Preservice teachers’ creation of dynamic geometry sketches to understand trigonometric relationships

Dynamic geometry software can help teachers highlight mathematical relationships in ways not possible with static diagrams. However, these opportunities are mediated by teachers' abilities to construct sketches that focus users' attention on the desired variant or invariant relationships. This paper looks at two cohorts of preservice secondary mathematics teachers and their attempts to build dynamic geometry sketches that highlighted the trigonometric relationship between the angle and slope of a line on the coordinate plane. We identify common challenges in the construction of these sketches and present examples for readers to interact with that highlight these issues. Lastly, we discuss ways that mathematics teacher educators can help beginning teachers understand common pitfalls in the building of dynamic geometry sketches, which can cause sketches not to operate as intended

Active Learning Approaches to Teaching Soil Science at the College Level

Traditional passive approaches to teaching, such as lectures, are not particularly effective at promoting student learning, or at developing the qualities that employers seek in graduates from soil science programs, such as problem-solving and critical thinking skills. In contrast, active learning approaches have been shown to promote these very qualities in students. Here, I discuss my use of active learning approaches to teach soil science at the introductory and advanced levels, with particular focus on problem-based learning (PBL), and combined just-in-time teaching (JITT) and peer instruction (PI). A brief description of the each pedagogical approach is followed by evidence of its impact on student learning in general and, when available, its use in soil science courses. I describe and discuss my experiences using these approaches teaching introductory soil science (face-to-face and online), soil chemistry and soil microbiology courses, and provide examples of some of the problems I use. I have found the benefits to student learning in terms of student engagement, ownership of learning, and development of critical thinking and problem-solving skills easily outweigh the additional effort required, and are clear relative to traditional, passive approaches to teaching

Migrating Successful Student Engagement Strategies Online: Opportunities and Challenges Using Jigsaw Groups and Problem-Based Learning

Online courses may be criticized for failing to engage students. Faculty members teaching in the classroom often employ a number of strategies that capture the interest of students, but may find the migration to the online environment a daunting prospect. This paper describes the transitioning of two common strategies to engage students in the classroom – jigsaw groups and problem-based learning – from face-to-face to online courses in sociology and soil science, respectively. The paper discusses the challenges and opportunities that were found to be common to the implementation of both these strategies online, and provides suggestions for faculty considering this transition

Métodos de reducción de escala : aplicaciones al tiempo, clima, variabilidad climática y cambio climático

Los Modelos de Circulación General Atmosféricos-Oceánicos Acoplados muestran buena habilidad para simular la evolución de las circulaciones de escala global. Sin embargo, esta bondad no es muy útil para el estudio de impactos locales debido a que la resolución espacial de esos modelos está por encima de la escala de los impactos locales que se desean analizar. Es importante tomar esto en cuenta al estudiar impactos del clima en las actividades del hombre, en la biodiversidad, en ambientes marino-costeros y en arrecifes en las regiones tropicales, por ejemplo. Existen dos aproximaciones para lidiar con esta diferencia de escala e información: los métodos de reducción de escala dinámica y estadística. En este trabajo, se discuten los elementos básicos del sistema climático y las posibles causas de los cambios atmosféricos observados en este sistema. Se discuten brevemente los principales conceptos físicos del sistema climático, el clima de una región, la variabilidad climática y las generalidades del problema del cambio climático global con énfasis en el aspecto regional del mismo. Se describen también los esquemas metodológicos del proceso de reducción de escala y se presenta una discusión sobre sus ventajas y limitaciones, así como algunas aplicaciones al tiempo atmosférico y clima regional.Coupled Atmosphere-Ocean General Circulation Models demonstrate good skill in simulating large scale circulations. However this output is not very useful to study local impacts, as its spatial resolution is courser than the scale of local impacts. It is very important to consider this issue when studying, for instance, climate impacts on human activities, coastal-marine biodiversity and tropical coral reefs. In general terms, there have been two different approaches to deal with this scale and information difference: the dynamic and the statistic downscaling methods. In this work, the basic climate elements are presented and the possible physical causes of atmospheric changes are discussed. Also, a summary of the main physical concepts that define the climate system as well as the climate and climate variability of a region with respect to the mean atmospheric state and the general aspects of the problem of climate change with emphasis on regional scales, is presented. In addition, this study describes the methodological schemes of the downscaling process and presents a discussion of downscaling advantages and disadvantages, while providing applications for regional weather and climate as well as for socio-economic benefits in coastal, agricultural and tourism activities, among others