Evolution of the Modern ODE Course

The rapid development of technology in the latter part of the twentieth century has revolutionized the teaching of differential equations. In this paper we will try to trace the evolution of this important change. We tried to include the most important efforts in this regard, but we apologize in advance if some efforts have slipped our attention

A Method for Knowledge Representation to Design Intelligent Problems Solver in Mathematics Based on Rela-Ops Model

Knowledge-base is a fundamental platform in the architecture of an intelligent system. Relations and operators are popular knowledge in practice knowledge domains. In this paper, we propose a method to represent the model by combining these kinds of knowledge, called the Rela-Ops model. This model includes foundation components consisting of concepts, relations, operators, and inference rules. It is built based on ontology and object-oriented approaches. Besides the structure, each concept of the Rela-Ops model is a class of objects which also have behaviors to solve problems on their own. The processing of algorithms for solving problems on the Rela-Ops model combines the knowledge of relations and operators in the reasoning. Furthermore, we also propose a knowledge model for multiple knowledge domains, in which each sub-domain has the form as the Rela-Ops model. These representation methods have been applied to build knowledge bases of Intelligent Problems Solver (IPS) in mathematics. The knowledge base of 2D-Analytical Geometry in a high-school is built by using the Rela-Ops model, and the knowledge base of Linear Algebra in university is designed by using the model for multiple knowledge domains. The IPS system can automatically solve basic and advanced exercises in respective courses. The reasoning of their solutions is done in a step-by-step approach. It is similar to the solving method by humans. The solutions are also pedagogical and suitable for the learner’s level and easy to be used by students studying 2D-Analytical Geometry in high-school and Linear Algebra in university.This work was supported in part by the Universiti Teknologi Malaysia (UTM) under Research University Grant Vot-20H04, in part by the Malaysia Research University Network (MRUN) Vot 4L876 and in part by the Fundamental Research Grant Scheme (FRGS) Vot 5F073 through the Ministry of Education Malaysia

GRNsight: a web application and service for visualizing models of small- to medium-scale gene regulatory networks

GRNsight is a web application and service for visualizing models of gene regulatory networks (GRNs). A gene regulatory network (GRN) consists of genes, transcription factors, and the regulatory connections between them which govern the level of expression of mRNA and protein from genes. The original motivation came from our efforts to perform parameter estimation and forward simulation of the dynamics of a differential equations model of a small GRN with 21 nodes and 31 edges. We wanted a quick and easy way to visualize the weight parameters from the model which represent the direction and magnitude of the influence of a transcription factor on its target gene, so we created GRNsight. GRNsight automatically lays out either an unweighted or weighted network graph based on an Excel spreadsheet containing an adjacency matrix where regulators are named in the columns and target genes in the rows, a Simple Interaction Format (SIF) text file, or a GraphML XML file. When a user uploads an input file specifying an unweighted network, GRNsight automatically lays out the graph using black lines and pointed arrowheads. For a weighted network, GRNsight uses pointed and blunt arrowheads, and colors the edges and adjusts their thicknesses based on the sign (positive for activation or negative for repression) and magnitude of the weight parameter. GRNsight is written in JavaScript, with diagrams facilitated by D3.js, a data visualization library. Node.js and the Express framework handle server-side functions. GRNsight’s diagrams are based on D3.js’s force graph layout algorithm, which was then extensively customized to support the specific needs of GRNs. Nodes are rectangular and support gene labels of up to 12 characters. The edges are arcs, which become straight lines when the nodes are close together. Self-regulatory edges are indicated by a loop. When a user mouses over an edge, the numerical value of the weight parameter is displayed. Visualizations can be modified by sliders that adjust the force graph layout parameters and through manual node dragging. GRNsight is best-suited for visualizing networks of fewer than 35 nodes and 70 edges, although it accepts networks of up to 75 nodes or 150 edges. GRNsight has general applicability for displaying any small, unweighted or weighted network with directed edges for systems biology or other application domains. GRNsight serves as an example of following and teaching best practices for scientific computing and complying with FAIR principles, using an open and test-driven development model with rigorous documentation of requirements and issues on GitHub. An exhaustive unit testing framework using Mocha and the Chai assertion library consists of around 160 automated unit tests that examine nearly 530 test files to ensure that the program is running as expected. The GRNsight application (http://dondi.github.io/GRNsight/) and code (https://github.com/dondi/GRNsight) are available under the open source BSD license

