Calculus Subject Research Articles

Evaluation of the perception of a virtual learning object with activities to promote study habits in the subject of differential calculus

The study and understanding of Differential Calculus are essential for Engineering, providing the bases for the topics in the development of Competences of Integral Calculus, Vector Calculus, Differential Equations and physics subjects. This study proposes to evaluate the perception of a virtual learning object with activities to promote study habits in the subject of differential calculus. The proposal consists of analyzing the perception of a virtual learning object about Functions of the Differential Calculus subject, which includes activities of study habits, obtained from a group of students of the second semester of engineering level. The results are encouraging since the students identified as positive aspects the dynamism of the object, the usefulness of using technological tools to strengthen learning.

Analysis of Course Learning Outcomes: Student Errors in The Calculus Subject among Engineering Students

Analysis of Course Learning Outcomes: Student Errors in The Calculus Subject among Engineering Students

인공지능을 위한 대학에서의 미적분학 교육

This study investigates the relationship between calculus education in current universities and the mathematical knowledge required for artificial intelligence and examines ways to address topics related to mathematics required for artificial intelligence in calculus subjects. As technologies related to artificial intelligence become established in daily life, education related to artificial intelligence has become essential in secondary education and universities. However, in a reality where the barrier to entry to acquire knowledge related to artificial intelligence is very high, we provide a curriculum that allows students to obtain mathematical knowledge related to artificial intelligence in a relatively easy calculus course rather than a difficult class in a major subject. we will provide direction for improvement.

INVESTIGATING THE ATTITUDES TOWARDS LEARNING CALCULUS AMONG SCIENCE AND TECHNOLOGY STUDENTS: A CASE STUDY IN UITM JOHOR, MALAYSIA

Calculus is widely regarded as one of the difficult branches of Mathematics and is considered an intimidating subject even to Science and Technology students. Majority of the students find themselves struggling. This is due to the fact that a student's attitude has an impact on how effectively they learn Calculus and as a result, affecting their performance in course grades in university level. Therefore, this study was conducted to investigate the students’ attitude towards Calculus at UiTM Segamat Branch, Johor. This study also aims to determine the differences in attitudes scores between program courses and gender as well as to examine the relationship between students’ attitude and their Calculus achievement. The target population of this study is undergraduate students comprising Diploma in Computer Science (CS110) and Diploma in Mathematical Sciences (CS143) students who have enrolled in Calculus subject. Data was collected using an online questionnaire and a cross-sectional research design was used for this study. Descriptive statistics such as mean and standard deviation, independent t-test and correlation analysis were conducted. The findings of this study revealed that students showed a positive moderate attitude towards Calculus. Meanwhile, there is no significant difference in attitudes scores across program courses as well as gender. Also, students with a negative attitude tend to have a low level in terms of Calculus achievement. Students’ attitudes towards Calculus may change over time because it could be influenced by other elements but the most important element that influences the students are lecturers. In order to encourage the development of a positive attitude towards Calculus, lecturers must constantly monitor students' attitudes toward the subject and offer the necessary support.

Sosialisasi Penggunaan Aplikasi GeoGebra dalam Meningkatkan Minat BelajarSiswa Kelas VI pada Pelajaran Bangun Ruang di SDIT Buah Hati Padang

Community Service (PKM) is one of the forms of Higher Education's Tri Dharma. PKM is proposed to carry out activities that focus on socialization and education. Learning mathematics is about understanding abstract ideas or concepts, structures, and their logically and systematically organized relationships. Media is a communication component that serves as a carrier of messages from the communicator to the communicant. One of the learning media used to facilitate students is the Geogebra application. Geogebra is a computer application created to facilitate mathematics learning, especially in geometry, algebra, and calculus subjects. By using the Geogebra application, it can improve students' mathematics learning outcomes. The method used in this PKM is education and direct practice of the "jarimatika" method in multiplication problems. As a result, participants become more understanding of the Geogebra application.

