Investigating Elementary Mathematics Curricula: Focus on Students With Learning Disabilities

The purpose of this study was to investigate three elementary mathematics curricula to examine the accessibility for students with learning disabilities (LD) with regards to challenges associated with working memory. We chose to focus on students' experiences when finding the area of composite shapes due to the multiple steps involved for solving these problems and the potential for these problems to tax working memory. We conducted a qualitative analysis of how each curriculum provided opportunities for students with LD to engage with these problems. During our analysis, we focused on instruction that emphasized visual representations (e.g., manipulatives, drawings, and diagrams), facilitated mathematical conversations, and developed cognitive and metacognitive skills. Our findings indicated a need for practitioners to consider how each curriculum provides instruction for storage and organization of information as well as how each curriculum develops students' thinking processes and conceptual understanding of mathematics. We concluded that all three curricula provide potentially effective strategies for teaching students with LD to solve multi‐step problems, such as area of composite shapes problems, but teachers using any of these curricula will likely need to supplement the curriculum to meet the needs of students with LD.     

Diameters of 3-sphere quotients

Let G⊂O(4) act isometrically on S³. In this article we calculate a lower bound for the diameter of the quotient spaces S³/G. We find it to be , which is exactly the value of the lower bound for diameters of the spherical space forms. In the process, we are also able to find a lower bound for diameters for the spherical Aleksandrov spaces, Sn/G, of cohomogeneities 1 and 2, as well as for cohomogeneity 3 (with some restrictions on the group type). This leads us to conjecture that the diameter of Sn/G is increasing as the cohomogeneity of the group G increases.     

The Zoo Connection: A Cooperative Project Between Formal and Informal Educational Institutions

This project was a cooperative effort between university faculty, elementary school teachers, and members of the Education Department at the Indianapolis Zoo. The purpose of this project was to develop, evaluate, and disseminate a set of fourteen K-6 science lessons that could be used in conjunction with field trips to the zoo. These lessons, titled The Zoo Connection, follow the Learning Cycle teaching model. In addition to following the model, the development of the lessons was based on the premise that teachers should focus on a specific science concept or set of related concepts when visiting a zoo. Workshop sessions were conducted to introduce teachers to the materials and to provide them with strategies for implementing the materials in their science instruction. An evaluation was conducted for each workshop session to determine teachers' perceptions of the materials and to determine whether they felt prepared to use them with their students. The materials were also field-tested in several elementary schools to assess their effectiveness for presenting science concepts to elementary school children. Results indicate that teachers felt the workshops adequately prepared them to use the materials and that the materials were effective for presenting science concepts.     

Azobenzene on Cu(110): adsorption site-dependent diffusion

Azobenzene and its derivatives can undergo reversible trans-cis isomerizations when irradiated with light, making them potential candidates for optically sensitive materials and devices. The adsorption and diffusion of azobenzene on the Cu(110) surface was investigated with a variable-temperature scanning tunneling microscope. The trans-isomer was observed and found to occupy two adsorption geometries-an energetically stable and a metastable state. Diffusion occurred along the closed-packed [1 -1 0] direction of the surface, and the diffusivity for the two adsorption states was found to differ by approximately 1 order of magnitude.     

Film formation of Ag nanoparticles at the organic-aqueous liquid interface

We report a wet-chemical method to make films by spontaneous assembly of passivated Ag nanoparticles at the organic-aqueous liquid interface. The interfacial films exhibit a blue opalescence and are characterized with transmission electron microscopy and UV-vis spectrophotometry. Measurements indicate that nanoparticles in the interfacial film can form superlattices and in some cases nanostructures.