Integral Calculus Courses Research Articles

Students' Mathematical Spatial Ability in Integral Calculus Lectures

Based on preliminary analysis, problems were found in the lecture material that many students got low grades for the integral calculus course. This is because students still experience difficulties in understanding the concepts explained and finding solutions to integral calculus problems, especially in topics that require students to involve understanding perspective, geometric shapes, and the ability to transform shapes. This type of research is mixed methods research, which is a research step that combines two forms of research approaches, namely quantitative and qualitative. The research method used is mixed research, namely a research approach that combines quantitative research with qualitative research. The research instruments are written tests and interview guidelines. Quantitative data analysis techniques use scoring and data tabulation. Qualitative data analysis techniques are data reduction, data presentation, and verification. The results of the research show: mathematical spatial abilities for the spatial visualization component are in the good category, spatial orientation is in the poor category, and spatial rotation is in the medium category. Therefore, students need to be familiarized with questions that train mathematical spatial abilities

The Impact of Mathematical Reasoning and Critical Thinking Skills on Mathematical Literacy Skills

For learning mathematics, mathematical skills are needed, some of which are mathematical reasoning skills, mathematical critical thinking skill, and mathematical literacy skills. This research aims to obtain information regarding the impact of mathematical reasoning and critical thinking skills on mathematical literacy skills. This research used a quantitative approach using an associative method with a correlational technique. The sample of this research was comprised 51 students who took integral calculus course in the Department of Mathematics and Mathematics Education, Faculty of Mathematics and Science in Universitas Negeri Jakarta, which were collected randomly using simple random sampling. The statistical analysis used in this research was multiple regression analysis. The results of this research showed that: 1) There was a positive impact of mathematical reasoning on mathematical literacy. 2) There was a positive impact of mathematical critical thinking skill on mathematical literacy. 3) There was an impact of both mathematical reasoning skill and mathematical critical thinking skill together on mathematical literacy. Further research is needed related to the impact of mathematical reasoning and critical thinking skills on mathematical literacy skills reviewed from the student’s initial mathematical skill. Keywords: critical thinking skills, mathematical literacy skills, mathematical reasoning

3D Manipulatives in Integral Calculus: Student Achievement and Confidence in Solids-Of-Revolution Tasks

ABSTRACT In this university study, sections of an integral calculus course were randomly assigned to either a control or treatment group for a lesson on volumes of revolution. Both groups were given similar collaborative tasks, but only the students in the treatment group were given access to a set of 3D manipulatives. Pre- and post-assessments were administered to measure student achievement and confidence on the tasks comparing results for the control and treatment groups as well as for the male and female students. No statistically significant differences in student achievement were detected for the control or treatment group or by reported gender on either an immediate posttest or a delayed posttest. There was statistical significance in confidence after engaging in the 3D manipulative tasks favoring the treatment group. However, further inspection by gender revealed that while males in the treatment group were more likely to report higher confidence ratings than males in the control group, the reverse was true for females.

RELATIONSHIP BETWEEN STUDENT DIFFERENTIAL AND INTEGRAL CALCULUS LEARNING OUTCOMES TO STUDENT DIFFERENTIAL EQUATIONS LEARNING OUTCOMES

Differential calculus and integral calculus courses are the foundations of mathematics that are important in understanding and applying differential equations. Students can take the Differential Equation course on condition that they have graduated from the Differential Calculus and Integral Calculus courses. This study aims to determine the relationship between the understanding of differential and integral calculus with students' learning outcomes of differential equations. The population in this study were all 2020 Pattimura University Teaching and Teacher Training Faculty Mathematics Education students who had taken differential calculus, integral calculus, and differential equations courses with a total sample of 33 people. The research method used is quantitative research with correlational methods. This study uses multiple regression analysis which has the aim of finding the form and influence between the independent variables and the dependent variable. Data analysis technique using multiple regression test. Based on the results of the data analysis, it was concluded that there was a significant contribution between learning outcomes of differential calculus on learning outcomes of differential equations seen in the relative contribution of learning outcomes of differential calculus on learning outcomes of differential equations based on the calculation results obtained 56.45% while the relative contribution of learning outcomes of integral calculus 43 .54% of the learning outcomes of differential equations. So it shows that there is a big influence between learning outcomes of differential calculus and integral calculus on learning outcomes of differential equation.

