A Q-Methodology approach to investigating the relationship between level of reflection and typologies among prospective teachers in the physics learning assistant program at Florida International University

The purpose of this mixed methods study was to understand physics Learning Assistants' (LAs) views on reflective teaching, expertise in teaching, and LA program teaching experience and to determine if views predicted level of reflection evident in writing. Interviews were conducted in Phase One, Q methodology was used in Phase Two, and level of reflection in participants' writing was assessed using a rubric based on Hatton and Smith's (1995) "Criteria for the Recognition of Evidence for Different Types of Reflective Writing" in Phase Three. Interview analysis revealed varying perspectives on content knowledge, pedagogical knowledge, and experience in relation to expertise in teaching. Participants revealed that they engaged in reflection on their teaching, believed reflection helps teachers improve, and found peer reflection beneficial. Participants believed teaching experience in the LA program provided preparation for teaching, but that more preparation was needed to teach. Three typologies emerged in Phase Two. Type One LAs found participation in the LA program rewarding and believed expertise in teaching does not require expertise in content or pedagogy, but it develops over time from reflection. Type Two LAs valued reflection, but not writing reflections, felt the LA program teaching experience helped them decide on non-teaching careers and helped them confront gaps in their physics knowledge. Type Three LAs valued reflection, believed expertise in content and pedagogy are necessary for expert teaching, and felt LA program teaching experience increased their likelihood of becoming teachers, but did not prepare them for teaching. Writing assignments submitted in Phase Three were categorized as 19% descriptive writing, 60% descriptive reflections, and 21% dialogic reflections. No assignments were categorized as critical reflection. Using ordinal logistic regression, typologies that emerged in Phase Two were not found to be predictors for the level of reflection evident in the writing assignments. In conclusion, viewpoints of physics LAs were revealed, typologies among them were discovered, and their writing gave evidence of their ability to reflect on teaching. These findings may benefit faculty and staff in the LA program by helping them better understand the views of physics LAs and how to assess their various forms of reflection.

The relationship between selected standardized test scores and performance in advanced placement math and science exams: Analyzing the differential effectiveness of scores for course identification and placement

There is a national need to increase the STEM-related workforce. Among factors leading towards STEM careers include the number of advanced high school mathematics and science courses students complete. Florida's enrollment patterns in STEM-related Advanced Placement (AP) courses, however, reveal that only a small percentage of students enroll into these classes. Therefore, screening tools are needed to find more students for these courses, who are academically ready, yet have not been identified. The purpose of this study was to investigate the extent to which scores from a national standardized test, Preliminary Scholastic Assessment Test/ National Merit Qualifying Test (PSAT/NMSQT), in conjunction with and compared to a state-mandated standardized test, Florida Comprehensive Assessment Test (FCAT), are related to selected AP exam performance in Seminole County Public Schools. An ex post facto correlational study was conducted using 6,189 student records from the 2010 - 2012 academic years. Multiple regression analyses using simultaneous Full Model testing showed differential moderate to strong relationships between scores in eight of the nine AP courses (i.e., Biology, Environmental Science, Chemistry, Physics B, Physics C Electrical, Physics C Mechanical, Statistics, Calculus AB and BC) examined. For example, the significant unique contribution to overall variance in AP scores was a linear combination of PSAT Math (M), Critical Reading (CR) and FCAT Reading (R) for Biology and Environmental Science. Moderate relationships for Chemistry included a linear combination of PSAT M, W (Writing) and FCAT M; a combination of FCAT M and PSAT M was most significantly associated with Calculus AB performance. These findings have implications for both research and practice. FCAT scores, in conjunction with PSAT scores, can potentially be used for specific STEM-related AP courses, as part of a systematic approach towards AP course identification and placement. For courses with moderate to strong relationships, validation studies and development of expectancy tables, which estimate the probability of successful performance on these AP exams, are recommended. Also, findings established a need to examine other related research issues including, but not limited to, extensive longitudinal studies and analyses of other available or prospective standardized test scores.

Fibonacci Series, Golden Proportions, and the Human Biology

Pythagoras, Plato and Euclid’s paved the way for Classical Geometry. The idea of shapes that can be mathematically defined by equations led to the creation of great structures of modern and ancient civilizations, and milestones in mathematics and science. However, classical geometry fails to explain the complexity of non-linear shapes replete in nature such as the curvature of a flower or the wings of a Butterfly. Such non-linearity can be explained by fractal geometry which creates shapes that emulate those found in nature with remarkable accuracy. Such phenomenon begs the question of architectural origin for biological existence within the universe. While the concept of a unifying equation of life has yet to be discovered, the Fibonacci sequence may establish an origin for such a development. The observation of the Fibonacci sequence is existent in almost all aspects of life ranging from the leaves of a fern tree, architecture, and even paintings, makes it highly unlikely to be a stochastic phenomenon. Despite its wide-spread occurrence and existence, the Fibonacci series and the Rule of Golden Proportions has not been widely documented in the human body. This paper serves to review the observed documentation of the Fibonacci sequence in the human body.

Integrating Technology in a Statistics Course for a Special Program at Florida International University

A special undergraduate program for selected biology majors was recently inaugurated at Florida International University. The curriculum emphasizes science, mathematics, and statistics. A statistics course was implemented for this program integrating PowerPoint, statistical software (SPSS), and data from biological/biomedical studies. This didactic experience is discussed here.