The growth of cities in the Fourth District

Many Fourth District cities have experienced relatively weak population growth over the past half century. One possible reason some cities have recently grown more is because they have better educated workforces. Recent research suggests that the educational attainment of residents is critical to population growth, particularly for cities in the Northeast and Midwest.Cities and towns ; Population ; Federal Reserve District, 4th

Meeting the requirements of both classroom-based and systemic assessment of mathematics proficiency: the potential of Rasch measurement theory

The challenges inherent in assessing mathematical proficiency depend on a number of factors, amongst which are an explicit view of what constitutes mathematical proficiency, an understanding of how children learn and the purpose and function of teaching. All of these factors impact on the choice of approach to assessment. In this article we distinguish between two broad types of assessment, classroom-based and systemic assessment. We argue that the process of assessment informed by Rasch measurement theory (RMT) can potentially support the demands of both classroom-based and systemic assessment, particularly if a developmental approach to learning is adopted, and an underlying model of developing mathematical proficiency is explicit in the assessment instruments and their supporting material. An example of a mathematics instrument and its analysis which illustrates this approach, is presented. We note that the role of assessment in the 21st century is potentially powerful. This influential role can only be justified if the assessments are of high quality and can be selected to match suitable moments in learning progress and the teaching process. Users of assessment data must have sufficient knowledge and insight to interpret the resulting numbers validly, and have sufficient discernment to make considered educational inferences from the data for teaching and learning responses

Many Points of View: Visibility Mapping for Marine Spatial Planning

In order to manage and facilitate economic growth while safeguarding environmental objectives in the marine environment, new European legislation mandating the development of Marine Spatial Planning (MSP) using an ecosystem approach has been introduced. One critical component of the ecosystem approach is the inclusion of ecosystem services into management decisions. In order to contribute to the planning process a map of the visibility of the entire Scottish national Exclusive Economic Zone was produced using cumulative viewshed analysis and displayed using a novel dynamic web display system. The layer maps the spatial distribution of one aspect of cultural ecosystem services, the visual amenity of coastal areas and is being used in the Scottish Marine Spatial Planning process

Mathematics, curriculum and assessment : the role of taxonomies in the quest for coherence

A challenge encountered when monitoring mathematics teaching and learning at high school is that taxonomies such as Bloom’s, and variations of this work, are not entirely adequate for providing meaningful feedback to teachers beyond very general cognitive categories that are difficult to interpret. Challenges of this nature are also encountered in the setting of examinations, where the requirement is to cover a range of skills and cognitive domains. The contestation as to the cognitive level is inevitable as it is necessary to analyse the relationship between the problem and the learners’ background experience. The challenge in the project described in this article was to find descriptive terms that would be meaningful to teachers. The first attempt at providing explicit feedback was to apply the assessment frameworks that include a content component and a cognitive component, namely knowledge, routine procedures, complex procedures and problem solving, currently used in the South African curriculum documents. The second attempt investigated various taxonomies, including those used in international assessments and in mathematics education research, for constructs that teachers of mathematics might find meaningful. The final outcome of this investigation was to apply the dimensions required to understand a mathematical concept proposed by Usiskin (2012): the skills-algorithm, property-proof, use-application and representation-metaphor dimension. A feature of these dimensions is that they are not hierarchical; rather, within each of the dimensions, the mathematical task may demand recall but may also demand the highest level of creativity. For our purpose, we developed a two-way matrix using Usiskin’s dimensions on one axis and a variation of Bloom’s revised taxonomy on the second axis. Our findings are that this two-way matrix provides an alternative to current taxonomies, is more directly applicable to mathematics and provides the necessary coherence required when reporting test results to classroom teachers. In conclusion we discuss the limitations associated with taxonomies for mathematics.Michael and Susan Dell Foundationhttp://www.pythagoras.org.zatm201

An application of the Rasch measurement theory to an assessment of geometric thinking levels

The purpose of this study is to apply the Rasch model to investigate both the Van Hiele theory for geometric development and an associated test. In terms of the test, the objective is to investigate the functioning of a classic 25-item instrument designed to identify levels of geometric proficiency. The data set consists of responses by 244 students (106 for a pre-test and 138 for a post-test) of which 76 students sat both the pre-test and the post-test. The summary item statistics do not show statistically discernible differences between observed and expected scores under the Rasch model (Chi-square statistic). The Rasch analysis confirms to some strong extent the Van Hiele theory of geometric development. The study identifies some problematic test items as they only require knowledge of a specific aspect of geometry instead of testing geometric reasoning. In terms of the Van Hiele theory, the Rasch analyses identified as problematic some items about class inclusion, an issue which has also been raised in other studies.http://www.tandfonline.com/loi/rmse202016-01-31hb201