Integrasi Pendekatan STEAM dalam Perkuliahan Kalkulus Integral

This research is a quantitative research that aims to improve student learning outcomes through the STEAM learning approach in Integral calculus courses. The populations in this study were all students taking the Integral Calculus course using a purposive sampling technique. The research design used was a quasi-experimental design with a nonequivalent control group design. Data were obtained from student learning outcomes tests in the form of pre-test and post-test. Data analysis used Mann-Whitney. The results showed that the sig (2-tailed) value for the experimental class was 0.000 <0.05, which means that the integration of the STEAM approach to Integral Calculus courses can improve student learning outcomes.

Development of Rational Function Integral E-Worksheet with Linear Factor Denominators to Improve Mathematical Creative Thinking Ability

There is no electronic worksheet that can help students to optimize their mathematical creative thinking skills in the Integral Integration technique of rational functions with the denominator is a linear factor being the background for this research. This research aims to produce an e-worksheet that can be used in integral calculus courses, especially material for Integral Integration techniques of rational functions with the denominators being linear factors, and can improve the ability to think creatively mathematically. The research was conducted using the ADDIE development model. The research subjects were 15 students of Mathematics Education at the University of Riau. Data collection instruments used questionnaires and tests with quantitative and qualitative descriptive analysis. From the calculation of the validation score, overall, the e-worksheet is valid and can be used by Mathematics Education students in Integral Calculus courses. Based on the results of the second student response questionnaire, the e-worksheet met the practical criteria with the achievement of e-worksheet 1 of 83.33% and e-worksheet 2 of 76.3%. From the results of the worksheet effectiveness test, there has been an increase in students' mathematical creative thinking ability after using e-worksheet from 2.73 to 7.6 and is in the medium category. Referring to the results of this study means that the developed e-worksheet is feasible to use and can improve students' mathematical creative thinking abilities.

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.

Articulación entre Modelización y Espacios de Trabajo Matemático. Análisis de una Tarea bajo el ciclo de Blomhøj en Educación Superior

Background: The Mathematical Working Spaces (MWS) theoretical framework has developed a growing interest in how mathematical modelling is recognised, analysed, and articulated from its theoretical and empirical scopes. Given the articulations identified in the literature, it is interesting to determine whether new networks with the MWS provide powerful strategies for analysing mathematical modelling task resolution. Objective: to characterise the modelling activity from the network composed by the Blomhøj modelling cycle and the MWS in engineering students. Design: This work is a case study with a qualitative approach, which analyses the resolution of a modelling task through the proposed network. Setting and participants: The experimentation was carried out in an integral calculus course for a computer civil engineering career at a Chilean university. Modelling practices are not usual in this second-year subject, although enhancing their use in professional education is necessary. Data collection and analysis: We collected the written records of the students, selecting one to perform the in-depth analysis due to its high representativeness and clarity, as evidenced in the documents. Three steps were followed to characterise the modelling activity in the written record: description, analysis, and interpretation. Results: The Blomhøj modelling cycle might present connections with the MWS at the formulation of the problem and not only at the systematisation, which is a novelty in this field of research. Conclusions: A novel approach with which to develop the network between the MWS and modelling emerges, emphasising the investigation of mathematical problems using the student’s reality in higher education.