Engineering Students’ Utterances about Evaluation and Its Roles in the Courses of Physics and Calculus

Context: Assessment could provide feedback to both students and teachers on teaching and learning processes. However, this perspective coexists with an evaluation dynamic focused on performance and results. Objectives: This research intends to problematize what a group of Engineering students says about the evaluation processes and their purposes in Mathematics and Physics subjects, offered in the context of remote teaching. Design: Ideas from qualitative research in a Foucauldian perspective. Environment and participants: The sample consisted of 85 engineering students, enrolled in Physics and Calculus subjects, in the first semester of 2021. Data collection and analysis: Application of an online questionnaire, with six Physics or Calculus classes, in a community university of Rio Grande do Sul. Results: The discourse analysis according to the Foucauldian perspective produced two analysis units that indicate how the eighty-seven participating students conceive evaluation in their utterances. The first one indicates that they think evaluation enables their own learning to be monitored and assessed, and decisions to be made by professors. The other one points out that students conceive evaluation as classifying and meritocratic, focusing on performance, outcomes, and grade measurement. Conclusions: Contradictory and complementary conceptions coexist, indicative of the different roles attributed to assessment in formal education contexts. In general, the research participants evidence the reproduction of statements that circulate socially about the evaluation and its roles. Such results can be productive for teachers and institutions to understand that they also meet the expectations of an evaluation system with an emphasis on regulation and control.

Integration of STEM Education in Differential and Integral Calculus classes: Aspects Evidenced in a Mathematical Modelling Activity

Background: The integration of STEM areas (science, technology, engineering and mathematics) in engineering courses has been the focus of research in the educational context and mathematical modelling has the potential for its success. Objectives: The research question that guides the discussion is: What aspects of STEM education can be evidenced when engineering students develop mathematical modelling activities in a virtual environment within the scope of a Differential and Integral Calculus course? Design: Qualitative research carried out in the second half of 2020, based on research design guidelines, in the Differential and Integral Calculus subject during remote teaching. Setting and Participants: Virtual environment shared by two classes with 72 students from different courses for the development of a mathematical modelling activity. Data collection and analysis: Data from 18 groups were collected virtually from notes on the wiki, audio or video recordings of group meetings or orientation meetings, activity communication video and individual response to a questionnaire. The analysis was based on an initial coding of data from all groups, carried out with the support of AtlasTi, in which three groups were selected for a detailed analysis related to aspects of STEM education. Results: Some groups naturally integrate the four STEM areas and others carry out this integration in a partial way. Conclusions: The virtual environment made it possible for students to interact in their groups and collaborate with each other to solve a problem in a way that knowledge of basic sciences and mathematics were articulated.

CALCULUS TEACHER’S COMPETENCIES AS CORRELATES OF STUDENTS’ LEARNING EXPERIENCES

The good qualities of a calculus teacher are an asset in producing great results for students and themselves. This study aimed to investigate the different competencies of a calculus teacher as correlates of students' experiences in learning at Visayas State University, Philippines. The study employed selected secondary data from the existing study literature such as competencies in teaching calculus subjects and different types of learning experiences of students. The study used some descriptive statistical measures to summarize the selected data and employed Spearman rho correlation to predict significant factors (teacher's competencies) that might influence the student's learning experiences. Results showed that teachers' competencies such as "prepared", "knowledgeable", "mastery", "organized", "decent", and "approachable" are highly correlated to the different learning experiences of students at a 1% level of significance. Hence, calculus teachers must be always knowledgeable in a class through rigorous preparation and studying. It is also concluded that teachers must develop a mastery of calculus subjects and apply an organized routine during class discussions to obtain desired academic performance for students. In addition, a well-groomed and professional may be integrated in front of students as well as open-mindedness and good personality to make interactive and stimulating class discussions. It is recommended that calculus teachers may undergo some rigorous training for calculus teaching to become a knowledgeable and competitive educators. Furthermore, teachers who will teach college calculus must be holding at least a master's degree in line with mathematics education or pure mathematics.

Undergraduate Education Students' Perceptions and Challenges of Learning Calculus Through Blended Learning

Blended learning has recently gained popularity in training and education. It was a combination of two learning styles, which are face-to-face teaching and some of the technological aids that have been widely used in teaching and learning. This study is meant to be an addition to the in-class lectures and to assist students in understanding calculus subjects at their own pace and time. The purpose of this study is to describe students' perceptions of blended learning and to determine whether blended learning affects their readiness and challenges in learning calculus. A total of 86 Mathematics Education students were involved in this study, in which a series of questionnaires were distributed to evaluate their readiness and learning perceptions. Based on the findings, a conclusion has been made regarding the role of blended learning in supporting teaching and learning. The results showed that students demonstrate positive perceptions using the blended learning approach in some of the subjects.

