Examples of applications of equilibrium-based methods for multicomponent separations usually require the use of simulation packages, which do not allow students to follow the involved algorithms step by step. Excel spreadsheets with examples of six such rigorous methods have been used with MSc students of Chemical Engineering of the University of…

Takers of educational tests often receive proficiency levels instead of or in addition to scaled scores. For example, proficiency levels are reported for the Advanced Placement (AP®) and U.S. Medical Licensing examinations. Technical difficulties and other unforeseen events occasionally lead to missing item scores and hence to incomplete data on…

There is broad consensus on the assumption that adults solve single-digit multiplication problems almost exclusively by fact retrieval from memory. In contrast, there has been a long-standing debate on the cognitive processes involved in solving single-digit addition problems. This debate has evolved around two theoretical accounts. Proponents of…

In this research, we explore the potential for computational thinking (CT) to benefit the spatial reasoning abilities of thirty-three middle-school students (aged 11-13) in grades 6 and 7. There is an increasing focus on the explicit development of spatial reasoning throughout the mathematics curriculum, such as geometry, as students' success in…

Policy-makers, research managers, and donors are interested in knowing the outputs, outcomes, and impacts of investment in agricultural research. Several institutions are engaged in rice research and impact assessment of rice research requires area coverage information for rice varieties. The area coverage information for individual varieties is…

Through a constructivist teaching experiment, we studied how a 6th-grade student (Adam, pseudonym) struggling in mathematics may reorganize his available additive scheme (count-up-to) into a more advanced scheme involving the decomposition of composite units (break-apart-make-ten, or BAMT). First, we posed a task that led us to infer Adam was yet…

Students exhibiting mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly select the most effective and efficient problem-solving strategies (McIntosh et al., 1997; Reys et al., 1999; Yang, 2005). Despite being highlighted in national standards and policy documents (CCSS, 2010; NCTM, 2000, 2014),…

In this article, researchers conducted a study that integrates Augmented Reality application with Computational Thinking into Geometry Topics. Three variables were measured, Computational Thinking, Visualisation Skills and Geometry Topic achievement. The study was implemented with 124 students in two different schools using quasi-experimental…

Numerous studies have shown a significant positive relationship between the mental representation of hands in young children and their calculation performance. The literature indicates that certain components of manual motor skills may be critical to the quality of this relationship. The main objective of this study is to measure the benefit of an…

Number line estimation (NLE) tasks are widely used to investigate numerical cognition, learning, and development, and as an instructional tool. Interpretation of these tasks generally involves an implicit expectation that responses are driven by the overall magnitudes of target numerals, in the sense that the particular digits conveying those…

This article presents an intervention proposal that seeks to develop computational thinking in Early Childhood Education, using an educational ground robot with programmed directionality controls. Within the observational methodology, it has been possible to characterize computational thinking in children of Early Childhood Education -- 5 years…

In this paper we consider implications of the current world-wide inclusion of computational thinking in relation to children's development of algebraic thinking. Little is known about how newly developed visual programming environments such as Scratch could enhance early algebra learning. The study is based on examples of programming activities…

We investigate two non-iterative estimation procedures for Rasch models, the pair-wise estimation procedure (PAIR) and the Eigenvector method (EVM), and identify theoretical issues with EVM for rating scale model (RSM) threshold estimation. We develop a new procedure to resolve these issues--the conditional pairwise adjacent thresholds procedure…

In the multivariable calculus course, a standard application of triple integration is to find volumes of bounded regions in R[superscript 3]. In this article, we consider the problem of computing volumes, by way of examples, of regions bounded by planes and quadric surfaces. For illustration, we present the solution to two basic but non-standard…

We face complex global issues such as climate change that challenge our ability as humans to manage them. Models have been used as a pivotal science and engineering tool to investigate, represent, explain, and predict phenomena or solve problems that involve multi-faceted systems across many fields. To fully explain complex phenomena or solve…