The problem of assessing problem solving: can comparative judgement help?

School mathematics examination papers are typically dominated by short, structured items that fail to assess sustained reasoning or problem solving. A contributory factor to this situation is the need for student work to be marked reliably by a large number of markers of varied experience and competence. We report a study that tested an alternative approach to assessment, called comparative judgement, which may represent a superior method for assessing open-ended questions that encourage a range of unpredictable responses. An innovative problem solving examination paper was specially designed by examiners, evaluated by mathematics teachers, and administered to 750 secondary school students of varied mathematical achievement. The students’ work was then assessed by mathematics education experts using comparative judgement as well as a specially designed, resourceintensive marking procedure. We report two main findings from the research. First, the examination paper writers, when freed from the traditional constraint of producing a mark scheme, designed questions that were less structured and more problem-based than is typical in current school mathematics examination papers. Second, the comparative judgement approach to assessing the student work proved successful by our measures of inter-rater reliability and validity. These findings open new avenues for how school mathematics, and indeed other areas of the curriculum, might be assessed in the future

Coevolution of Camouflage

Camouflage in nature seems to arise from competition between predator and prey. To survive, predators must find prey, and prey must avoid being found. This work simulates an abstract model of that adversarial relationship. It looks at crypsis through evolving prey camouflage patterns (as color textures) in competition with evolving predator vision. During their "lifetime" predators learn to better locate camouflaged prey. The environment for this 2D simulation is provided by a set of photographs, typically of natural scenes. This model is based on two evolving populations, one of prey and another of predators. Mutual conflict between these populations can produce both effective prey camouflage and predators skilled at "breaking" camouflage. The result is an open source artificial life model to help study camouflage in nature, and the perceptual phenomenon of camouflage more generally.Comment: 16 pages, 20 figure

Center for Grassland Studies Newsletter, Fall 2008, Volume 14, No. 4

Contents: Managing Grasslands for Structural Heterogeneity by Alexander Smart, Department of Animal and Range Sciences, South Dakota State University Yellow Nutsedge: The Scourge of Lawns and Landscapes in Nebraska by Roch Gaussoin, Department of Agronomy and Horticulture, UNL Targeting Habitat Dollars with Computers: Maximizing the Value of Data for Conservation by Drew Tyre, School of Natural Resources, UNL, with Naikoa Aguilar-Amustechegui, University of North Carolina-Wilmington and Max Post van der Burg, SNR, UNL 2008 Nebraska Grazing Conference Best Yet

A Tangible Construction Kit for Exploring Graph Theory

ABSTRACT Graphs are a versatile representation of many systems in computer science, the social sciences, and mathematics, but graph theory is not taught in schools. We present our work on Graphmaster, a computationally enhanced construction kit that enables children to build graphs of their own and investigate their properties by experimenting with algorithms that operate on them. The system is distributed; microcontrollers inside each node execute an interpreted language in parallel. Graphmaster, with its magnetic connectors, illuminated edges, and capacitive sensing, encourages children to develop intuitions about connectivity long before they are introduced to the notation and formulas of graph theory

AN INVESTIGATION OF LOWER SECONDARY PUPILS' IMAGES OF MATHEMATICS AND MATHEMATICIANS

This thesis reports on a three-part research project in which the images of mathematics and mathematicians held by lower secondary pupils were investigated. A survey tool which asked pupils to draw a picture of a mathematician at work, and which included a Likert-type scale and open-ended writing prompts, was designed and developed for use in an international study of pupils in five countries (n = 476). The results indicate that while some pupils hold stereotypical images in common, all pupils appear to know very little about mathematicians and the work they do. Mathematicians' invisibility to pupils of this age appears to affect their images of mathematics. The tool was refined and utilised again as part of two interventions in the United States: the first attempted to see if images would be affected by a unit in graph theory and discrete mathematics topics (n = 28); the second brought pupils (n = 174) together with a panel of mathematicians. Each intervention had different strengths, but both widened pupils' views of mathematics, enabling them to see it as more than just a study of numbers. In a third small study, professionals in the mathematics field (n = 106) from ten countries were asked in a short survey to comment on Who is a mathematician? and Who may call oneself one? Findings of this portion of the study indicate a lack of a unified vision among members of the mathematics community and some evidence of an elitism which would restrict who may define themselves as a mathematician

Patent Law: Cases & Materials ~ Version 2.0

The book contains edited cases, patent figures, and excerpts, along with brief introductions on patent law. This book is designed for use in close conjunction with a specific softcover hornbook published by Wolters Kluwer, Janice Mueller’s, Patent Law, Fourth Edition (Aspen Student Treatise Series 2013). If you decide to use this case collection to teach a course of your own — as I hope people will — please check back to ensure that you have the most up-to-date version. This version, which is 2.0, was posted in June 2015. Reproduced and linked with permission of the author.https://digitalcommons.law.uga.edu/books/1101/thumbnail.jp

Mathematical warrants, objects and actions in higher school mathematics

'Higher school mathematics' connotes typical upper secondary school and early college mathematics. The mathematics at this level is characterised by moves to (1) rigour in justification,(2) abstraction in content and (3) fluency in symbolic manipulation. This thesis investigates these three transitions - towards rigour, abstraction, and tluencyusing philosophical method: for each of the three transitions a proposition is presented and arguments are given in favour of that proposition. These arguments employ concepts and results from contemporary English language-medium philosophy and also rely crucially on classroom issues or accounts of mathematical experience both to elucidate meaning and for the domain of application. These three propositions, with their arguments, are the three sub-theses at the centre of the thesis as a whole. The first of these sub-theses (1) argues that logical deduction, quasi-empiricism and visualisation are mathematical warrants, while authoritatively based justification is essentially non-mathematical. The second sub-thesis (2) argues that the reality of mathematical entities of the sort encountered in the higher school mathematics curriculum is actual not metaphoric. The third sub-thesis (3) claims that certain 'mathematical action' can be construed as non-propositional mathematical knowledge. The application of these general propositions to mathematics in education yields the following: 'coming to know mathematics' involves:(1) using mathematical warrants for justification and self conviction; (2) ontological commitment to mathematical objects; and (3)developing a capability to execute some mathematical procedures automatically

Proceedings of the Fifth Mediterranean Conference on Information Systems: Professional Development Consortium

Collection of position statements of doctoral students and junior faculty in the Professional Development Consortium at the the Fifth Mediterranean Conference on Information Systems, Tel Aviv - Yafo