Interest and learning achievement of mathematics on blended learning in West Papua

The purpose of this research is to find out the interests and learning outcomes of students through blended learning. This research is quantitative and descriptive. The subjects of this study were thirty-one students in the second semester of the Mathematics Education Study Program at Muhammadiyah University of Education, West Papua, Indonesia. Data collection techniques were carried out by tests and non-tests, and the instruments used were interest in learning questionnaires and learning achievement tests, as well as documentation. Learning outcomes in general indicate that the average student score is seventy-six, which indicates that the interpretation of student scores is "AB," or 3.50, and the average indicator of competency achievement in the overall integral calculus course is in the high category. The results of the total analysis of the interest in learning questionnaire obtained 90.91% results in the remarkably high category. The average percentage of each interest indicator is in the "very high" category range. The results of the study show that blended learning can arouse students' interest and attention and have a positive impact on learning outcomes, so when applying blended learning, all supporting components must be considered to create an optimal learning experience.

Development of Integral Calculus Teaching Materials to Improve Mathematical Reasoning Ability of Mathematics Education Students at HKBP Nommensen Pematangsiantar University

Integral is one of the main subjects in the school mathematics curriculum and is the compulsory subject in the Mathematics Education Study Program at HKBP Nommensen Pematangsiantar University, namely the Integral calculus course. Therefore the status of this material is the subject matter for SMA/MK students and students in mathematics education study programs. This study aims to discover how to develop integral calculus to improve the mathematical reasoning abilities of mathematics education students at HKBP Nommensen Pematangsiantar University. Research on the development of integral calculus teaching materials uses the analysis, design, development, implementation, and evaluation stages. Initial and limited field trials were conducted at the Teaching and Education Faculty (FKIP) HKBP University Nommensen Pematangsiantar. The normality analysis of gain (n-gain) in the experimental student class has increased with an average n-gain value of 0.87. Feasibility of Integral Calculus Teaching Materials Integral Calculus obtained percentage values from experts and subjects studied as follows: (1) Post-test scores reached an average of 83 compared to pretest average scores of 48, there was a significant increase. This shows an increase in learning outcomes after using the results of the product development of Integral Calculus teaching materials. Acquisition of the development value of Integral Calculus Teaching Materials has a high level of attractiveness based on the assessment of material/content experts reaching 93.75%; (2) The acquisition of the value of developing Integral Calculus has a high level of attractiveness based on the assessment of design experts getting 86.53%. Also, the importance of developing Integral Calculus has a high level of beauty based on field test assessments reaching 91%.

The construction of the integral for the arc length of a curve based on van Heuraet and Fermat’s works

We present the research outcomes of a project in Mathematics Education about the design and implementation of an instrument to learn the integral for the arc length of a function by using differential elements as the strategy for its construction. The research was done via a didactic intervention in a regular Integral Calculus course. The instrument was designed based on historical-epistemological analyses of the works of van Heuraet and Fermat. The main result of this research was that students achieve a more robust conceptualization of the integral for the arc length, supported by its construction with differential elements and its geometric foundation.

DEVELOPMENTS OF INSTRUCTIONAL MODELS BASED ON MATHEMATICS COMMUNICATION SKILLS IN INTEGRAL CONCEPTS AND APPLICATIONS

The problem of this research is the low mathematical communication skills of students in integral calculus courses. The purpose of this study was to develop a learning model based on Mathematical Communication skills on integral concepts and applications, and to determine the feasibility and effectiveness of learning models based on Mathematical Communication skills on integral concepts and applications. This research method is a research and development method. The research subjects were 43 students of the Mathematics Education Department at Halu Oleo University. Data collection techniques using questionnaires, interviews and test techniques. Data analysis was carried out in a quantitative and qualitative descriptive manner. The results of the data analysis showed that the integral concept and application learning materials based on the assessment of mathematics learning experts and learning design experts reached 86.3% and 89.16% in the very good category. While the results of the student assessment showed 87.5%. The small group evaluation results showed an average percentage of 88.2% with a very good category. The results of the large group trial reached a percentage value of 90.1% in the very good category. Therefore, the development of a learning model is able to improve students' mathematical communication skills on integral concepts and applications