Examining Multiple Intelligences and Performance of Science, Technology, Engineering, and Mathematics (STEM) Students in the Specialized Subjects

This study generally examined the multiple intelligences of the Senior high school (SHS) students under the Science, Technology, Engineering, and Mathematics (STEM) strand and their performance in the specialized subjects. Descriptive and comparative research designs were utilized to measure the variation among the identified study variables. It involved 193 STEM students (composed of 94 males and 99 females) who were selected using complete enumeration sampling. Secondary data on students' performance in the specialized subjects and an adopted Multiple Intelligence Inventory survey questionnaire were employed to collect the data. The T-test for two independent samples was likewise used to examine the significant difference between the performance in the specialized subjects of students with STEM strand as their preferred choice and those who do not prefer STEM. Based on the results, interpersonal intelligence was shown to be the most dominant intelligence type among STEM students, whereas logical intelligence was determined to be the least dominant. On the specialized subjects’ performance, the students demonstrated very good to superior performance in pre-calculus, general biology, and basic calculus subjects. Meanwhile, the study indicated no significant difference in the specialized subjects’ performance between students with STEM strand as their preferred choice and those who do not prefer STEM. Career guidance orientation for students must be reinforced so that they can be advised on what career track or stand to take in senior high school. Future related studies are suggested to further substantiate the results.

Students’ satisfaction on learning calculus using open and distance learning method during COVID-19 pandemic

In early 2020, due to the COVID-19 outbreak in Malaysia, all higher education institutions had to switch from face-to-face learning to open and distance learning (ODL) method. The main purpose was to prevent any further spread of the COVID-19 virus. This study aimed to identify factors carrying impacts on students’ satisfaction in learning calculus using ODL method. The sample consists of 224 students of Universiti Teknologi MARA (UiTM) Perak Branch, Tapah Campus who took calculus subjects using ODL method during the COVID-19 lockdown in Malaysia. Five factors are found to influence students’ satisfaction towards ODL method: student-lecturer interaction; lecturer performance; ODL course evaluation; design; and technical. By using partial least square (PLS)–SEM method, the results showed that lecturer performance has a large effect size on students’ satisfaction. Technical and design factors have medium effect sizes, while the ODL course evaluation and student-lecturer interaction have small effect sizes. This research provided useful insights for an effective planning of online calculus courses by considering all factors that influence students’ satisfaction.

Application of C5.0 Algorithm in Prediction of Learning Outcomes in Calculus Subject

Calculus is one of the basic subject that must be studied at the computer science faculty of the informatics engineering study program. For some students, especially in the Faculty of Informatics Engineering, calculus is a subject that is considered quite difficult, even though this subject is important for them. And the resulted for some students having to repeat this subject. For this reason, predictions of calculus learning outcomes are carried out by applying the data mining process and using the C5.0 method for the prediction process based on the classification concept that will be carried out. This study applies the Cross Industry Standard Process for Data Mining (CRISP – DM) methodology with the C5.0 algorithm. The results are in the form of a decision tree (Decision tree) and the rules in it using the attributes of guardian, number of family members, status of residence, internet, activity, desire to continue study, the last education of parents (father and mother), parents' occupations, grades on assignments, UAS, and UTS. The C5.0 algorithm is able to predict the results of learning calculus. The evaluation results show that the applied C5.0 algorithm has an accuracy of 95%.

A Comparison Study of Students Performance for Vector Calculus Subject

The research objective was to compare the performance of Engineering students in a pretest and post-test of Vector Calculus subject between programmes during their first year of study at the Faculty of Engineering and Built Environment (FKAB), Universiti Kebangsaan Malaysia (UKM). This paper also aims to investigate the student's knowledge in Vector Calculus, particularly in main topics including partial derivatives, vector functions, line integrals, double integrals, triple integrals, Green's Theorem, Stokes' theorem, Gauss' theorem, and basic differentiation and integration of complex functions. Each topic is included in Course learning outcomes to analyze either the students show a good or bad performance for Vector calculus subject. 412 first year engineering students from different programmes JKAS, JKMB, JKKP and JKEES were needed to seat for pretest and post-test (Test 1, 2 and 3). The pretest was performed in early of the semester, while the post-test was held afterwards. The analysis results revealed that the performance of students in the post-test was outstanding to their pretest performance. Data analysis of student performance indicated that most students did not seem to understand the basic ideas in each chapter prior to the beginning of the semester.

