A typical introductory course in ordinary differential equations (ODEs) exposes students to exact solution methods. However, many differential equations must be approximated with numerical methods. Textbooks commonly include explicit methods such as Euler's and Improved Euler's. Implicit methods are typically introduced in more advanced courses…

Proofs that the area of a circle is nr[superscript 2] can be found in mathematical literature dating as far back as the time of the Greeks. The early proofs, e.g. Archimedes, involved dividing the circle into wedges and then fitting the wedges together in a way to approximate a rectangle. Later more sophisticated proofs relied on arguments…

Several mathematicians struggled to solve cubic equations, and in 1515 Scipione del Ferro reportedly solved the cubic while participating in a local mathematical contest, but did not bother to publish his method. Then it was Cardano (1539) who first published the solution to the general cubic equation in his book "The Great Art, or, The Rules of…

Background: The results of the Programme for International Student Assessment (PISA) 2012 showed that Indonesia, Malaysia, and Thailand underperformed and were positioned in the bottom third out of 65 participating countries for mathematics, science, and reading literacies. The wide gap between these three countries and the top performing…

Team-based learning (TBL) is a form of student-centered active learning in which students independently study new conceptual material before it is treated in the classroom, and then subsequently spend considerable classroom time working in groups on increasingly challenging problems and applications based on that new material. TBL provides…

Few studies on the role of bilingualism in mathematics classrooms explore the intersection of biliteracy, language use, mathematical discourse, and numeracy--especially at the middle school level. Drawing from biliteracy development theory and reform mathematics education literature, this qualitative case study of a dual-language mathematics…

Deictic linking gestures, hand and arm motions that physically embody links being communicated between two or more objects in the shared communicative environment, are explored in a cross-cultural sample of mathematics instruction. Linking gestures are specifically examined here when they occur in the context of communicative analogies designed to…

This study aimed to investigate the effect of conceptual change text (CCT) in the REACT strategy for students' conceptions of solutions. A quasi-experimental method was used in the study. The study was carried out in the spring term of the 2012-2013 academic year with 61 freshmen students (aged 18-20 years) studying in the Elementary Education…

Linear programming (LP) is taught in different departments across college campuses with engineering and management curricula. Modeling an LP problem is taught in every linear programming class. As faculty teaching in Engineering and Management departments, the depth to which teachers should expect students to master this particular type of…

Raven Elementary teachers collaboratively adhered to a systematic reading program, administered frequent assessments, and their students' test scores improved over time. Our findings indicate that, though effective for improving certain outcomes, such a tightly designed and narrowly focused system created a limiting learning environment for…

Summer vacations interrupt the rhythm of learning and may result in a loss of knowledge and skills. This study investigates summer learning losses in an Austrian sample with nine-week summer vacations. The results show losses as well as gains for students in lower secondary education (182 students between 10 and 12 years old). Students experienced…

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) identifies the strategic use of appropriate tools as one of the mathematical practices and emphasizes the use of pictures and diagrams as reasoning tools. Starting with the early elementary grades, CCSSM discusses students' solving of problems "by drawing." In later…

Contemporary office work is becoming increasingly challenging as many routine tasks are automated or outsourced. The remaining problem solving activities may also offer potential for lifelong learning in the workplace. In this study, we analyzed problem solving in an office work setting using an Internet-based, semi-standardized diary to collect…

Problems with handwriting can negatively impact the writing of students with learning disabilities. In this article, an example is provided of a fourth-grade special education teacher's efforts to assist a new student by using a problem-solving approach to help determine an efficient course of action for special education teachers who are trying…

In this study, we investigated and compared solitary and collaborative modes of game-based learning in promoting students' science learning and motivation. A total of fifty seventh grade students participated in this study. The results showed that students who played in a solitary or collaborative mode demonstrated improvement in learning…