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A state-space model (SSM) integrating physical parameters is proposed and developed in this work, to describe the increase of global average temperature and the subsequent changes in regional climate and hydrology. This SSM approach aims at providing updated and improved forecasts, based on observations and using Bayesian inference, and at facilitating flexible engineering decision-making schemes. Global climate model simulations are used for informing the distribution of the parameters of the SSM. The case study of the Colorado River Basin serves as a preliminary application of the method, to forecast changes in the upper basin natural flow. The method projects that the post-2000 low flow volume will continue, or become even lower on average, although such projections are subject to large uncertainty. Given the increasing need of climate projections in the design, operation, and management of infrastructure, the SSM approach can serve as a useful tool, informed by historical records, to facilitate engineering applications. 

Although it is well known that motivational and cognitive resources influence secondary teachers’ instructional quality, less is known about the tertiary instructional factors that influence secondary teachers’ development of these resources. To address this gap, we report on factors that prospective secondary teachers attribute to their learning. We draw on survey responses of 70 prospective secondary teachers enrolled in mathematics courses for teachers using Mathematics of Doing, Understanding, Learning, and Educating for Secondary Schools (MODULE(S2)) materials in one of four content areas. We triangulate response themes with data from 300 prospective secondary teachers on their perceptions of instructional practices used in a mathematics course for teachers using the same suite of materials. Then, we compare these themes with literature documenting implementation of mathematics curricula in these courses. We argue that coordinating mathematics content, applications of mathematics to teaching practices, and tertiary instructional practices are key to success of these mathematics courses. 

In the past two decades, there has been a trend in materials for mathematics courses for prospective secondary teachers: more opportunities for teachers to “apply mathematics to teaching”. That is, materials increasingly highlight how mathematical knowledge learned in the course can be useful in secondary teaching, and provide opportunities for teachers to harness this knowledge in simulations of teaching. There is little known about the effects of this curricular reform on teachers’ competence. In this report, we use data from the Mathematics of Doing, Understanding, Learning, and Educating for Secondary Schools MODULE(S2) project to examine the potential impact of using such curricular materials. The data include over 300 prospective secondary teachers’ responses to 3 sets of Likert pre-/post-term surveys addressing: mathematical knowledge for teaching; expectancy for enacting selected core teaching practices; and valuing of enacting these practices. We found mean increases across the survey results. We conclude with directions for future research on the impact of this curricular reform.