Learning Calculus Research Articles

Spaced Retrieval Practice Imposes Desirable Difficulty in Calculus Learning

After being taught how to perform a new mathematical operation, students are often given several practice problems in a single set, such as a homework assignment or quiz (i.e., massed practice). An alternative approach is to distribute problems across multiple homeworks or quizzes, increasing the temporal interval between practice (i.e., spaced practice). Spaced practice has been shown to increase the long-term retention of various types of mathematics knowledge. Less clear is whether spacing decreases performance during practice, with some studies indicating that it does and others indicating it does not. To increase clarity, we tested whether spacing produces long-term retention gains, but short-term practice costs, in a calculus course. On practice quizzes, students worked problems on various learning objectives in either massed fashion (3 problems on a single quiz) or spaced fashion (3 problems across 3 quizzes). Spacing increased retention of learning objectives on an end-of-semester test but reduced performance on the practice quizzes. The reduction in practice performance was nuanced: Spacing reduced performance only on the first two quiz questions, leaving performance on the third question unaffected. We interpret these findings as evidence that spacing led to more protracted, but ultimately more robust, learning. We, therefore, conclude that spacing imposes a desirable form of difficulty in calculus learning.

Analysis of Calculus Textbook Problems via Bloom's Taxonomy

In calculus courses, instructors often use the end-of-section problems in a textbook in homework assignments or other course assessments. As a result, these problems influence the teaching and learning of calculus. In this study, we examine the levels of cognitive demand of these problems in a mainstream calculus textbook and classify them within the framework of Bloom's Taxonomy. We provide examples of the types of problems assigned to each of the six categories in this taxonomy and share some of the deliberations that led us to these assignments. Finally, we discuss the implications of our results for teaching calculus courses. We believe that our analysis will help calculus instructors be more cognizant of the cognitive demand of problems when assigning them for homework and, as a result, help them to appropriately support, assess, and enhance their students' understanding of the topics.

Optimizing the Use of Matlab GUI Attributes in the Creation of Calculus Learning Media: An Effort to Measure Students' Innovative Attitudes

Calculus learning requires a high level of visualization in instilling concepts optimally to students. Therefore, the purpose of this study is to look at students' innovative attitudes in developing matlab GUI-based learning media in solving calculus problems and see the influence of the ability to use matlab GUI attributes on the level of innovation of the students in developing learning media. In the early stages, the students developed media according to the given topic. In the second stage, the product was assessed in terms of its validity. The students' innovative attitudes were assessed by a team of experts using questionnaires with 5-point Likert scale. From the 16 media successfully developed, validation results were obtained with an average score of 3.83 which means "valid". Meanwhile, from the assessment of innovative attitudes, the students’ attitudes are in the category of "innovative" with an average score of 3.61. In addition, the results of the regression tests revealed that the innovative attitudes are influenced by the ability to use the matlab GUI attributes by 84.2%. The rest is influenced by other factors with similarities: . Lastly, the results of the assessment showed that the media belonged to the category of "very effective" (score 81.2%).

Analysis of Students' Learning Motivation in Calculus on the Usage of Learning Video Media during the Covid-19 Pandemic

The Covid-19 pandemic has changed the process of teaching-learning activities from offline to online. Implementing this activity causes a lack of motivation and self-confidence for undergraduate students. This study describes undergraduate students' learning motivation for using video media in integral calculus lectures for integral application materials to calculate the shape area during the Covid-19 pandemic. This research is quantitative descriptive research. The research participants were 23 undergraduate students from Ahmad Dahlan University in mathematics education. Data was collected by distributing questionnaires via Google Form consisting of 32 statements with five alternative answer choices and eight questions about learning motivation when utilizing learning video media. The analytical technique used was quantitative descriptive analysis. The results show that learning video media effectively motivates student learning in integral calculus during the Covid-19 pandemic with an average percentage result of 90.625% with very high criteria.

Dynamic gesture recognition based on 2D convolutional neural network and feature fusion

Gesture recognition is one of the most popular techniques in the field of computer vision today. In recent years, many algorithms for gesture recognition have been proposed, but most of them do not have a good balance between recognition efficiency and accuracy. Therefore, proposing a dynamic gesture recognition algorithm that balances efficiency and accuracy is still a meaningful work. Currently, most of the commonly used dynamic gesture recognition algorithms are based on 3D convolutional neural networks. Although 3D convolutional neural networks consider both spatial and temporal features, the networks are too complex, which is the main reason for the low efficiency of the algorithms. To improve this problem, we propose a recognition method based on a strategy combining 2D convolutional neural networks with feature fusion. The original keyframes and optical flow keyframes are used to represent spatial and temporal features respectively, which are then sent to the 2D convolutional neural network for feature fusion and final recognition. To ensure the quality of the extracted optical flow graph without increasing the complexity of the network, we use the fractional-order method to extract the optical flow graph, creatively combine fractional calculus and deep learning. Finally, we use Cambridge Hand Gesture dataset and Northwestern University Hand Gesture dataset to verify the effectiveness of our algorithm. The experimental results show that our algorithm has a high accuracy while ensuring low network complexity.

