Not only are rubber bands great for binding objects together, but they can be used in a simple science experiment that involves predicting, problem solving, measuring, graphing, and experimenting. In this article, the author describes how rubber bands can be used to teach the force of mass.

In order to facilitate the transition from learning from worked examples in earlier stages of skill acquisition to problem solving in later stages, it is effective to successively fade out worked solution steps--in comparison to the traditional method of employing example--problem pairs that is frequently used in cognitive-load research. In the…

This article reports on an exploratory study of the relationship between grounding and problem solving in multimodal computer-mediated collaboration. This article examines two different media, a shared whiteboard and a MOO environment that includes a text chat facility. A study was done on how the acknowledgment rate (how often partners give…

The current study examined compensation and capitalization treatment models with specific reference to problem-solving appraisal and problem-solving treatment of suicidal behavior (M. D. Rudd, T. Joiner, & M. H. Rajab, 2000). A sample of 98 young adults (mean age = 22), who had recently attempted suicide or ideated about suicide to the degree that…

As an elementary physical education specialist teaching 740 students in a diverse public school, the author is constantly looking for classroom management strategies that are age appropriate, build relationships, and allow students to take responsibility in solving their own problems beyond that of the author's basic behavior management plan.…

In this paper we examine the roles that metonymy may play in student reasoning. To organize this discussion we use the lens of a structured derivative framework. The derivative framework consists of three layers of process-object pairs, one each for ratio, limit, and function. Each of the layers can then be illustrated in any appropriate context,…

Several developments during the last decades have provoked spectacular changes in both Mathematics Teaching and the Education of Mathematics Teachers. From this perspective of renovation, we wish to define a new context in mathematics teacher education in which we consider that "pedagogical content knowledge" (Shulman, 1993, Mellado,…

Results from an earlier study conducted by the researchers [Cai, J., & Cifarelli, V.V. (2005). "Exploring mathematical exploration: How two college students formulated and solved their own mathematical problems?" "Focus on Learning Problems in Mathematics," 27(3), 43-72] illustrated and explained several characteristics of the solvers'…

Stimulated recall (SR) is a family of introspective research procedures through which cognitive processes can be investigated by inviting subjects to recall, when prompted by a video sequence, their concurrent thinking during that event. Variations of the generic approach are widely used and many of the studies treat SR as non-problematic. The…

Given three points in the plane, interest is in the locus of all points for which the sum of the distances to the given points is a prescribed constant. These curves turn out to be sixth degree polynominals in x and y , and thus are complicated. However, it turns out that often there is a point, within the triangle formed by the three given…

Given two circles C 1 and C 2 in a plane such that neither one of the two circles is contained in the other, there are either four common tangents when the circles do not intersect at all or the circles have three common tangents when they touch each other externally or only two common tangents when the circles intersect exactly at two points. The…

This note contains material to be presented to students in a first course in differential equations immediately after they have completed studying first-order differential equations and their applications. The purpose of presenting this material is four-fold: to review definitions studied previously; to provide a historical context which cites the…

Technical problem solving as a model for instructional design (ID) has its strengths, and it has done much to provide designers strategies for their work, but it has substantial limitations as well. For one, it does not do a good job in describing how designers actually think. Slavish adherence to its methods can also be considered responsible for…

The literature notes that natural disasters, including wildfires, that damage human settlements often have the short-term effect of "bringing people together." Less recognized is the fact that such events can also generate social conflict at the local level. This study examines the specific sources of such social conflict during and after…

An integral, either definite or improper, cannot always be computed by elementary methods, such as reversed usage of differentiation formulae. Graphical properties, in particular symmetries, can be useful to compute the integral, via an auxiliary computation. We present graded examples, then prove a general result. (Contains 4 figures.)