Innovation Plaza: Improving Teaching and Learning in Engineering Education

Innovation-Plaza at the University of New Mexico represents a significant advance in improvement in instruction, higher rates of student retention and graduation, and greater success for students traditionally underserved by engineering programs. Through the employment of improved teaching methods in a key ECE course; dual-credit courses for high school students; and outreach to public schools, industry, government and international organizations, Innovation-Plaza has already improved the prospects for academic and professional success for some students in the ECE program at UNM. Expansion and dissemination of the innovations piloted in this program can serve an important role in improving the prospects for students traditionally underserved by engineering and other higher education STEM programs, change that is essential if the United States is to remain competitive with other nations in science and technology. Given continued attention to the need to build on, replicate and disseminate successful aspects of the Innovation-Plaza program via improved pedagogy in ECE and other STEM courses; outreach to secondary school students, Hispanics, women, foreign students and other populations currently underserved by engineering and other STEM academic programs; and increased collaboration with educational institutions, governments, and industry, it can be expected that the Innovation-Plaza program will continue to experience growth and success in fulfilling its mission to better serve students in engineering and other STEM fields

UTB/TSC Graduate Catalog 2013-2015

https://scholarworks.utrgv.edu/brownsvillelegacycatalogs/1004/thumbnail.jp

Active Learning in Physics, Astronomy and Engineering with NASA’s General Mission Analysis Tool

Astrodynamics is the study of the motion of artificial satellites and spacecraft, subject to both natural and artificially induced forces. It combines celestial mechanics, attitude dynamics and aspects of positional astronomy to describe spacecraft motion and enable the planning and analysis of missions. It is of significant interdisciplinary interest with relevance to physics, astronomy and spaceflight engineering, but can be challenging to deliver in an effective, engaging manner because of the often abstract nature of some concepts, the four-dimensional nature of the problems, and the computation required to explore realistic astrodynamics behaviour. The University of Leicester has adopted NASA’s General Mission Analysis Tool as a core resource to support active learning in this subject for students at Level 6 (BSc) and Level 7 (MSc). This paper describes our approach to the implementation of GMAT as an essential element of teaching and learning in the subject

Mapping the relationship between curriculum, pedagogy and digital technology to develop a predictive model for the improvement in students' attainment

The relationship between learning, pedagogy and technology is a complex area of injury. Working with, and analysing data generated by, twenty teachers and two hundred seventy-eight students from the Institute of Applied Technology (IAT) in the United Arab Emirates, I was able to drill down into the complex interactions between curriculum, pedagogy and technology. From this work, I developed an original predictive model, which outlines the improvement in students' attainment due to the complex interactions of three critical elements - curriculum (C), pedagogy (P), and digital technology (T), what I call the CPT model. My analysis indicated that digital technology impacted positively on students' attainment when it was used with science subjects but less so when it was used with humanities subjects. Based on the literature review, the relationship between C, P and T had been widely investigated (see, for example, Mishra and Koehler (2006; 2013), Archambault and Barnett (2010), Angeli and Valanides (2009), Voogt et al. (2012)). However, none of the researchers dealt with this relationship and its impact on students' learning and attainment quantitatively or using a mathematical perspective. This study aims to highlight how the CPT model can predict the improvement in students' attainment as an outcome of using educational technology (the impact factor) and locate the most effective strategies of learning. This research fills the knowledge gap by developing a new model that explores the C, P, T correlations using three-dimensional equations that I have developed. As such, the study makes a significant contribution to educational technology literature through exploring the C, P, T impact on students' attainment. The research offers educators, policymakers and curriculum developers opportunities to leverage digital technology as a mean for enhancing attainment. Understanding the CPT relationship enables the development of focussed digital technology-supported curricular for students regardless of their academic level. I concluded this by arguing that the CPT model can guide both teachers and policymakers to locate the most effective strategy of learning to maximise the impact of digital technology on students' attainment. This PhD study contributes to knowledge by a new educational term called Tranology, which is a combination of two main types of learning, traditional and digital technology-based learning, please refer to sections 2.9 and 8.4. Furthermore, this study suggests the application of the vector space concept to organise the relationship between the elements C, P and T. In turn, this implies that these elements overlap over three-dimensional space, which is addressed in this study as the CPT space, rather than, overlapping over two-dimensional plane as demonstrated by Mishra and Koehler (2005; 2006; 2008), please refer to chapter 5. In terms of future scientific understanding and theoretical insights, the CPT model can be transformed from three-dimensional model (C, P and T) to four-dimensional model (4-D) that comprises the three dimensions of curriculum, pedagogy and digital technology (C, P and T) and the one dimension of a student's attitude towards learning (S) to produce 4-D model called the CPT-S curvatures. Please refer to section 8.6