Interactive Learning System for Learning Calculus

Background: IT tools assist in creating a more participative and independent learning environment. They have brought a new perspective to collaborative learning where students do not just sit in a chair and swallow lecture content but instead participate in creating and sharing knowledge. However, interactivity promoted through the implementation of technology is limited in many cases. Purpose: This research develops an interactive application for learning calculus that promotes human-system interaction via augmented reality (AR) and human-human interaction through chat functions. The study examines the effect of both interactivities on learning experience and how that learning experience affects the performance of learning. Methods: The research adopted a quasi-experimental study design and pre-post test data analysis to evaluate the effect of interactivities on learning experience and consequently the effect of learning experience on learning performance. The subjects were exposed to the developed application for learning the calculus chapter ‘Revolution of Solids” in a controlled environment. The study validated its research framework through partial least squares path modelling and tested three hypotheses via pre-and post-test evaluation. Conclusions: The results found that both interactivities affect learning experience positively; human-human interactivity has a higher impact than human-system interactivity. It was also found that learning performance as part of the learning experience increased from pre-test to post-test.

Use of Maple Software to Reduce Senior High School Students’ Errors in Integral Calculus

A quasi-experimental non-equivalent group design research was conducted to use Maple software to reduce students’ errors in integral calculus in a senior high school in the Oti region of Ghana. Convenience and simple random sampling techniques were employed to obtain a sample of 80 students, which comprised 40 students in the control group and 40 in the experimental group. Tests in integral calculus and questionnaire were used for data gathering. The analysis revealed that students committed many conceptual, procedural and technical errors when solving integral calculus tasks. The results also indicated that the students of the experimental group exposed to the use of Maple software in learning integral calculus significantly outperformed their counterparts in the control group exposed to traditional method. The researcher recommends the Maple assisted instruction in the teaching and learning of integral calculus and also the need to employed blended teaching approach using the Maple software to complement the traditional teaching strategy

The Influence of Learning Method toward Learning Outcome Kalkulus Diferensial of Students’ Mathematic Education

This article aimed to find out the effect of learning methods on differential calculus learning outcomes and knowing how much influence learning methods on differential calculus learning outcomes of Mathematics Education students at Universitas Nahdlatul Ulama Lampung. This research was quantitative research with survey method. The research sample was 34 students. The collecting data used close questionnaire to measure the variables of learning methods and documentation to determine the learning outcomes of the differential calculus course. The test of the learning method questionnaire obtained 43 valid statement items with a reliability of 0.90. The result shows that there was an influence between the way of learning on the learning outcomes of Differential Calculus in Mathematics Education students at Nahdlatul Ulama University Lampung. Analysis of the data used is simple regression, with the results obtained by the correlation tcount of 3.148, ttable of 1.694 at a significance level of 5%, and R2 of 0.236, then the results obtained tcount 3.146 > ttable 1.694. Hence, it can be concluded that there was an effect of learning methods on the learning outcomes of Differential Calculus in Mathematics Education Students at Nahdlatul Ulama University Lampung.
 Keywords: Learning Outcome, Kalkulus Diferensial, Learning Method

The necessity of teaching Vedic methods for learning calculus to undergraduate students

India, the sacred land's narrative, boasts a rich cultural heritage. Rishis' discoveries in ancient India can point the way to the rest of the globe. The Vedas and other ancient literature provide a never-ending supply of information. One of ancient India's offerings is Vedic Mathematics. It enables us to answer nearly any mathematical problems in a shorter amount of time using only mental calculations. There isn't much of a requirement for paperwork. In today's competitive world, every fraction of a second counts in competitive exams involving power tests.

APP test system: a case study of calculus

COVID-19 has had a broad impact on society, and a profound impact on education, thus, distance online courses are seen as a way to continue schooling during the pandemic. This study employed Android Studio to develop an APP calculus learning test system which can be used for self-review exercises and allows students to make good use of mobile apps to conduct post-learning and self-testing of calculus at home, and immediately determine their learning results. In addition, through back-end access, teachers can view students' learning scores and the number of wrong and correct questions, and thus, know the effect of individual students' self-review. During the COVID-19 pandemic, as teachers and students cannot interact in class at school, teachers can use the APP calculus learning test system to provide distance remedial teaching to students who fall behind during the course.

CALCULUS LEARNING VIA SCREENCAST-O-MATIC DURING THE PANDEMIC: AN EXPLORATION TOWARDS STUDENTS’ PERCEPTION OF MATH ANXIETY

The emergence of the Covid-19 pandemic has transformed the learning system into an online mode, where students' anxiety became the spotlight for educators to create a learning environment that actively engages them. Many educators are competing in maximizing the use of technology to ensure students are engaged in the learning process. The study aims to explore students’ perception of math anxiety through the implementation of Screencast-O-Matic in calculus learning. This study involves 41 students at the university level and is conducted in mixed methods, using statistics and narrative descriptives. Questionnaires and open-ended questions are used to investigate students’ testimonies about the video made by Screencast-O-Matic and their perceptions of math anxiety after learning with the video given. The results showed that the implementation of Screencast-O-Matic video gradually reduces students’ mathematics anxiety during online calculus learning. Screencast-O-Matic offers educators the opportunity to build a web-based lecture learning system in audio-visual media to minimize students' anxiety levels. Furthermore, the most important things to consider while creating an educational video are clarity of message, user-friendliness, good visualization, and easy access to students anytime and anywhere.

