Numerical Methods Course Research Articles

Reflective Questions: Promoting Metacognition Through Discussion Board Prompts

During two semesters, a numerical methods course for mechanical engineering students at a large US southeastern university used discussion board questions to promote reflection and metacognition. The course covered eight chapters, each with a related discussion question. The students could choose to answer these questions and receive 2% extra credit for the course. This was intended to help the students who missed some of the 30 online homework assignments that comprised 15% of the final course grade. The questions were also meant to encourage the students to think deeply and creatively. The students could see other students’ responses after they posted their own. The questions ranged from making a meme, writing a nursery rhyme, and explaining a complex or easy concept. Only 64% of the total possible responses were submitted by students, and there was a small-to-medium practical but no statistical significance between the levels of participation among the high- or low-performing students. The submissions were analyzed and determined to be at the low level of Bloom’s taxonomy. They identified complex topics to inform future instruction.

Studi kasus: Analisis kriteria konvergensi iterasi sederhana berdasarkan tebakan awal

The simple iteration material in the numerical methods course is material related to functions and derivatives. Apart from this, simple iteration material requires one or two initial guesses that do not require bracketing the roots. This method will produce a root approximation as a solution, which will show convergent or divergent results. The convergence criteria are influenced by the derived results and the initial guesses provided. Because of this, this research aims to analyze the results of student answers to prove the convergence criteria of a given simple iterative problem. The method used in this research is a case study, analyzing the results of the answers of five randomly selected students studying numerical methods courses. Based on the results of the analysis of the convergence criteria based on initial guesses, it was concluded that only 5 students could prove the convergence criteria correctly. In general, students made mistakes in deriving algebraic functions, carried out division operations, and incorrectly determined the convergence criteria because they only proved the possibility of the function. given so that students only focus on convergence criteria without carrying out iterative analysis.

ENHANCING STUDENT NUMERACY AND LITERACY WITH GEOGEBRA: A CASE IN NUMERICAL METHODS

Rapid advancement in technology has increased the significance of numerical literacy skills. The numerical methods course requires numerical literacy skills. The course enables students to solve a mathematical problem by interpreting the answer using an approximation rather than an actual value. This research used a descriptive quantitative method. The population of this study consisted of 80 university students enrolled in a numerical methods course. The sampling technique used a saturated sample, which involved everyone in the population as the sample. Data were collected from the learning outcomes test and questionnaire responses. The data were analyzed using a quantitative descriptive statistical analysis technique, and the data analysis computations were performed using SPSS Statistics 2. The study showed that the students' Numeracy and Literacy Skills improved when GeoGebra-assisted teaching materials were implemented in the numerical methods.

Active learning modules for a numerical methods course

Education research has suggested that students who receive a wider variety of sensory inputs during the learning process will be able to make more connections and more deeply understand course content. To this end, three physical hands-on laboratory learning modules were designed for a computational numerical methods course to help students develop intuition for physical systems, to allow for a comparison of real data against numerical solutions of physics equations, and to increase student engagement. These modules were designed to reinforce specific topics covered in the numerical methods curriculum, including numerical differentiation and numerical solution of ordinary differential equations. Pre- and post-tests showed an increase in student knowledge after module completion. In addition, end-of-term surveys showed that a strong majority of students believed modules helped them visualize and understand key numerical methods concepts, and that most would be interested in learning new material with similar modules in the future.

Effectiveness of Using Video Project and Google Classroom in Mathematics Learning of Numerical Methods Course

Effectiveness of Using Video Project and Google Classroom in Mathematics Learning of Numerical Methods Course

Course Prophet: A System for Predicting Course Failures with Machine Learning: A Numerical Methods Case Study

In this study, our purpose was to conceptualize a machine-learning-driven system capable of predicting whether a given student is at risk of failing a course, relying exclusively on their performance in prerequisite courses. Our research centers around students pursuing a bachelor’s degree in systems engineering at the University of Córdoba, Colombia. Specifically, we concentrate on the predictive task of identifying students who are at risk of failing the numerical methods course. To achieve this goal, we collected a dataset sourced from the academic histories of 103 students, encompassing both those who failed and those who successfully passed the aforementioned course. We used this dataset to conduct an empirical study to evaluate various machine learning methods. The results of this study revealed that the Gaussian process with Matern kernel outperformed the other methods we studied. This particular method attained the highest accuracy (80.45%), demonstrating a favorable trade-off between precision and recall. The harmonic mean of precision and recall stood at 72.52%. As far as we know, prior research utilizing a similar vector representation of students’ academic histories, as employed in our study, had not achieved this level of prediction accuracy. In conclusion, the main contribution of this research is the inception of the prototype named Course Prophet. Leveraging the Gaussian process, this tool adeptly identifies students who face a higher probability of encountering challenges in the numerical methods course, based on their performance in prerequisite courses.

