Geometry students need challenges. They need to apply what they already know to new contexts. As a result, high school teacher Wayne Nirode is always looking for groups of related problems of theorems to challenge his geometry students. He came across one such group or problems when reading Jun's (2012) one-page abstract posted online for the 12th…

The simulation of human mind often helps in the understanding of abstract concept by representing it in a realistic model and simplistic way so that a learner develops an understanding of the key concepts. Bian (1873) and James (1890) in their work suggested that thoughts and body activity result from interactions among neurons within the brain.…

Just about everyone loves the "idea" of cooperative learning, children working productively and excitedly in groups, everyone getting along and enthusiastically helping one another learn. This article presents five strategies that teachers can use to get the greatest benefit possible from cooperative learning and ensure that…

Today, the Common Core State Standards for Mathematics (CCSSI 2010) expect students in as early as eighth grade to be knowledgeable about irrational numbers. Yet a common tendency in classrooms and on standardized tests is to avoid rational and irrational solutions to problems in favor of integer solutions, which are easier for students to…

This article describes an exciting exploration-based activity in which students develop an alternative definition of factor that can help them solve problems like the one presented above. Students work in groups to collect data, analyze the data to make conjectures, and then spend a significant amount of time debating and justifying their…

This article examines the attitudes of some precalculus students to solve trigonometric and logarithmic equations and systems using the concepts of elementary algebra. With the goal of enticing the students to search for and use connections among mathematical topics, they are asked to solve equations or systems specifically designed to allow…

"We know that progress depends on discovery, inventions, creativity and design, but we have simply supposed that it happens anyway," de Bono (1999 p. 43). Technology education is ostensibly a foundation for future designers and creative thinking. However evidence of good design or creative thinking in outcomes displayed in school…

The educational concept of "Zone of Proximal Development", introduced by Vygotskij, stems from the identification of a strong need for adaptation of the learning activities, both traditional classroom and modern e-learning ones, to the present state of learner's knowledge and abilities. Furthermore, Vygotskij's educational…

As part of a larger study to understand instructors' considerations regarding the learning and teaching of problem solving in an introductory physics course, we investigated beliefs of first-year graduate teaching assistants (TAs) regarding the use of example solutions in introductory physics. In particular, we examine how the goal of promoting…

High failure rates in introductory large lecture chemistry courses for STEM majors have been of concern for years. Through our weekly Team Approach to Successful Learning (TASL) workshops, students learn and apply problem-solving strategies, coached by specially trained peer learning coaches (LCs). These coaches concurrently enroll in Chemistry…

Multiple models of the gene are used to explore genetic phenomena in scientific practices and in the classroom. In genetics curricula, the classical and molecular models are presented in disconnected domains. Research demonstrates that, without explicit connections, students have difficulty developing an understanding of the gene that spans…

This paper analyses pre-service secondary mathematics teachers' responses to a hypothetical situation concerning a student's struggle to determine the area of an irregular hexagon. The analysis focuses on individuals' Knowledge at the Mathematical Horizon, as it relates to philosophical notions of inner and outer horizons. Specifically, the paper…

This study used a multiple probe across participants design to examine the effects of concrete-representational-abstract sequence of instruction on solving equations using inverse operations with high school students with mild intellectual disability. Results demonstrated a functional relation between the Abstract sequence of instruction and…

We explored transformations that teachers made to modify geometry proof problems into investigation problems and analyzed how these transformations differ in teachers who use a dynamic geometry environment (DGE) in their classes and those who do not. We devised a framework for the analysis of problem transformations and types of teacher-generated…

Innovation is central to modern industry. It can and should be taught in schools. Not only does providing students a background in innovation benefit them later in life and industry, but it also promotes and further develops their critical thinking and collaboration skills. Despite the need for innovation, many have struggled with how to teach it.…