Borrowing the concept of story grammar from reading comprehension literature, the purpose of this study was to examine the effect of teaching word problem (WP) story grammar on arithmetic WP solving that emphasizes the algebraic expression of mathematical relations in conceptual models. Participants were five students in Grades 4 and 5 with or at risk for mathematics disabilities in two urban public elementary schools in the Midwest. An adapted multipleprobe-across-participants design was used to assess the functional relation between the intervention and students' problem-solving performance. The results indicated that conceptual model-based representation prompted by WP story grammar improved students' performance on arithmetic WP solving and promoted prealgebra concept and skill acquisition. The practical implications of integrating algebraic reasoning in elementary mathematics are discussed.

We show that the height of a nonzero algebraic number α that lies in an abelian extension of the rationals and is not a root of unity must satisfy h(α) > 0.155097.

A B S T R A C TA study to assess the sea water cooling (SWC) feasibility in southeast Florida was conducted using simulated and measured sea water temperatures. These data were input into a representative SWC system model to quantify potential energy savings over conventional cooling systems. The HYbrid Coordinate Ocean Model was used to characterize near-bottom temperatures statewide, predicting that minimum temperatures needed for effective SWC are closest to the shore off the coasts of Fort Lauderdale and Miami. Numerous in situ data sets recently collected near Fort Lauderdale/Miami are presented alongside several historic data sets to further enhance temperature resource information. These data suggest that a cold water resource with a mean temperature of 8°C-10°C is present off Fort Lauderdale in 160-220 m of water and 7°C-9°C is present off Miami in 200-300 m of water. Both cold water resources are located approximately 6 km from the shore. These temperatures vary significantly at frequencies between 2 days and 2 weeks, with cooler temperatures during the summer suggesting a seasonal variation. An SWC plant model is presented that was used to predict the electric power needed to operate a generic 10-MW (2,857-ton) AC system, which is compared with a traditional unassisted AC system. The plant model, with 3 years of HYbrid Coordinate Ocean Model temperature data, predicted that, in South Miami, an SWC system can operate using the least amount of average electrical power in the state. At this location, the chilling system is estimated to operate at an average power savings of 86.9%, and a total comfort cooling system is estimated to operate at an average power savings of 58%, when compared with a traditional AC system.

No abstract

Background Applied Calculus courses serve hundreds of thousands of undergraduates as quantitative preparation and gatekeepers across diverse fields of study. The current study investigated how motivational factors are associated with students’ learning outcomes in Applied Calculus courses from the perspective of self-determination theory—a sound comprehensive motivation theory that has been supported by considerable research in psychology and education. In order to have a nuanced understanding of students’ motivation and learning in Applied Calculus courses, we used three different types of learning measures to investigate students’ mathematics achievement, including course grades, a standardized knowledge exam, and students’ perceived knowledge transferability. Results We tested the relationships between motivational factors and learning outcomes with a multi-semester sample of 3226 undergraduates from 188 Applied Calculus classrooms. To increase the precision of our analysis, we controlled for three demographic variables that are suggested to be relevant to mathematics achievement: gender, minority group status, and socioeconomic status. With a series of multilevel modeling analyses, the results reveal that: (1) competence satisfaction predicts college students’ mathematics achievement over and above the satisfaction of needs for autonomy and relatedness; and (2) autonomous motivation is a more powerful predictor of college students’ mathematics achievement than controlled motivation and amotivation. These findings are consistent across different types of learning outcomes. Conclusions Self-determination theory provides an effective framework for understanding college students’ motivation and learning in Applied Calculus courses. This study extends self-determination theory in the field of mathematics education and contributes to the dialogue on advancing undergraduate science, technology, engineering, and mathematics (STEM) education by providing evidence to understand how motivational factors are associated with students’ learning outcomes in undergraduate mathematics courses.