Challenges of Digitalization of Small Credit Point Courses for Large Classes

The paper is devoted to the development of digital competences of second year bachelor students at the Faculty of Computer Science and Information Technology of the Riga Technical University for the course in numerical methods. The structure of the course is described in detail. The key component in the organization of the lectures and lab sessions is interactivity. Many interactive components (presentations, tests) in H5P format are available for students. The digital proficiency Levels 7 and 8 in accordance with DigComp 2.1 framework is expected to be achieved by carefully selecting topics and practical tasks to be solved during the course. The e-book written for the course and published by the Publishing house of the Riga Technical University is one of the teaching resources available to students. The course is fully digitalized so that it can be given in any of the three formats: (a) classroom and lab instruction, (b) fully online course or (c) mixed mode (blended learning). The preference is given to option (c). Both synchronous and asynchronous teaching methods are used. The organization of tests and exams (in the form of online tests) allows instructors to organize the grading effectively without spending too much time on it but at the same time effectively testing students’ knowledge.

An introduction to modelling through a microbial interaction application

This paper describes a teaching experiment in a Numerical Methods course for Master of Science students. The experiment uses scientific papers to develop modelling studies in the context of wine fermentation microbial interactions. The course involves theoretical and laboratory classes that focus on implementing numerical methods using Matlab for Initial Value Problems and Boundary Value Problems. The students are asked to formalise the mathematical model and build their own experiments using the information provided in the papers. Additionally, a parameter estimation experiment is organised, which involves generating synthetic data and computing noisy data to estimate the natural death rate of sensitive yeast. The results show that data noise significantly affects the parameter estimate and that scaling the data can help reduce the impact of measurement errors. The presented results can be used to investigate other possible assignments, such as how the evaluation of the Jacobian affects the estimation performance and compare different optimisation algorithms.

On learning platform metrics as markers for student success in a course

AbstractAdaptive learning platforms are increasingly being used as part of varying instructional modalities. Particularly relevant to this paper, adaptive learning is a critical component of personalized, preclass learning in a flipped classroom. Previously inaccessible, data generated by adaptive learning platforms regarding student engagement with the course content provides an invaluable opportunity to gain a deeper understanding of the learning process and improve upon it. We aim to investigate the relationships between adaptive learning platform interactions and overall student success in the course and identify the variables most influential to student success. We present a comprehensive analysis of our adaptive learning platform data collected in a Numerical Methods course, including aggregate statistics, frequency analysis, and Principal Component Analysis, to determine which variables exhibited the most variability and, therefore, the most information in the data. Subsequently, we used the Partitioning Around Medoids clustering approach to investigate naturally occurring clusters of students and how these clusters relate to overall performance in the course. Our results show that overall performance in the course, as measured by the final course grade, is strongly associated with (1) the behavioral interactions of students with the adaptive platform and (2) their performance on the adaptive learning assessments. We also found distinct student clusters (as defined by success in the course) that exhibited distinctly different behaviors. These findings provide qualitative and quantitative information to identify students needing support and to craft an evidence‐based support strategy for these students.

A hybrid-flipped course in numerical methods for chemical engineers

In 2022, the numerical methods course taught at the Technion's Faculty of Chemical Engineering was transformed to hybrid-flipped format based on seven years of successful experience. This course involves three phases each week: (1) online pre-class preparation by students, (2) face-to-face class meeting with the instructor to introduce open-ended problem solving, and (3) an online active tutorial, where students solve problems for themselves. This paper describes the course learning objectives, content and format, data on students’ engagement and perceptions, learning analytics tools used, and the summative outcomes assessment, as brought by the final exam results. The main conclusions are: (a) High-engaging students indicated that their confidence in mastery significantly improves with each phase, with the low-engagers indicating no significant improvement, and (b) High-engagers significantly outperformed low-engagers in learning outcomes: 86% of the students scoring over 90 were high-engagers, and 83% of the students who failed the exam were low-engagers.

NAO robots as context to teach numerical methods

This article examines the contextual role that NAO humanoid robots play in the learning environment of a numerical methods course through a design-based research approach. Under the design of intentional and reflective planning that emanates from the socio-critical paradigm in education, the feasibility of using this type of robot in the classroom as a motivation element to engage students in understanding numerical analysis issues is addressed. In particular, the active learning of engineering students is achieved by studying such robots' forward and inverse kinematics. The didactical sequence to teach the generalized Newton–Raphson method for solving non-linear equation systems is validated as part of a Hypothetical Learning Trajectory proposed. Besides, this research provides a brief theoretical discussion on reflection-in-action of the teacher of Higher Education level.

