Utilization of novel digital techniques in mathematics education

This article discusses the challenges of mathematics education in the age of digital technologies. Education analysis and design, educator roles, and reflection on the difficulties encountered in this area are all of importance. It is also important to investigate the characteristics and elements that contribute to the transformation of educational practices at various levels. Mathematics is a duplex subject: on the one hand, it contains computations and methods; on the other hand, it contains logic and ideas. Throughout the world, Faculty and students rely largely on the incorporation of digital technology into their teaching and learning activities to be effective and efficient. Digital learning enables and enhances students' pedagogical activities. The research inquiry concludes by identifying and providing important success aspects and tools. To illustrate this paradigm, we will present our study's conclusion that these success elements and tools are critical for facilitating mathematics learning using digital technology and some crucial facts

Monitoring Trails and Disturbance in Joshua Tree National Park

Joshua Tree National Park, well known for its recreation activities, is in need of improved vegetation and trail monitoring programs. Specifically, social trails, or trails created by users that deviate from designated paths, are major contributors to vegetation disturbance and loss. Current activity levels are beginning to negatively affect surrounding landscapes. This project was developed to enable staff to monitor large regions of the park without expending significant man-hours or costs. With this in mind, the project was developed using QuickBird satellite imagery as the main component for feature extraction from an ESRI system with the Feature Analyst (FA) and Spatial Analyst extensions. The deliverables for this project were a master geodatabase, vegetation index, and a feature class containing all the social trails within a given region. A customized ArcToolbox and model were developed, in addition to a complete process-flow highlighting the steps required to process and analyze the data. The implemented tools and methods in the project enabled the client to monitor large regions of the park with less effort than field data collection

Web-based Simulation and Training Environment for Laparoscopic Camera Calibration

Endoscopic cameras are increasingly employed in image-guidance procedures, where the video images must be registered to data from other modalities. However, such cameras are susceptible to distortions, requiring calibration before images can be used for registration, tracking and 3D reconstruction. Camera calibration is learned in a laboratory setting, where configuring and adjusting the physical setup is tedious and not necessarily conducive to learning. A centralized resource that utilizes 3D interactive components needs to be available for training on camera calibration. In this project, a web-based training environment for camera calibration is implemented called SimCAM. SimCAM was developed using the Web Graphics Library (WebGL), Open Computer Vision (OpenCV) library, and custom software components. WebGL and OpenCV were used to simulate camera distortions and the calibration task. The main contributions include the implementation and validation of SimCAM. SimCAM was validated with a content validity study, where it was found to be useful as an introduction to camera calibration. Future work involves improving the supporting material and implementing more features, such as uncertainty propogation

Creating Individualized Self-Scoring Assessments for Agricultural Economics Undergraduates

What is an individualized self-scoring assessment for an agricultural economics major? It is a homework assignment that is unique for each student in the class and provides immediate feedback to the student on the correctness of the work. The principle is to generate unique problems, whether it is as simple as the basic intercept and slope of supply and demand equations for an introductory economics class, the parameters of a production function for a production economics, or the interest rate for agricultural finance. One must be aware in constructing the generator algorithms for problem parameters that any necessary conditions will be satisfied a priori such as downward sloping demand, concavity or convexity for maximization or minimization. These assignments are created in an Excel spreadsheet format. Once the basic template is created, the process for self-scoring immediate feedback is relatively easy. Create a copy of the original uncompleted problem sheet in the same workbook and provide the correct formulae to serve as a key. Create a second copy to serve as a check page and replace the formulae with an IF statement comparing the value or formula in the original to the second. It is best to provide some tolerance in the comparison such as checking that the absolute difference in the original and second sheet is less than some critical value. This is especially true for optimization problems. By hiding the key worksheet and protecting the workbook structure, students can not access the correct formulae. However, if the correct formulae or number is entered in the problem sheet, the student can view the check worksheet to see if the answer is correct. A simple GETFORMULA add-in allows the worksheet to check model setups in optimization problems. The key advantage of this technique to the students is the immediate feedback. Also by generating unique assignments, students can cooperate and learn among themselves without being able to directly copy from their peers. Additionally, graphical representations of their problems can often be provided simultaneously. Lastly, the students find that their spreadsheet skills are greatly enhanced. From the instructor perspective, the assessments are already scored when submitted. Students will seek help prior to turning in the assignment. And there is little need to sacrifice complexity to create problems that work out to neat answers. Empirical evidence of improvement in student evaluations indicates the technique is successful.Teaching/Communication/Extension/Profession,

Approximation of the inverse kinematics of a robotic manipulator using a neural network

A fundamental property of a robotic manipulator system is that it is capable of accurately following complex position trajectories in three-dimensional space. An essential component of the robotic control system is the solution of the inverse kinematics problem which allows determination of the joint angle trajectories from the desired trajectory in the Cartesian space. There are several traditional methods based on the known geometry of robotic manipulators to solve the inverse kinematics problem. These methods can become impractical in a robot-vision control system where the environmental parameters can alter. Artificial neural networks with their inherent learning ability can approximate the inverse kinematics function and do not require any knowledge of the manipulator geometry. This thesis concentrates on developing a practical solution using a radial basis function network to approximate the inverse kinematics of a robot manipulator. This approach is distinct from existing approaches as the centres of the hidden-layer units are regularly distributed in the workspace, constrained training data is used and the training phase is performed using either the strict interpolation or the least mean square algorithms. An online retraining approach is also proposed to modify the network function approximation to cope with the situation where the initial training and application environments are different. Simulation results for two and three-link manipulators verify the approach. A novel real-time visual measurement system, based on a video camera and image processing software, has been developed to measure the position of the robotic manipulator in the three-dimensional workspace. Practical experiments have been performed with a Mitsubishi PA10-6CE manipulator and this visual measurement system. The performance of the radial basis function network is analysed for the manipulator operating in two and three-dimensional space and the practical results are compared to the simulation results. Advantages and disadvantages of the proposed approach are discussed

