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We study the ideas about teaching and learning mathematics that undergraduate students generate when they encounter tasks designed to embed approximations of teaching practice in mathematics courses taken by a general population of students. These tasks attend to the dual goals of developing an understanding of mathematics content and an understanding of how teachers provide classroom experiences that foster mathematics learning. The study employs a qualitative, multiple-case study methodology, with four cases bounded by the content areas of abstract algebra, single variable calculus, discrete mathematics, and introductory statistics. The data for the study come from undergraduate students' written work on mathematical tasks, interviews with a subset of students from each course, and interviews with each instructor throughout the term during which they implemented the tasks. Our findings indicate that students identified the broad applicability of teaching skills (discussed by 32 of the 61 interviewed students), recognized the value of examining hypothetical learners' mathematical work (discussed by 59 of the 61 interviewed students), and reported empathy for hypothetical learners (discussed by 38 of the 61 interviewed students). These findings persisted across the course content and course levels we studied, leading us to conclude that our findings can transfer to additional mathematics courses in secondary mathematics teacher preparation.

This paper introduces lessons designed to incorporate applications to teaching high school mathematics in an undergraduate Discrete Mathematics course. Because many prospective high school teachers do not take courses that are specifically designed for teachers, providing materials aimed at teacher preparation that can be easily integrated into courses that serve a general mathematics major is one strategy for addressing mathematics teacher preparation. We developed lessons using four guiding features: choosing appropriate content; making school mathematics connections; incorporating active learning; and providing robust lesson notes. Our interview-based findings document how the lessons were used by instructors and analyze the mathematical ideas and understandings that arose from the use of the lessons at two different sites.

We describe the design and implementation of lessons in undergraduate abstract algebra that integrate applications to teaching high school mathematics. Each lesson consists of a pre-activity, class activity, homework set, assessment questions and detailed instructor notes. The included applications intend to bridge advanced mathematics concepts to secondary school mathematics content for prospective secondary mathematics teachers, as well as provide instructors with a useful resource. Each lesson includes four guiding features: addressing meaningful content; making connections to mathematics teaching; emphasizing active learning; and providing comprehensive notes for instructors. Interviews with instructors and their students document how the instructors adapted the lessons to their classrooms and how the lessons influenced undergraduates' mathematical understanding.

Transfer efficiency is the proportion of energy passed between nodes in food webs. It is an emergent, unitless property that is difficult to measure, and responds dynamically to environmental and ecosystem changes. Because the consequences of changes in transfer efficiency compound through ecosystems, slight variations can have large effects on food availability for top predators. Here, we review the processes controlling transfer efficiency, approaches to estimate it, and known variations across ocean biomes. Both process-level analysis and observed macroscale variations suggest that ecosystem-scale transfer efficiency is highly variable, impacted by fishing, and will decline with climate change. It is important that we more fully resolve the processes controlling transfer efficiency in models to effectively anticipate changes in marine ecosystems and fisheries resources.

Projections of climate change impacts on marine ecosystems have revealed long-term declines in global marine animal biomass and unevenly distributed impacts on fisheries. Here we apply an enhanced suite of global marine ecosystem models from the Fisheries and Marine Ecosystem Model Intercomparison Project (Fish-MIP), forced by new-generation Earth system model outputs from Phase 6 of the Coupled Model Intercomparison Project (CMIP6), to provide insights into how projected climate change will affect future ocean ecosystems. Compared with the previous generation CMIP5-forced Fish-MIP ensemble, the new ensemble ecosystem simulations show a greater decline in mean global ocean animal biomass under both strong-mitigation and high-emissions scenarios due to elevated warming, despite greater uncertainty in net primary production in the high-emissions scenario. Regional shifts in the direction of biomass changes highlight the continued and urgent need to reduce uncertainty in the projected responses of marine ecosystems to climate change to help support adaptation planning.

While the physical dimensions of climate change are now routinely assessed through multimodel intercomparisons, projected impacts on the global ocean ecosystem generally rely on individual models with a specific set of assumptions. To address these single-model limitations, we present standardized ensemble projections from six global marine ecosystem models forced with two Earth system models and four emission scenarios with and without fishing. We derive average biomass trends and associated uncertainties across the marine food web. Without fishing, mean global animal biomass decreased by 5% (±4% SD) under low emissions and 17% (±11% SD) under high emissions by 2100, with an average 5% decline for every 1 °C of warming. Projected biomass declines were primarily driven by increasing temperature and decreasing primary production, and were more pronounced at higher trophic levels, a process known as trophic amplification. Fishing did not substantially alter the effects of climate change. Considerable regional variation featured strong biomass increases at high latitudes and decreases at middle to low latitudes, with good model agreement on the direction of change but variable magnitude. Uncertainties due to variations in marine ecosystem and Earth system models were similar. Ensemble projections performed well compared with empirical data, emphasizing the benefits of multimodel inference to project future outcomes. Our results indicate that global ocean animal biomass consistently declines with climate change, and that these impacts are amplified at higher trophic levels. Next steps for model development include dynamic scenarios of fishing, cumulative human impacts, and the effects of management measures on future ocean biomass trends.

The fifth-grade curriculum presents many opportunities to use students' prior mathematical knowledge as a way to bridge new and more difficult mathematical ideas. In this article, the authors document an area tiling task given to fifth-grade students to connect aspects of area measurement covered in earlier grades to grade-level standards such as: (1) investigating number patterns; (2) converting between different-sized units of measure; and (3) understanding fraction operations through an area model. The area model is interwoven through many of the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) and can act as a common thread for discussing and relating mathematical ideas that are more complex. The LEGO® task stemmed from research surrounding preservice elementary school teachers' (PSTs') conceptions of area tiling tasks. This task can be used with elementary school students to elicit different strategies through an area investigation and to foster connections between representations and numerical strategies. The task provides opportunities for mathematical discourse to occur among multiple viewpoints. Physical tools can be powerful in helping students create mathematics and understand more deeply the strategies they employ. The LEGO® bricks elicited and extended students' thinking about number and operations in relation to area measurement. The task gave students an opportunity to use known mathematics to connect to grade-level standards and beyond as well as to visualize the mathematics in their strategies through physical representations.

At the current stage of plug-in electric vehicle (PEV) market development, sales rates vary dramatically across different countries and regions. For policy-makers and other stakeholders it is useful to understand the major social, economic, and policy drivers of vehicle adoption. This paper provides insights into the developing PEV markets in Norway, Netherlands, California, United States, France, Japan, and Germany. This is accomplished by applying a Technological Innovation System (TIS) approach that systematically identifies the role of different factors in promulgating new markets. Our comparison between markets shows that in all studied regions, sales of PEVs are supported through various types of government incentives, government resources, and other legitimation activities. However, regions with relatively strong PEV markets have a greater focus on market formation activities and relatively higher costs savings associated with operating an electric vehicle as compared to a conventional vehicle. To determine whether these factors are the primary determinants of PEV market shares, further research should be undertaken that also incorporates analysis related to the presence and government support for entrepreneurial activities related to electric vehicle innovation.