Why Use Multiple Representations in the Mathematics Classroom? Views of English and German Preservice Teachers

Dealing with multiple representations and their connections plays a key role for learners to build up conceptual knowledge in the mathematics classroom. Hence, professional knowledge and views of mathematics teachers regarding the use of multiple representations certainly merit attention. In particular, investigating such views of preservice teachers affords identifying corresponding needs for teacher education. However, specific empirical research is scarce. Taking into account the possible role of culture, this study consequently focuses on views about using multiple representations held by more than 100 English and more than 200 German preservice teachers. The results indicate that there are culture-dependent aspects of preservice teachers’ views, but also that there are common needs for professional development.

     

Science Instruction for Students with Learning Disabilities: A Meta‐Analysis

Although science has received much attention as a political and educational initiative, students with learning disabilities (LD) perform significantly lower than their nondisabled peers. This meta‐analysis evaluates the effectiveness of instructional strategies in science for students with LD. Twelve studies were examined, summarized, and grouped according to the type of strategy implemented. Effect sizes (ES) were calculated for each study. Across all studies, a mean ES of .78 was obtained, indicating a moderate positive effect on students with LD science achievement. Findings also align with past reviews of inquiry‐based instruction for students with special needs, indicating that students with LD need structure within an inquiry science approach in order to be successful. Additionally, results suggest that mnemonic instruction is highly effective at increasing learning disabled students' acquisition and retention of science facts.     

Symbolic Management of the Degree of Information Security by Integer Splitting

This paper demonstrates the application of module arithmetic for controlling the level of information security by a new technique referred as integer splitting. The basic definitions and concepts of the method are provided. The mathematical function of arising transformation is described in detail; its properties were studied and the basic theorems were proven that justify the use of splitting in practical applications. An active system was designed and characteristic cases of its operation are considered.     

A Campus-Wide Investigation of Clicker Implementation: The Status of Peer Discussion in STEM Classes

At the University of Maine, middle and high school teachers observed more than 250 university science, technology, engineering, and mathematics classes and collected information on the nature of instruction, including how clickers were being used. Comparisons of classes taught with (n = 80) and without (n = 184) clickers show that, while instructional behaviors differ, the use of clickers alone does not significantly impact the time instructors spend lecturing. One possible explanation stems from the observation of three distinct modes of clicker use: peer discussion, in which students had the opportunity to talk with one another during clicker questions; individual thinking, in which no peer discussion was observed; and alternative collaboration, in which students had time for discussion, but it was not paired with clicker questions. Investigation of these modes revealed differences in the range of behaviors, the amount of time instructors lecture, and how challenging the clicker questions were to answer. Because instructors can vary their instructional style from one clicker question to the next, we also explored differences in how individual instructors incorporated peer discussion during clicker questions. These findings provide new insights into the range of clicker implementation at a campus-wide level and how such findings can be used to inform targeted professional development for faculty.