Analisis terhadap Kesulitan Belajar Mahasiswa Teknik Informatika pada Mata Kuliah Kalkulus

This article was a qualitative research with using phenomenology approach. The researchers were the main research instruments in this study in order to analyze the type of informatics engineering studenet’s learning obstacles in calculus subject, its causative factors and the ways to overcome the students’ learning obstacles. Researcher as the lecturer used test, questionnaire, observation sheet and interview technique to collect the data. The subject of this study was 47 students of informatics engineering study programme, while the object of this study was the students’ learning obstacles. According to the data analysis results, the findings of this study are: (1) the type of informatics engineering studenet’s learning obstacles in calculus subject are in the principle, concept, operation and fact; (2) the causative factors of informatics engineering students’ learning obstacles in calculus subject are: less using of learning media, using incorrect methods, less of study needs, the lowerness of students’ intelligence, the lowerness of students’ motivation in learning mathematics and the lowerness of students’ prior mathematical knowledge; and (3) to overcome the informatics engineering students’ learning obstacles in calculus subjectare: rearrange learning schedule at home, give guidance to the students, using variatif methods, using clear learning methods and multiplicate the supportive learning facilities.

Computer algebra in physics: The hidden SO(4) symmetry of the hydrogen atom

Pauli first noticed the hidden SO(4) symmetry for the hydrogen atom in the early stages of quantum mechanics [1]. Starting from that symmetry, one can recover the spectrum of a spinless hydrogen atom and the degeneracy of its states without explicitly solving Schrödinger's equation [2], [3]. In this paper, we derive that SO(4) symmetry and spectrum using a computer algebra system (CAS). While this problem is well known [4], [5], its solution involves several steps of manipulating expressions with tensorial quantum operators, including simplifying them by taking into account a combination of commutator rules and Einstein's sum rule for repeated indices. Therefore, it is an excellent model to test the current status of CAS concerning this kind of quantum-and-tensor-algebra computations and to showcase the CAS technique. Generally speaking, when capable, CAS can significantly help with manipulations that, like non-commutative tensor calculus subject to algebra rules, are tedious, time-consuming and error-prone. The presentation also shows two alternative patterns of computer algebra steps that can be used for systematically tackling more complicated symbolic problems of this kind. Program summaryProgram Title: Maple specific worksheetCPC Library link to program files:https://doi.org/10.17632/knbckjrwfc.1Developer's repository link:https://www.maplesoft.com/applications/view.aspx?SID=154764Licensing provisions: GPLv3Programming language: Maple (Maplesoft)Nature of problem: Provide a general framework to handle Quantum Mechanics' non-commutative algebra systematically. Non-commutative tensor calculus, subject to algebra rules, is tedious, time-consuming and error-prone. This Maple worksheet provides a general framework to implement, test and address a wide range of non-commutative problems commonly found in advanced quantum mechanics. It can be customized and adapted to potentially more complicated algebra problems.Solution method: Make use of Maple's Physics package. First, configure the problem parameters: space dimension, tensor objects and non-commutative quantities. Then provide the most basic commutation rules, such as position, linear and angular momentum commutators. From there, using the Simplify command and a short set of other key commands, demonstrate further commutation rules until the complete target algebra is reconstructed. One should notice that the Physics package commands employed here take into account custom algebra rules, the sum rule for repeated indices, and use tensor-simplification algorithms.Additional comments including restrictions and unusual features: This article mirrors a Maple worksheet. As such, it is not an usual code intended to make a computation for a given set of parameters. It is rather a general template or guideline, useful to extend the present problem with new computations or, more generally, widely open to tackle new quantum mechanics problem involving tensor and commutator heavy calculus.

Realidad aumentada como técnica didáctica en la enseñanza de temas de cálculo en la educación superior. Estudio de caso

En este documento se presenta un estudio cuasiexperimental para medir el impacto de la realidad aumentada en el proceso de enseñanza-aprendizaje con alumnos del Tecnológico Nacional de México, campus Jerez, de la carrera de Contador Público. Se consideró un grupo de control y un grupo experimental. En el grupo experimental se utilizó una app de realidad aumentada como herramienta de apoyo, mientras que en el grupo de control se realizaron las clases de manera tradicional. En ambos casos la intervención se llevó a cabo exclusivamente en la asignatura de “Cálculo diferencial e integral”. Se utilizó la prueba no paramétrica de Mann-Whitney-Wilcoxon para mostrar si había diferencia entre ambos grupos. Los resultados muestran que no hay diferencia si se utiliza realidad aumentada como herramienta de apoyo o se presentan las clases de forma tradicional. Sin embargo, los estudiantes que utilizaron la realidad aumentada consideraron que esta les ayudó a mantener la atención en el transcurso de la asignatura, así como a despertar o aumentar el interés por el contenido impartido.