IMPLEMENTASI TEKNOLOGI DIGITAL DALAM PERKULIAHAN MATAKULIAH KALKULUS INTEGRAL DALAM PENYELESAIAN LUAS DAERAH ANTARKURVA

In today's digital era, the use of digital technology is essential in learning mathematics to create exploratory learning spaces. From an early age, technology in learning needs to be known that it does not only produce manual calculators, but that extensive learning support is realized from various applications or websites used in learning at school or in lectures. However, the lack of knowledge of prospective teacher students is a limiting space for learning space. First, in the integral calculus course, students seem monotonous by only using pencil and paper in learning. This article aims to present the implementation of the use of digital technology in integral calculus lectures in determining the area between curves. The method used is descriptive to describe the implementation of the technology. This was obtained in the implementation of the website using geogebra and wolframalpha as an exploratory tool to create a comprehensive learning space in answering their needs regarding the difficulty of drawing graphs, the difficulty of determining intervals of curve areas, and integral calculations assisted by geogebra and wolframalpha. However, in its use, it is necessary to have a basic understanding of calculating the area between the curves as the main basis for the direction of implementing digital technology.

THE EFFECTIVENESS OF GEOGEBRA ASSISTED INTEGRAL CALCULUS MODULE

This research activity was motivated by the low learning outcomes of students in the Integral Calculus course and the unavailability of the GeoGebra-assisted Integral Calculus module in the Mathematics Education study program, Malikussaleh University. The purpose of the study was to determine the effectiveness of the GeoGebra-assisted Integral Calculus module. The type of research is development research with the Plomp development model which includes three stages of preliminary research, prototyping phase, and assessment phase. The test subjects were students of the Mathematics Education Study Program, Malikussaleh University. The instruments of this research are observation sheets of learning activities, student response questionnaires, observer response questionnaires to modules and test instruments. Based on the results of the study, it is known that the GeoGebra-assisted Integral Calculus module meets the effective criteria because the results of the learning activity observation sheets are in the very good category, student and observer responses to the module are in very good criteria and student test results have increased.

PENGEMBANGAN E-MODUL BERBANTUAN GEOGEBRA PADA MATAKULIAH KALKULUS INTEGRAL LIPAT

The lack of interaction between students and lecturers in learning causes information not to be conveyed optimally. Moreover, fold integral calculus is an abstract material. Therefore, learning innovations are applied that can support more independent learning and are able to visualize abstract material. This study aims to determine the feasibility of the geogebra-assisted electronic module in the fold integral calculus course. This research is classified as development research which refers to Sugiyono development model but is only limited to 7 stages. The stages carried out in the research, namely potential and problems, data collection, product design, design validation, design revision, product testing and product revision. The instruments used in this study were validation sheets, user response questionnaires, and learning outcomes tests. Indicators of achievement of the results of this study are e-modules are declared suitable for use and students who get optimal learning outcomes are more than 70%. The results showed that the folding integral calculus e-module that was made was feasible to use. This is shown as much as 74% of students achieve optimal learning outcomes.

PENGEMBANGAN E-MODUL BERBANTUAN GEOGEBRA PADA MATAKULIAH KALKULUS INTEGRAL LIPAT

The lack of interaction between students and lecturers in learning causes information not to be conveyed optimally. Moreover, fold integral calculus is an abstract material. Therefore, learning innovations are applied that can support more independent learning and are able to visualize abstract material. This study aims to determine the feasibility of the geogebra-assisted electronic module in the fold integral calculus course. This research is classified as development research which refers to Sugiyono development model but is only limited to 7 stages. The stages carried out in the research, namely potential and problems, data collection, product design, design validation, design revision, product testing and product revision. The instruments used in this study were validation sheets, user response questionnaires, and learning outcomes tests. Indicators of achievement of the results of this study are e-modules are declared suitable for use and students who get optimal learning outcomes are more than 70%. The results showed that the folding integral calculus e-module that was made was feasible to use. This is shown as much as 74% of students achieve optimal learning outcomes.

