Creating Your Own Symbols: Beginning Algebraic Thinking With Indigenous Students

Because mathematics education devalues Indigenous culture, Indigenous students continue to be the most mathematically disadvantaged group in Australia. Conventional wisdom with regard to Indigenous mathematics education is to utilise practical and visual teaching methods, yet the power of mathematics and the opportunities it brings for advancement lie in symbolic understanding. This paper reports on a Maths as Story Telling (MAST) teaching approach to assist Indigenous students understand algebra through creating and manipulating their own symbols for equations. It discusses effective Indigenous mathematics teaching, describes the MAST approach, analyses it in terms of Ernest’s (2005) semiotic processes, discusses its applications, and draws implications for Indigenous mathematics learning

Evaluation of Kapton pyrolysis, arc tracking, and flashover on SiO(x)-coated polyimide insulated samples of flat flexible current carriers for Space Station Freedom

Kapton polyimide wiring insulation was found to be vulnerable to pyrolization, arc tracking, and flashover when momentary short-circuit arcs have occurred on aircraft power systems. Short-circuit arcs between wire pairs can pyrolize the polyimide resulting in a conductive char between conductors that may sustain the arc (arc tracking). Furthermore, the arc tracking may spread (flashover) to other wire pairs within a wire bundle. Polyimide Kapton will also be used as the insulating material for the flexible current carrier (FCC) of Space Station Freedom (SSF). The FCC, with conductors in a planar type geometric layout as opposed to bundles, is known to sustain arc tracking at proposed SSF power levels. Tests were conducted in a vacuum bell jar that was designed to conduct polyimide pyrolysis, arc tracking, and flashover studies on samples of SSF's FCC. Test results will be reported concerning the minimal power level needed to sustain arc tracking and the FCC susceptibility to flashover. Results of the FCC arc tracking tests indicate that only 22 volt amps were necessary to sustain arc tracking (proposed SSF power level is 400 watts). FCC flashover studies indicate that the flashover event is highly unlikely

Designing scattering-free isotropic index profiles using phase-amplitude equations

The Helmholtz equation can be written as coupled equations for the amplitude and phase. By considering spatial phase distributions corresponding to reflectionless wave propagation in the plane and solving for the amplitude in terms of this phase, we designed two-dimensional graded-index media which do not scatter light. We give two illustrative examples, the first of which is a periodic grating for which diffraction is completely suppressed at a single frequency at normal incidence to the periodicity. The second example is a medium which behaves as a 'beam shifter' at a single frequency; acting to laterally shift a plane wave, or sufficiently wide beam, without reflection.Comment: 10 pages, 10 figure

An attentive neural architecture for joint segmentation and parsing and its application to real estate ads

In processing human produced text using natural language processing (NLP) techniques, two fundamental subtasks that arise are (i) segmentation of the plain text into meaningful subunits (e.g., entities), and (ii) dependency parsing, to establish relations between subunits. In this paper, we develop a relatively simple and effective neural joint model that performs both segmentation and dependency parsing together, instead of one after the other as in most state-of-the-art works. We will focus in particular on the real estate ad setting, aiming to convert an ad to a structured description, which we name property tree, comprising the tasks of (1) identifying important entities of a property (e.g., rooms) from classifieds and (2) structuring them into a tree format. In this work, we propose a new joint model that is able to tackle the two tasks simultaneously and construct the property tree by (i) avoiding the error propagation that would arise from the subtasks one after the other in a pipelined fashion, and (ii) exploiting the interactions between the subtasks. For this purpose, we perform an extensive comparative study of the pipeline methods and the new proposed joint model, reporting an improvement of over three percentage points in the overall edge F1 score of the property tree. Also, we propose attention methods, to encourage our model to focus on salient tokens during the construction of the property tree. Thus we experimentally demonstrate the usefulness of attentive neural architectures for the proposed joint model, showcasing a further improvement of two percentage points in edge F1 score for our application.Comment: Preprint - Accepted for publication in Expert Systems with Application

Exploratory modeling: Extracting causality from complexity

On 22 May 2011 a massive tornado tore through Joplin, Mo., killing 158 people. With winds blowing faster than 200 miles per hour, the tornado was the most deadly in the United States since modern record keeping began in the 1950s. ©2014. American Geophysical Union. All Rights Reserved