Mathematical Dispositions of Graduating Students of the College of Engineering, University of Eastern Philippines (UEP)

This study was conducted to determine the mathematical disposition of graduating engineering students of the UEP College of Engineering in the School Year 2016-2017. Specifically, the study assessed the profile of the graduating students in terms of their age, sex, average grade in calculus and academic performance in professional subjects; the mathematical disposition in terms of self-efficacy component; math as sensible component; and perseverance component; the relationship between the profile and mathematical disposition of students, and between the mathematical disposition and academic performance in professional subjects of the respondents.
 The 132 graduating students taking up Bachelor of Science in Agricultural Engineering (BSAE), Bachelor of Science in Civil Engineering (BSCE), Bachelor of Science in Electrical Engineering (BSEE), and Bachelor of Science in Mechanical Engineering (BSME) who are officially enrolled in the second semester of the school year 2016-2017 were the respondents of this study.
 The study found out that there were more graduating engineering students whose age is beyond 22 to 24 years old; more males; and have passing performance in calculus subjects.
 Generally, the graduating engineering students for the school year 2016-2017 have good mathematical disposition, specifically described as more efficacious, sensible, and more persevering.
 The students’ performance in calculus subjects was significantly related to mathematical disposition, while the age and sex of respondents have nothing to do with mathematical disposition.
 Specifically, respondents’ age and sex did not affect the three components of mathematical disposition, while average grade in calculus subjects was found to have something to do with their sensibility and perseverance level in mathematics.
 On the relationship between mathematical disposition components and the academic performance in professional subjects of graduating engineering students, it was found out that only the math as sensible component affected their performance in professional subjects.
 The result of this study also revealed that these students who were more efficacious, more sensible and more persevering performed good in their professional subjects.

Development of a GeoGebra-Assisted Calculus Worksheet to Enhance Students’ Understanding

The goal of this study is to develop a GeoGebra-assisted worksheet to enhance students' understanding of calculus. Many studies report that students have difficulty understanding calculus. GeoGebra provides an alternative method to overcome the difficulties associated with calculus. The Plomp development model consists of three phases: specifically, preliminary analysis, prototype development and an assessment was used in this study. The subjects of this study were 37 students. The results of this study are valid in terms of content, presentation, linguistics and graphics and practical in terms of implementation, time, ease of use and effective in terms of its potential impact on students' mathematical understanding. The GeoGebra-assisted worksheet can help students rediscover the given concept, while the use of visualization of the calculus concept can significantly enhance students’ mathematical understanding. Likewise, GeoGebra-assisted worksheets can be used to enhance students’ understanding of calculus. Teachers are suggested using GeoGebra in order to build students’ understanding on calculus subject.

Identifying Cognitive Obstacle on the Topic of Definite Integral among Prospective Teacher

In the calculus subject, there is definite integral material, and on that material, students often encounter obstacles. Obstacles are all things that hinder students from learning. Cognitive obstacles are one of four known types of obstacles, three of which are: epistemological obstacles, didactive obstacles, and ontogenic obstacles. Cognitive obstacles are the knowledge a person has and are usually sufficient to solve a particular problem, but this knowledge is inadequate when the person is confronted with a new problem. This study was conducted at the Mathematics Education Study Program, a university in the city of Semarang by taking two subjects. Both of these subjects experience cognitive obstacles when completing definite integral tasks.

The Effect of Blended Learning on Student Learning Outcomes in Calculus Vector Course

Rapid development of technology has become an inseparable part of life. This poses a challenge for the world of education to be able to take advantage of technological developments in achieving educational goals. However, switching from a direct learning model to technology-based learning requires a lot of effort and money. However, this can be started with the Blended Learning Model. This study aims to analyse whether student learning outcomes are better with the application of Blended Learning using e-learning and to describe how student learning activities with the Blended Learning model. This type of research is a combination of quasy-experiment and descriptive research. The research data are the value of the midterm exam and the final semester test scores after the implementation of the learning Blended Learning model which will be analysed. Therefore, it can be compared students’ learning outcomes using the Blended Learning model with student learning outcomes with the conventional learning model. Based on the results of data analysis, it can be concluded that the N-gain test results obtained from the control class are better than the experimental class, which means that the use of the Blended Learning model is less effective in improving student learning outcomes in vector calculus subjects.