This article explores ways of conceptualizing the design of innovative learning tools as emergent from dialectics between designers and learner-users of those tools. More specifically, I focus on the reciprocities between a designer's objectives for student learning and a user's situated activity in a learning environment, as these interact and…

When the author first used "VisiCalc," the author thought it a very useful tool when he had the formulas. But how could he design a spreadsheet if there was no known formula for the quantities he was trying to predict? A few months later, the author relates he learned to use multiple linear regression software and suddenly it all clicked into…

The performances of 4- and 5-year-olds and rhesus monkeys were compared using a computerized task for quantity assessment. Participants first learned two quantity anchor values and then responded to intermediate values by classifying them as similar to either the large anchor or the small anchor. Of primary interest was an assessment of where the…

This has been a big year for Kim Kulawik, a technology education teacher at Mooresville (NC) Middle School: He has been named a 2008 North Carolina Technology Student Association Advisor of the Year, a 2008 International Technology Association Teacher of the Year--and now he and his students are receiving the December 2008 "Tech…

In a study conducted by the authors regarding children's use of library books and computers during the summer, the authors found that children in low-income and middle-income neighborhoods use such resources differently. Although the authors found that both sets of children used public libraries heavily, wealthier children were exposed to more…

What makes Dynamic Geometry Environment (DGE) a powerful mathematical knowledge acquisition microworld is its ability to visually make explicit the implicit dynamism of thinking about mathematical geometrical concepts. One of DGE's powers is to equip us with the ability to retain the background of a geometrical configuration while we can…

Lecturers in mathematical modelling courses are always on the lookout for new examples to illustrate the modelling process. A physical phenomenon, documented as early as the nineteenth century, was recalled: when a wineglass "sings", waves are visible on the surface of the wine. These surface waves are used as an exercise in mathematical…

Games are a useful and fun way to review material in class, and encourage students to actively participate in review sessions. In fact, researchers have concluded that playing games can be an effective learning tool, especially in mathematics, in situations where the goal is to reinforce specific ideas or concepts. Two places this type of…

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…