Developing multiplicative reasoning is an important milestone for elementary school students, which influences their learning of later mathematical concepts (Hackenberg and Tillema 2009). For children to conceptually understand multiplication, one should move beyond merely counting by ones to dealing with composites (twos, fives, etc.) and other…

As teachers seek activities to assist students in understanding division as more than just the algorithm, they find many examples of division as fair sharing. However, teachers have few activities to engage students in a quotative (measurement) model of division. Efraim Fischbein and his colleagues (1985) defined two types of whole-number…

A hypothetical artwork is an artwork that exists only as a fictional creation of an art theorist. The explicatory powers of such hypothetical artworks are mainly used by an art theorist to reflect on an art theoretical issue under consideration. Such an artwork has an intriguing and paradoxical nature. On the one hand, it is only fictitious, but,…

A simple but physically intuitive double-source model is proposed to explain the interferogram of a laser-capillary system, where two effective virtual sources are used to describe the rays reflected by and transmitted through the capillary. The locations of the two virtual sources are functions of the observing positions on the target screen. An…

As teachers of writing, the authors know that choices matter: the more choices they can give their students, the better their writing will be--and the better writers they'll become. Many teachers design their courses as writing workshops, so that students make choices about the genres they compose in. They structure writing assignments so that…

Conceptually, students are typically introduced to light as a type of wave. However, children struggle to understand this model because it is highly abstract. Light can be represented more concretely using the photon model. According to this scientific model, light emanates from sources as tiny "packets" of energy (called "photons") that move in…

Beautiful colored interference rings can be produced by using transparent plates such as window glass. A simple model explains this effect, which was described by Newton but has almost been forgotten. (Contains 11 figures.)

Appropriate concrete and pictorial models allow students to construct meaning for rational numbers and operations with the numbers. To develop deep understanding of rational number, sixth through eighth graders must experience a variety of models (NCTM 2000). Since 1979, personnel from the Rational Number Project (RNP), a cooperative research and…

Observers made speeded old-new recognition judgments of color stimuli embedded in a multidimensional similarity space. The paradigm used multiple lists but with the underlying similarity structures repeated across lists, to allow for quantitative modeling of the data at the individual-participant and individual-item levels. Correct rejection…

Genetics is often a fascinating but difficult subject for middle level students. They can see the results of genes in every organism, but trying to visualize what happens at the level of genes is challenging for concrete thinkers. The author discusses an approach that helps students understand how genotypes can translate into phenotypes, then…

Xerography is one of the major channels through which a union in art and technology can be achieved. As a result of a three-year research study of xerography and such a union, the following examples have been developed: XIOPP Model, art historical perspective, visual literacy exhibition and vocabulary. The XIOPP Model is an illustration and…

Describes a computer application that uses graphics, color, and animation to make the learning of statistical reasoning with uncertainty easier and more fun. Notes that the initial implementation focuses on the Dempster-Shafer model, although the design is a framework that can incorporate other models. Also discusses how the tool may be used to…

Four experiments are reported exploring whether distractor pictures activate their phonological properties in the course of speech production. In Experiment 1, participants were presented with two pictures and were asked to name one while ignoring the other. Distractor pictures were phonologically related, semantically related or unrelated to the…

Students must understand the fundamental process of convection before they can grasp a wide variety of Earth processes, many of which may seem abstract because of the scales on which they operate. Presentation of a very visual, concrete model prior to instruction on these topics may facilitate students' understanding of processes that are largely…

The "Central Dogma" of genetics states that one gene, located in a DNA molecule, is ultimately translated into one protein. As important as this idea is, many teachers shy away from teaching the actual mechanism of gene translation, and many students find the concepts abstract and inaccessible. This article describes a unit, called Genetics…