Chinese Culture Integrated into the Science and Engineering Courses

China’s excellent traditional culture has a history of thousands of years, which may influence the students’ thinking and behavior, therefore, it will be good if the China’s excellent traditional culture is integrated into the teaching. In this paper, the problems that are faced following the integration of “Numerical Calculation Methods” course with the China’s traditional culture, and ideological and political into teaching, were analyzed. Further, the strategy and specific implementation plan for the integration of traditional culture, ideological and political elements with the numerical calculation methods course was proposed. This provides a new platform, and experiences following the integration of basic mathematics courses in colleges and universities with curriculum traditional culture, ideological and political education.

ANALISIS KEBUTUHAN PENGEMBANGAN E-MODUL BERBANTU LIVEWORKSHEET PADA MATA KULIAH METODE NUMERIK

The purpose of this study was to determine the numerical method e-module that needs to be developed for mathematics education students. This research is a qualitative descriptive study. The subjects in this study were mathematics education students who took the numerical methods course for the 2021/2022 academic year at the University of Muhammadiyah Metro. The sample in this study was obtained by purposive sampling technique. The research data were collected by using observation, interview, and questionnaire techniques. The results showed that teaching materials in numerical method lectures still use one old teaching material, students need teaching materials that are easy to understand and can be used independently, which are used whenever and wherever they are, and students need teaching materials that support online learning. Based on the results of the study, it was concluded that it was necessary to develop teaching materials using numerical methods according to the characteristics of students and the development of existing technology. Teaching materials in the form of e-modules assisted by live worksheets are an alternative to teaching materials for numerical methods that are needed to facilitate online learning. In addition, with e-modules containing questions that can guide students in finding knowledge independently.

Adaptive learning: Helpful to the flipped classroom in the online environment of COVID?

Flipped instruction in an undergraduate numerical methods course in the online, remote environment during the COVID‐19 pandemic was conducted with and without the use of adaptive‐learning lessons for pre‐class preparation. This comparison was made to explore potential differences with and without adaptive software relative to exam and concept inventory performance and student perceptions of the classroom environment, learning and motivation, and benefits and drawbacks. Student perceptions were gathered via the College and University Classroom Environment Inventory (CUCEI) and a survey designed to capture feedback specific to flipped instruction. The analysis was made possible by a current NSF grant to study adaptive learning in the flipped classroom at three universities and extensive prior research with the flipped classroom and adaptive learning by the authors. Results gathered in the online flipped classroom with adaptive learning suggested positive changes in the following: classroom environmental perceptions, preference for flipped instruction, perceived responsibility imposed, motivation for independent learning, and perceived learning. Furthermore, based on an open‐ended question, there was a significant decrease in the proportion of students who experienced load, burden, or stressors in the online flipped classroom when adaptive learning was available versus not. Multiple‐choice exam and concept‐inventory results were slightly higher with adaptive lessons (although not significantly so), with the most promising results occurring for Pell grant recipients. The emerging medical education literature has suggested that adaptive learning and flipped instruction will be key to post‐pandemic education. The present article begins advocacy for adaptive learning with flipped instruction in engineering education.

Introducing students to research codes: A short course on solving partial differential equations in Python

Recent releases of open-source research codes and solvers for numerically solving partial differential equations in Python present a great opportunity for educators to integrate these codes into the classroom in a variety of ways. The ease with which a problem can be implemented and solved using these codes reduce the barrier to entry for users. We demonstrate how one of these codes, FiPy, can be introduced to students through a short course using progression as the guiding philosophy. Four exercises of increasing complexity were developed. Basic concepts from more advanced numerical methods courses are also introduced at appropriate points. To further engage students, we demonstrate how an open research problem can be readily implemented and also incorporate the use of ParaView to post-process their results. Student engagement and learning outcomes were evaluated through a pre and post-course survey and a focus group discussion. Students broadly found the course to be engaging and useful with the ability to easily visualise the solution to PDEs being greatly valued. Due to the introductory nature of the course, due care in terms of set-up and the design of learning activities during the course is essential. This course, if integrated with appropriate level of support, can encourage students to use the provided codes and improve their understanding of concepts used in numerical analysis and PDEs.

