficacy, community college

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  • 2013

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An investigation of the teaching and learning of function inverse

Description

Based on poor student performance in past studies, the incoherence present in the teaching of inverse functions, and teachers' own accounts of their struggles to teach this topic, it is

Based on poor student performance in past studies, the incoherence present in the teaching of inverse functions, and teachers' own accounts of their struggles to teach this topic, it is apparent that the idea of function inverse deserves a closer look and an improved pedagogical approach. This improvement must enhance students' opportunity to construct a meaning for a function's inverse and, out of that meaning, produce ways to define a function's inverse without memorizing some procedure. This paper presents a proposed instructional sequence that promotes reflective abstraction in order to help students develop a process conception of function and further understand the meaning of a function inverse. The instructional sequence was used in a teaching experiment with three subjects and the results are presented here. The evidence presented in this paper supports the claim that the proposed instructional sequence has the potential to help students construct meanings needed for understanding function inverse. The results of this study revealed shifts in the understandings of all three subjects. I conjecture that these shifts were achieved by posing questions that promoted reflective abstraction. The questions and subsequent interactions appeared to result in all three students moving toward a process conception of function.

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  • 2014

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Students' ways of thinking about combinatorics solution sets

Description

Research on combinatorics education is sparse when compared with other fields in mathematics education. This research attempted to contribute to the dearth of literature by examining students' reasoning about enumerative

Research on combinatorics education is sparse when compared with other fields in mathematics education. This research attempted to contribute to the dearth of literature by examining students' reasoning about enumerative combinatorics problems and how students conceptualize the set of elements being counted in such problems, called the solution set. In particular, the focus was on the stable patterns of reasoning, known as ways of thinking, which students applied in a variety of combinatorial situations and tasks. This study catalogued students' ways of thinking about solution sets as they progressed through an instructional sequence. In addition, the relationships between the catalogued ways of thinking were explored. Further, the study investigated the challenges students experienced as they interacted with the tasks and instructional interventions, and how students' ways of thinking evolved as these challenges were overcome. Finally, it examined the role of instruction in guiding students to develop and extend their ways of thinking. Two pairs of undergraduate students with no formal experience with combinatorics participated in one of the two consecutive teaching experiments conducted in Spring 2012. Many ways of thinking emerged through the grounded theory analysis of the data, but only eight were identified as robust. These robust ways of thinking were classified into three categories: Subsets, Odometer, and Problem Posing. The Subsets category encompasses two ways of thinking, both of which ultimately involve envisioning the solution set as the union of subsets. The three ways of thinking in Odometer category involve holding an item or a set of items constant and systematically varying the other items involved in the counting process. The ways of thinking belonging to Problem Posing category involve spontaneously posing new, related combinatorics problems and finding relationships between the solution sets of the original and the new problem. The evolution of students' ways of thinking in the Problem Posing category was analyzed. This entailed examining the perturbation experienced by students and the resulting accommodation of their thinking. It was found that such perturbation and its resolution was often the result of an instructional intervention. Implications for teaching practice are discussed.

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Date Created
  • 2013

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Conditions that promote the academic performance of college students in a remedial mathematics course: academic competence, academic resilience, and the learning environment

Description

Researchers have postulated that math academic achievement increases student success in college (Lee, 2012; Silverman & Seidman, 2011; Vigdor, 2013), yet 80% of universities and 98% of community colleges require

Researchers have postulated that math academic achievement increases student success in college (Lee, 2012; Silverman & Seidman, 2011; Vigdor, 2013), yet 80% of universities and 98% of community colleges require many of their first-year students to be placed in remedial courses (Bettinger & Long, 2009). Many high school graduates are entering college ill prepared for the rigors of higher education, lacking understanding of basic and important principles (ACT, 2012). The desire to increase academic achievement is a wide held aspiration in education and the idea of adapting instruction to individuals is one approach to accomplish this goal (Lalley & Gentile, 2009a). Frequently, adaptive learning environments rely on a mastery learning approach, it is thought that when students are afforded the opportunity to master the material, deeper and more meaningful learning is likely to occur. Researchers generally agree that the learning environment, the teaching approach, and the students' attributes are all important to understanding the conditions that promote academic achievement (Bandura, 1977; Bloom, 1968; Guskey, 2010; Cassen, Feinstein & Graham, 2008; Changeiywo, Wambugu & Wachanga, 2011; Lee, 2012; Schunk, 1991; Van Dinther, Dochy & Segers, 2011). The present study investigated the role of college students' affective attributes and skills, such as academic competence and academic resilience, in an adaptive mastery-based learning environment on their academic performance, while enrolled in a remedial mathematics course. The results showed that the combined influence of students' affective attributes and academic resilience had a statistically significant effect on students' academic performance. Further, the mastery-based learning environment also had a significant effect on their academic competence and academic performance.

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  • 2013