Implementation of Blended Learning Models during the Pandemic

The COVID-19 pandemic has made the entire life order change substantially, including the education area. The atmosphere of face-to-face learning must undergo a transition in the form of online learning, by utilizing technology and various interaction media during learning, including tertiary education. Blended learning model is one model that can be used in this emergency situation. This study aims to look at students' perceptions, to what extent of the blended learning carried out by optimizing LMS Moodle and video conferencing as learning tools. Participants in this study were taken purposively and involved 78 students from three study programs, namely Biology, Mathematics, and Social Sciences Education, who were enrolled and participated in Ecology, Integral Calculus, and Geography courses. The instruments are COLLES questionnaires and open-ended questions to investigate deeper at the perceptions expressed by students. Research methods are used in the form of mixed methods to produce an in-depth interpretation of student perception. Quantitative data analysis is carried out with a one-way ANOVA conducted using SPSS 20. Qualitative analysis is carried out descriptively related to the response given by students in writing. This research found indications related to lecturers' ability to design discussion problems to stimulate student involvement during learning.

ANALISIS MATERI SULIT DIPAHAMI DAN MISKONSEPSI MAHASISWA DALAM MATA KULIAH KALKULUS INTEGRAL

This study aims to analyze and describe what materials are difficult in calculus courses and also materials that are misconceptions. This research was conducted to improve the competence of students in the future. The formulation of the problem in this study is "How to improve student competence in integral calculus courses?" The sub-problems are: 1) What materials do students have misconceptions in integral calculus courses? 2) What materials are difficult for students to understand in integral calculus courses? The research method used is descriptive qualitative by surveying students of Mathematics Education, Faculty of Teacher Training and Education, Tanjungpura University. From the overall results, there were 22 students (60%) did not experience misconceptions and 14 students (40%) experienced misconceptions in the first concept. In the second concept, 40% did not experience misconceptions and 60% of students experienced misconceptions. For the third concept, 70% of students experienced misconceptions and 30% of students did not experience misconceptions. In the fourth concept, 28% of students experienced misconceptions and 72% of students did not experience misconceptions. For the fifth concept, 6% of students experienced misconceptions and 94% of students did not experience misconceptions. And for the sixth concept there are 28% of students experiencing misconceptions and 72% of students not experiencing misconceptions.

Analisis Pemahaman Konsep Mahasiswa pada Pembelajaran Volume Benda Putar Berbasis Maple

Concept understanding is recognizing all of the materials, which the students not only know and understand but able to show the concept in from that easy to understand and also able to aplicated. The aim of this study is to analysis the concept understanding for the student in learning volume of revolution based on maple. This research method is descriptive qualitative. The participants of this study are the student of the mathematics education study program STKIP Soe who took integral calculus courses totaling 14 students. Research data were collected through observation, tests and interviews. The data analysis technique used is qualitative data analysis following the Miles and Huberman model. Test the validity of the data used is the extension of observations, triangulation techniques and negative case analysis. The results showed that learning the volume of a maple-based rotary object can help students understand the concept. Students in solving rotary object volume questions manually or the maple method show that most students have been able to achieve indicators of understanding mathematical concepts. Based on the results of this study, it is also known that there are still students who have not reached the indicator of concept understanding due to miscalculations and using the wrong concept in solving test questions on the material of rotating object volume due to the absence of students during the lecture process

Thinking Analogy in Solving Indirect Analogy Problems based on Information Processing Theory

Cognitive ability in solving analogy problems really needs the right information processing. The core cognitive process in analogy thinking occurs when students make a mapping between the target problem and the source problem. This research aims to describe analogical thinking in solving indirect analogy problems based on information processing theory. The method usesd in this research is qualitative descriptive. The subject in this study were third and fifth-semester students of the Mathematics Tadris Program FTK UIN Mataram. Instruments are source problems and target problems use indefinite integral problems in the Integral Calculus course. Data analysis is used by using triangulation of methods and data sources. The results showed that there were 51.06% able to solve the target problem where students are able to recall long-term memory information related to solving source problems that have similarities to solving target problems. Source problem-solving information taken from long-term memory is used by students in solving target problems in short-term memory. The processing of information in short-term memory depends on the mapping process with previous information in long-term memory. Therefore, as a mathematics teacher, he is able to emphasize certain materials which are initial knowledge to study further material.