We describe exercises in which students use PascGaloisJE to formulate conjectures about certain binomial identities which hold when the binomial coefficients are interpreted as elements in the cyclic group Z[subscript p] of integers modulo a prime integer "p". In addition to having an appealing visual component, these exercises are open-ended and…

This article discusses student difficulties in grasping concepts from linear algebra. Using an example from an interview with a student, we propose changes that might positively impact student understanding of concepts within a problem-solving context. In particular, we illustrate barriers to student understanding and suggest technological…

Imagine a school where every student has global wireless access and a visa to high tech, personalized instruction. Enter Baxter Springs, Kansas, where all the teachers and their students have individual laptops in a 24/7 environment. Such 1-to-1 initiatives actually meet the expectations of the digital generation and these students aren't forced…

We often look for a best-fit function to a set of data. This article describes how a "pretty good" fit might be better than a "best" fit when it comes to promoting conceptual understanding of functions. In a pretty good fit, students design the function themselves rather than choosing it from a menu; they use appropriate variable names; and they…

The term "Web 2.0"--a buzzword for a technological evolution that's been taking place online for some time--has many different definitions. In general, it refers to Web sites that go beyond simply presenting words and images, often allowing users to share information and collaborate in new ways. Content on the Web used to be largely static. One…

Many educators have attempted to implement a blog in educational contexts to enhance the communication environment among students and teachers. However, it is uncertain as to why traditional computer-mediated communication (CMC) applications should be replaced with blogs. It is time to comprehensively explore the effects of educational blogs by…

The 3D cube figures used by Shepard and Metzler [Shepard, R. N., & Metzler, J. (1971). "Mental rotation of three-dimensional objects." "Science," 171, 701-703] have been applied in a broad range of studies on mental rotation. This note provides a brief background on these figures, their general use in cognitive psychology and their role in…

The virtual online world called Second Life can be deceptive. It looks like a game, but the participants are not assigned goals. Indeed, it may be said that the goal of Second Life is to create one's own goals. As a result, the residents of Second Life choose to work in many different directions. Some choose to develop land; some try to earn…

The use of tablet PCs in teaching is a relatively new phenomenon. A cross between a notebook computer and a personal digital assistant (PDA), the tablet PC has all of the features of a notebook with the additional capability that the screen can also be used for input. Tablet PCs are usually equipped with a stylus that allows the user to write on…

Wireless networks are fast becoming ubiquitous in all aspects of society and the world economy. We describe a method for studying the impacts of combining such technology with dynamic, representationally-rich mathematics software, particularly on participation, expression and projection of identity from a local to a public, shared workspace. We…

The purpose of this study was to identify and analyse specific instances of transactive communication as children engaged in a paired melody writing task using a computer-based composing environment. Transactive communication has been identified as one of the features of general collaborative engagement that is most helpful in an educational…

In this study, qualitative themes and quantitative findings from previous research were used to justify the exploration of four experimental, note-taking conditions and the impact of those conditions on student learning from Web-based text. However, puzzling results obtained from dependent measures of student learning were quite inconsistent with…

New methodologies in science (or mathematics) learning process and scientific thinking in the classroom activity of engineer students with ICT (information and communication technology), including graphic calculator are presented: visual modelling with ICT, action research with graphic calculator, insight in classroom and communications and…

We don't have a lot of evidence of what people see and think about communities after the fact. What are their worldviews when they look at experiences in blended learning communities in retrospect? Which elements do they find most meaningful? This study explores the character, meaning, and impact of community using the lived experiences of…

Technology usage is increasing important for community college students, but whether nontraditional students differ from traditional students in technology usage and support was unclear. Further, it was not known whether Nontraditional and Traditional community college students feel equally connected to the college when using social networking…