A Community College Instructor’s Reflective Journey Toward Developing Pedagogical Content Knowledge for Nature of Science in a Non-majors Undergraduate Biology Course

Research supports an explicit-reflective approach to teaching about nature of science (NOS), but little is reported on teachers’ journeys as they attempt to integrate NOS into everyday lessons. This participatory action research paper reports the challenges and successes encountered by an in-service teacher, Sarah, implementing NOS for the first time throughout four units of a community college biology course (genetics, molecular biology, evolution, and ecology). Through the action research cycles of planning, implementing, and reflecting, Sarah identified areas of challenge and success. This paper reports emergent themes that assisted her in successfully embedding NOS within the science content. Data include weekly lesson plans and pre/post reflective journaling before and after each lesson of this lecture/lab combination class that met twice a week. This course was taught back to back semesters, and this study is based on the results of a year-long process. Developing pedagogical content knowledge (PCK) for NOS involves coming to understand the overlaps and connections between NOS, other science subject matter, pedagogical strategies, and student learning. Sarah found that through action research she was able to grow and assimilate her understanding of NOS within the biology content she was teaching. A shift in orientation toward teaching products of science to teaching science processes was a necessary shift for NOS pedagogical success. This process enabled Sarah’s development of PCK for NOS. As a practical example of putting research-based instructional recommendations into practice, this study may be very useful for other teachers who are learning to teach NOS.     

Cognitive preconditions of early reading and spelling: a latent-variable approach with longitudinal data

The aim of the present study was to empirically disentangle the interdependencies of the impact of nonverbal intelligence, working memory capacities, and phonological processing skills on early reading decoding and spelling within a latent variable approach. In a sample of 127 children, these cognitive preconditions were assessed before the onset of formal education, whereas reading as well as spelling achievement was measured at the end of grade 1. The findings indicate that working memory does contribute to the prediction of early reading and spelling, and that this contribution outperforms that of general intelligence and phonological recoding from long-term memory during the early steps of reading and spelling acquisition. Moreover, the results show that phonological awareness mediates the effects of working memory capacities on early literacy outcomes. The role of working memory and phonological awareness as key cognitive preconditions of early reading and spelling are discussed.     

Locating the equilibrium points of a predator–prey model by means of affine state feedback

A predator–prey model with prey-dependent functional response is considered. The set of all points in the positive quadrant of the state plane that can be made equilibrium points by means of an affine state-feedback control law is determined, and the values of the control parameters ensuring the desired equilibria are provided. It is shown how the asymptotic stability of the equilibrium points depends on simple geometric conditions. The problem of stabilizing unstable equilibrium points is also briefly discussed.     

Automatic testing and assessment of neuroanatomy using a digital brain atlas: Method and development of computer‐ and mobile‐based applications

Preparation of tests and student's assessment by the instructor are time consuming. We address these two tasks in neuroanatomy education by employing a digital media application with a three‐dimensional (3D), interactive, fully segmented, and labeled brain atlas. The anatomical and vascular models in the atlas are linked to Terminologia Anatomica. Because the cerebral models are fully segmented and labeled, our approach enables automatic and random atlas‐derived generation of questions to test location and naming of cerebral structures. This is done in four steps: test individualization by the instructor, test taking by the students at their convenience, automatic student assessment by the application, and communication of the individual assessment to the instructor. A computer‐based application with an interactive 3D atlas and a preliminary mobile‐based application were developed to realize this approach. The application works in two test modes: instructor and student. In the instructor mode, the instructor customizes the test by setting the scope of testing and student performance criteria, which takes a few seconds. In the student mode, the student is tested and automatically assessed. Self‐testing is also feasible at any time and pace. Our approach is automatic both with respect to test generation and student assessment. It is also objective, rapid, and customizable. We believe that this approach is novel from computer‐based, mobile‐based, and atlas‐assisted standpoints. Anat Sci Educ 2:244–252, 2009. © 2009 American Association of Anatomists.     

A method for the integer-order approximation of fractional-order systems

A procedure for approximating fractional-order systems by means of integer-order state-space models is presented. It is based on the rational approximation of fractional-order operators suggested by Oustaloup. First, a matrix differential equation is obtained from the original fractional-order representation. Then, this equation is realized in a state-space form that has a sparse block-companion structure. The dimension of the resulting integer-order model can be reduced using an efficient algorithm for rational L₂ approximation. Two numerical examples are worked out to show the performance of the suggested technique.     

Early development of quantity to number-word linkage as a precursor of mathematical school achievement and mathematical difficulties: Findings from a four-year longitudinal study

This article reports results of a four-year longitudinal study that investigated the impact of specific and non-specific precursors on mathematical school achievement. Preschool quantity-number competencies (QNC) predicted mathematical achievement in primary school. Furthermore, basic arithmetic fact retrieval in Grade 1 had an impact on early mathematics school achievement. The influence of socioeconomic status and number naming speed, assessed in kindergarten, became especially important at the end of Grade 4. Particularly, a subgroup of mathematically low-achieving children in Grade 4 had already performed more poorly than normal children in tasks assessing preschool QNC, number naming speed, and basic arithmetic fact retrieval, as well as nonverbal intelligence and socioeconomic status.     

Frequency-domain approach to robust PI control

The paper considers the problem of designing PI controllers for industrial processes approximated by a first-order time-delayed model. The suggested frequency-domain approach is based on a normalized open-loop transfer function and makes use of the loci of constant stability margins and other performance indices in the parameter space. In this way, it is possible to evaluate the effects of uncertainties in the process parameters and, thus, control system robustness. Some examples show how the procedure operates.     

Specific Preschool Executive Functions Predict Unique Aspects of Mathematics Development: A 3-Year Longitudinal Study

This study assessed the extent to which executive functions (EF), according to their factor structure in 5-year-olds (N = 244), influenced early quantity–number competencies, arithmetic fluency, and mathematics school achievement throughout first and second grades. A confirmatory factor analysis resulted in updating as a first, and inhibition and shifting as a combined second factor. In the structural equation model, updating significantly affected knowledge of the number word sequence, suggesting a facilitatory effect on basic encoding processes in numerical materials that can be learnt purely by rote. Shifting and inhibition significantly influenced quantity to number word linkages, indicating that these processes promote developing a profound understanding of numbers. These results show the supportive role of specific EF for specific aspects of a numerical foundation.