Adaptive Constrained Kinematic Control using Partial or Complete Task-Space Measurements

Recent advancements in constrained kinematic control make it an attractive strategy for controlling robots with arbitrary geometry in challenging tasks. Most current works assume that the robot kinematic model is precise enough for the task at hand. However, with increasing demands and safety requirements in robotic applications, there is a need for a controller that compensates online for kinematic inaccuracies. We propose an adaptive constrained kinematic control strategy based on quadratic programming, which uses partial or complete task-space measurements to compensate online for calibration errors. Our method is validated in experiments that show increased accuracy and safety compared to a state-of-the-art kinematic control strategy.Comment: Accepted on T-RO 2022, 16 Pages. Corrected a few typos and adjusted figure placemen

Adaptive Neuron Model: An architecture for the rapid learning of nonlinear topological transformations

A method for the rapid learning of nonlinear mappings and topological transformations using a dynamically reconfigurable artificial neural network is presented. This fully-recurrent Adaptive Neuron Model (ANM) network was applied to the highly degenerate inverse kinematics problem in robotics, and its performance evaluation is bench-marked. Once trained, the resulting neuromorphic architecture was implemented in custom analog neural network hardware and the parameters capturing the functional transformation downloaded onto the system. This neuroprocessor, capable of 10(exp 9) ops/sec, was interfaced directly to a three degree of freedom Heathkit robotic manipulator. Calculation of the hardware feed-forward pass for this mapping was benchmarked at approximately 10 microsec

The design and evaluation of non-visual information systems for blind users

This research was motivated by the sudden increase of hypermedia information (such as that found on CD-ROMs and on the World Wide Web), which was not initially accessible to blind people, although offered significant advantages over traditional braille and audiotape information. Existing non-visual information systems for blind people had very different designs and functionality, but none of them provided what was required according to user requirements studies: an easy-to-use non-visual interface to hypermedia material with a range of input devices for blind students. Furthermore, there was no single suitable design and evaluation methodology which could be used for the development of non-visual information systems. The aims of this research were therefore: (1) to develop a generic, iterative design and evaluation methodology consisting of a number of techniques suitable for formative evaluation of non-visual interfaces; (2) to explore non-visual interaction possibilities for a multimodal hypermedia browser for blind students based on user requirements; and (3) to apply the evaluation methodology to non-visual information systems at different stages of their development. The methodology developed and recommended consists of a range of complementary design and evaluation techniques, and successfully allowed the systematic development of prototype non-visual interfaces for blind users by identifying usability problems and developing solutions. Three prototype interfaces are described: the design and evaluation of two versions of a hypermedia browser; and an evaluation of a digital talking book. Recommendations made from the evaluations for an effective non-visual interface include the provision of a consistent multimodal interface, non-speech sounds for information and feedback, a range of simple and consistent commands for reading, navigation, orientation and output control, and support features. This research will inform developers of similar systems for blind users, and in addition, the methodology and design ideas are considered sufficiently generic, but also sufficiently detailed, that the findings could be applied successfully to the development of non-visual interfaces of any type

Conceptualizing routines of practice that support algebraic reasoning in elementary schools: a constructivist grounded theory

There is ample literature documenting that, for many decades, high school students view algebra as difficult and do not demonstrate understanding of algebraic concepts. Algebraic reasoning in elementary school aims at meaningfully introducing algebra to elementary school students in preparation for higher-level mathematics. While there is research on elementary school students' algebraic reasoning, there is a scarcity of research on how elementary school teachers implement algebraic reasoning curriculum and how their practices support algebraic reasoning. The purpose of this study therefore was to discover practices that promote algebraic reasoning in elementary classrooms by studying elementary school teachers' practices and algebraic reasoning that the practices co-constructed. Specifically, the questions that guided the study included (a) what were the teachers' routines of practice, and (b) in what ways did the routines of practice support algebraic reasoning. I sampled On Track Learn Math project and worked with six teachers to explore their routines of practice and students' algebraic reasoning. As a participant observer, I analyzed video data of the classroom activities, memos, field notes, students' written transcripts and interview data using constructivist grounded theory approach and descriptive statistics. Member checking, data triangulation, and data coding by multiple raters ensured consistency and trustworthiness of the results. Descriptive analysis of students' written generalizations showed that about 74% of the generalizations were explicit and about 55% of the generalizations included names of variables indicating that students were learning how to reason algebraically. Data analysis also revealed five routines of practice. These routines are; (a) maintaining open-endedness of the tasks, (b) nurturing co-construction of ideas, (c) fostering understanding of variable, (d) creating a context for mathematical connections and (e) promoting understanding of generalizations. Teachers maintained open-endedness by giving minimal instructions when launching the tasks and providing students with workspaces. They nurtured co-construction of ideas by creating opportunities for students to collaborate, fostering collaboration, and balancing the support of discourse and content. They fostered understanding of variable as a changing quantity and as a relationship. Teachers created a context for mathematical connections between On Track tasks and students' everyday experiences, between student strategies, between different tasks, between On Track tasks and other curriculum ideas, and between different representations. Teachers promoted understanding of generalizations by encouraging students to justify their conjectures, to apply and evaluate peers' generalizations among other practices. These practices were dependent and informed each other