Video games have tremendous potential in mathematics education, yet there is a push to simply add mathematics to a video game without regard to whether the game structure suits the mathematics, and without regard to the level of mathematical thought being learned in the game. Are students practicing facts, or are they problem-solving? This paper…

What is the relationship between addition and subtraction? How do individuals know whether an algorithm will always work? Can they explain why order matters in subtraction but not in addition, or why it is false to assert that the sum of any two whole numbers is greater than either number? It is organized around two big ideas and supported by…

The author presents the science and engineering practices from the recently released "A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas." He recognizes the changes implied by the new framework, and eventually a new generation of science education standards will present new perspectives for the science…

In this comparative essay, the author discusses the opposing educational theories of John Dewey and Gregory Bateson. While Dewey believed that the scientific method was the dominant method of solving problems and thereby acquiring knowledge that mattered, Bateson warned that this one-sided approach would lead to actions that could destroy the…

The "Golden Key" programme is a preschool education programme that is constructed on the basis of Vygotskij's cultural-historical theory. One of the most important aspects of this theory is not just the unity of intellect and affect, but the fact that the relationship between these two changes during the course of development. In infants, affect…

This study examined the representational competence of students as they solved problems dealing with the temperature-pressure relationship for ideal gases. Seven students enrolled in a first-semester general chemistry course and two advanced undergraduate science majors participated in the study. The written work and transcripts from videotaped…

"Teaching mathematics from a sense-making perspective entails more than solving non-routine problems" (NCTM 2007, p. 85). When teachers want students to see mathematics as something that makes sense, they must furnish opportunities for them to solve problems in their own way and use structures that nurture their reasoning and sense making. The…

The purpose of this article is to present two very active applied modeling projects that were successfully implemented in a first semester calculus course at Hollins University. The first project uses a logistic equation to model the spread of a new disease such as swine flu. The second project is a human take on the popular article "Do Dogs Know…

Professional doctorates were introduced in the 1990s for practitioners to research "real-world" problems relevant to their respective workplace communities and contexts. An array of difficulties faces professional doctoral students as they transition from professionals to practitioner researchers. This study sought to understand the…

Computation instruction continues to be one of the most important aspects of the mathematics curricula. Students who fail to understand and master the foundational components of addition, subtraction, multiplication, and division are likely to experience mathematics difficulties in both their school and post-school lives. A balanced instructional…

Being told procedures and concepts before problem solving can inadvertently undermine the learning of deep structures in physics. If students do not learn the underlying structure of physical phenomena, they will exhibit poor transfer. Two studies on teaching physics to adolescents compared the effects of "telling" students before and after…

How can a teacher use the practice of reflection to create rich mathematical learning environments that are engaging to students? In such environments, one can hear and see a seamless integration of Problem Solving, Reasoning and Proof, Communication, making mathematical Connections, and Representation (the NCTM Process Standards) through Number…

Spurred on by explosive technological developments and unprecedented access to information, leaders in the fields of business, industry, and education are all calling for creative, innovative workers. In an atmosphere of high-stakes testing and global competitiveness, educators around the world are examining their teaching methods to determine…

Student activities focused on discovering mathematics play an important role in the teaching and learning process. WebMathematics Interactive (WMI2) was developed to offer a fast and user-friendly on-line web interface to enhance the quality of both theoretical and applied mathematics courses. For the teacher, in the classroom, it provides…

Capturing progression in students' formal knowledge and employability skills is essential in higher education but evokes questions concerning how to assess and monitor progression. While methods for capturing students' formal knowledge progression have traditionally been at the forefront, methods for capturing employability skills have been less…