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The article discusses the geometric interpretation of the mathematical formula derived by Blaise Pascal for sums of powers of integers and arithmetic progressions. It illustrates how the total volume of the cubes can be obtained by deducting the excessive value from the enclosed right-angle square pyramid. It also presents the application of telescoping-sum technique in the binomial expansion of the hyper pyramid yields.

The article focuses on the possibility and probability lessons using problems in sports to teach combinations and permutations. It says that teaching probability with table tennis problem is used to help students realize the possibility to win a match by winning significantly less than half the total points. It states that using different colored cubes to represent the teams will help students solve the soccer problem. It also highlights the scoring in the National Football League.

The article focuses on the use of Earth geometry and the great circle in the conceptual understanding of trigonometry. It presents visual aids to help students visualise Earth geometry. It describes the teacher's instruction on angle measure. According to the authors, students should realize that they can use the definition of angle measure to find the distance between two points along a circle of longitude.

This review updates what is known about Betta fish species in Thailand and Southeast Asian countries. The text is made easy to read for an uninitiated audience. It covers wild nest-builders, wild mouthbrooders, their appearance, distribution, and habitats. A section on domesticated fish is included for the general public. Details for more serious readership can be found in photos, maps, a table, and a diagram. DNA analyses for species differentiation leading to a phylogenetic tree and ancestral relationships are discussed. [ABSTRACT FROM AUTHOR]

Abstract: In the recent years, diagnosing students’ learning problems after testing and providing learning suggestions for them are an important research issue. Many studies have been conducted to develop a method for analyzing learning barriers of students such that helpful learning suggestions or guidance can be provided based on the analysis results. In this paper, we present a new procedure for integrating test item–concept relationship opinions based on majority density of multiple experts in order to enhance a concept–effect relationship model used for generating personalized feedback. It provides a useful and practical way to decrease inconsistencies in the weighting criteria of multiple experts and to enhance the entire learning-diagnosis procedure for developing testing and diagnostic systems. [Copyright &y& Elsevier]

Background. Educational games are widely used in business classes in general, and supply chain management (SCM) classes in particular. These games are designed to familiarize students with the real business world. Most SCM games are ready-made, with pre-set learning objectives focusing on a certain module in a supply chain. Intervention. This article presents the new spreadsheet-based Flexible Supply Chain Management Game (FSCMG) and the findings of its pilot study. FSCMG's features are transparent to instructors and students alike. It is easily modifiable to suit an instructor's learning objectives. Method. Six groups of undergraduate students took turns playing three modules, namely a wholesaler, manufacturer, and supplier. There were two groups per module to represent two supply chains. The students' spreadsheets are analyzed and presented. Results. Students' spreadsheets revealed that they were able to employ SCM conceptual understanding in FSCMG, particularly pricing strategy, inventory management, forecasting, and the relationships within a supply chain. Conclusion. FSCGM helped the students apply their in-class knowledge in a real-world situation and be well prepared for their future careers where an extensive understanding is required. [ABSTRACT FROM AUTHOR]

The bubble-nesting Betta smaragdina Ladiges, 1972 can be distinguished from the 4 other species of bubble-nesting Betta Bleeker, 1850 by being reportedly confined to Northeastern Thailand. We found large populations of fish in Western Thailand that closely resemble those from the Northeastern Region. The new populations inhabit a variety of places encompassing lakes, marshes, and streams. Morphological studies of Betta fish from the 2 well-separated regions, together with DNA analyses, show that the western and the northeastern populations are the same species. [ABSTRACT FROM AUTHOR]