Transforming a blended learning course in numerical methods into a flexible digital course during the Covid-19 crisis

Mobile learning has had different paces in its acceptance: fast among technology developers and slow in some educational sectors and countries. Covid-19 crisis suddenly put an end to any possible delay in adopting educative technologies. This work describes the rapid adaptation of a blended learning course in Numerical Methods in higher education during the Covid-19 confinement. Its primary intention was to determine the impact of the transformation into a flexible digital course on students' performance discussing the elements introduced, the analytical methods, and the assessment tools (grading register, learning analytics, and a final student opinion survey). The analyses also revealed social and behavioural aspects related to social learning, focused on the students' virtual contact imposed by the health contingency. Observed students' adaptations of individual and team tasks under the new learning modality impacting their performance are discussed, highlighting and supporting the belief that the context strongly influences blended learning success.

Transforming a blended learning course in numerical methods into a flexible digital course during the Covid-19 crisis

Mobile learning has had different paces in its acceptance: fast among technology developers and slow in some educational sectors and countries. Covid-19 crisis suddenly put an end to any possible delay in adopting educative technologies. This work describes the rapid adaptation of a blended learning course in Numerical Methods in higher education during the Covid-19 confinement. Its primary intention was to determine the impact of the transformation into a flexible digital course on students' performance discussing the elements introduced, the analytical methods, and the assessment tools (grading register, learning analytics, and a final student opinion survey). The analyses also revealed social and behavioural aspects related to social learning, focused on the students' virtual contact imposed by the health contingency. Observed students' adaptations of individual and team tasks under the new learning modality impacting their performance are discussed, highlighting and supporting the belief that the context strongly influences blended learning success.

GeoGebra as learning tool for the search of the roots of functions in numerical methods

Physics is capable of describing, through equations, phenomena on a micro and macroscopic scale. However, most of these equations are non-linear and the identification of their roots requires the use of approximation methods, with numerical methods being a proposal based on a systematic and iterative process, that conclude only when a pre-established tolerance is satisfied. Traditional teaching of numerical methods involves the memorization of algorithms. However, this hinders student’s ability to understand the important aspects and then apply them for solving applied problems in subjects such as kinematics, dynamics, electromagnetism, etc. Therefore, this work proposes the use of GeoGebra, as a didactic tool to illustrate the functioning of single root searching algorithms. By using the dynamical graphic’s view of GeoGebra, a series of abstract and applied problems where solved by engineering students taking a numerical methods course. The scores of this test group was then compared to a test group, taught trough algorithm memorization. Results show can improve their understanding of how the bisection, false position, secant, and Newton-Raphson methods are able to find approximated solutions to polynomial and trigonometric equations. The results are compared against traditional learning, based on memorizing the steps of the algorithm for each method and the representation of the convergence of successive roots by numerical tables.

'Soft' skills identified by students who peer-led mathematics computing workshops

Increasingly, employers are suggesting that 'soft' skills, such as communication and teamwork, are equally important as 'hard' skills, such as discipline specific knowledge. This makes it imperative for university programs to build in opportunities for students to practise and demonstrate such soft skills. For some years, small groups of students in my second-year numerical methods course have acted as peer-leaders, with each student taking a turn to help run the computer workshops. In 2018, I introduced a PebblePad reflection to give the students the opportunity to identify the skills that they had developed, as well as to reflect on the process. In analysing the students' responses, I found that the students were very positive about the experience and that they were able to articulate a range of soft skills that they had practised and developed during the activity.

The Development of Teaching Materials for Subjects of Numerical Method Assisted by MATLAB Software in Mathematics Education Department Students

The purpose of this study was to develop teaching materials for numerical methods supported by valid, practical, and effective MATLAB software for students of Mathematics Education Department at UIN Alauddin Makassar. The type of research used was Research and Development with reference to the ADDIE development model, namely Analysis, Design, Development, Implementation, and Evaluation. The product developed in the form of teaching materials was a module which not only contains material in the Numerical Method course but also was equipped with MATLAB syntax that can help students actively in the teaching and learning process. The instruments used in this study were expert validation sheets, observation sheets for the implementation of teaching materials, student questionnaire responses, observation sheets for student activities, and learning achievement tests. Based on the results of trials conducted, it was found that (1) The validation results for teaching materials and all instruments are in the very valid category. (2) Practical, the average of all aspects are in the category implemented entirely and all aspects of student responses are very positive (3) Effective, student learning outcomes have met the completeness criteria and the average student activity using teaching materials assisted with MATLAB software is in the category very good. So it was concluded that the development of teaching materials assisted by MATLAB software in the numerical methods course of students Mathematics Education Department at UIN Alauddin Makassar had met the criteria of validity, practicality, and effectiveness.