A Construct-Modeling Approach to Develop a Learning Progression of how Students Understand the Structure of Matter

This paper builds on the current literature base about learning progressions in science to address the question, “What is the nature of the learning progression in the content domain of the structure of matter?” We introduce a learning progression in response to that question and illustrate a methodology, the Construct Modeling (Wilson, 2005) approach, for investigating the progression through a developmentally based iterative process. This study puts forth a progression of how students understand the structure of matter by empirically inter-relating constructs of different levels of sophistication using a sample of 1,087 middle grade students from a large diverse public school district in the western part of the United States. The study also shows that student thinking can be more complex than hypothesized as in the case of our discovery of a substructure of understanding in a single construct within the larger progression. Data were analyzed using a multidimensional Rasch model. Implications for teaching and learning are discussed—we suggest that the teacher’s choice of instructional approach needs to be fashioned in terms of a model, grounded in evidence, of the paths through which learning might best proceed, working toward the desired targets by a pedagogy which also cultivates students’ development as effective learners. This research sheds light on the need for assessment methods to be used as guides for formative work and as tools to ensure the learning goals have been achieved at the end of the learning period. The development and investigation of a learning progression of how students understand the structure of matter using the Construct Modeling approach makes an important contribution to the research on learning progressions and serves as a guide to the planning and implementation in the teaching of this topic. # 2017 Wiley Periodicals, Inc. J Res Sci Teach 54: 1024–1048, 201

An approximate theory for substructure propagation in clusters

The existence of dark matter can be proved in an astrophysical context by the discovery of a system in which the observed baryons and the inferred dark matter are spatially segregated, such as the bullet cluster (1E0657-558). The full descriptions of the dark matter halo and X-ray gas substructure motions are necessary to forecast the location of the dark halo from X-ray maps, which can be confirmed by the detection of a galaxy concentration or by gravitational lensing. We present an analytical hydrodynamic model to determine the distance between the X-ray and dark-matter components and the Mach number of the merger shock. An approximate solution is given for the problem of the substructure propagation in merging clusters. A new method to predict the position of a dark matter halo in clusters, where there is a separation between the X-ray gas and the dark halo, is proposed and applied to the clusters 1E0657-558 and Abell 1763.Comment: Accepted for publication in Astronomy & Astrophysic