Pengembangan Video Pembelajaran Kalkulus Untuk Memahamkan Konsep

This research is motivated by the difficulty of students understanding the concept of integration techniques through bold learning, so that a concept understanding-based learning video is needed for flat area material. This study aims to develop learning videos and determine the validity and practicality of the videos produced. This type of research is in the form of ADDIE model development research (Analysis, Design, Development, Implementation, Evaluation). The research subjects were class B students, batch 2020, the Ahmad Dahlan University Mathematics Education study program. The results of the assessment from material experts obtained an average score of 4.77 with very good criteria, from material experts obtained an average score of 4.55 with very good criteria, and from student responses a score of 3.50 was obtained with good criteria so that it can be concluded that the video Integral calculus learning is valid and practical to use. Keywords: integral calculus, learning videos, trigonometric functions

Higher-order thinking skills among male and female students: An experimental study of the problem-based calculus learning model in secondary schools

[English]: This study aims to examine the effectiveness of the problem-based calculus learning model (PB-CLM) towards students’ higher-order thinking skills (HOTS). PB-CLM is a modification of problem-based learning’s (PBL) syntax. It was a quasi-experimental with a group pretest-posttest design involving 351 11th-grade students as the population. Seventy-one students of two classes were randomly selected as a sample. Data was collected through pretest and posttest developed from three aspects of HOTS; analysis, evaluation, and synthesis. To determine the effectiveness of PB-CLM, paired sample t-test and independent sample t-test with a significance level of 5% (α = 0.05) were used. The results show that students’ activities during the learning process in PB-CLM has a positive effect on increasing their HOTS (mean difference = 30.141; sig one-tailed = 0.000). Furthermore, there was no significant difference in HOTS among male and female students, both at the pretest and posttest (mean difference = 0.81731; sig.= 0.295). Likewise, the increase in HOTS scores (posttest-pretest) did not differ significantly between gender (mean difference = 0.88141; sig. one-tailed = 0.740). [Bahasa]: Penelitian ini bertujuan untuk menguji keefektifan problem-based calculus learning model (PB-CLM) terhadap higher-order thinking skills (HOTS) siswa. PB-CLM merupakan modifikasi dari sintaks model problem-based learning (PBL). Penelitian ini menggunakan rancangan quasi eksperimen dengan desain one group pretest-posttest yang melibatkan 351 siswa kelas XI sebagai populasi penelitian. Tujuah puluh satu siswa dari 2 kelas dipilih secara acak sebagai sampel. Data penelitian dikumpulkan dengan menggunakan pretest dan posttest yang dikembangkan dari 3 aspek HOTS; analisis, evaluasi, dan sintesis. Untuk mengetahui keefektifan PB-CLM digunakan paired sample t-test dan independent sample t-test dengan taraf signifikansi 5% (α = 0,05). Hasil analisis menunjukkan aktivitas siswa selama pembelajaran dengan PB-CLM efektif dalam meningkatkan HOTS (mean difference = 30,141; sig.one-tailed = 0,000). Lebih lanjut, tidak ditemukan perbedaan yang signifikan antara HOTS siswa laki-laki dan perempuan, baik pada pretest maupun posttest (mean difference = 0,81731; sig.= 0,295). Begitu pula peningkatan skor HOTS (posttest-pretest) juga tidak berbeda signifikan antara siswa laki-laki dan perempuan (mean difference = 0,88141; sig. one-tailed = 0,740).

Student’s Learning Obstacle in Calculus Course

Calculus courses have become the basis of other mathematics courses. However, students often find obstacles in this course that cause low mastery of calculus. Therefore we need an in-depth analysis of students' obstacles in learning calculus to develop proper learning materials and methods. This research aims to analyze the students’ learning obstacles in solving mathematical problems in calculus courses. This research is a qualitative descriptive study. The subjects of this study were first-semester students of the Mathematics Department at one of the Islamic institutes in Jambi, Indonesia. The subject selection technique used is purposive sampling, while the data collection techniques used questionnaires and interviews. Based on data analysis, it was found that there were five types of errors made by students in solving mathematical problems in a calculus course, namely conceptual errors, algorithm errors, calculation errors, algebraic operations errors, and careless errors. Also, there were two types of learning obstacles experienced by students in the calculus course: epistemological obstacles and didactic obstacles. Epistemological obstacles related to conceptual errors, limited understanding of concepts, and errors in analyzing questions. While didactic obstacles related to difficulties in understanding teaching materials and inaccuracy of teaching methods. Further research is needed to overcome learning obstacles that occur in the form of developing appropriate learning materials according to the abilities and characteristics of students and applying appropriate learning models and methods.

Students’, Pre-Service Mathematics Teachers’, and In-Service Mathematics Teachers’ Perception on Calculus Learning Video

Calculus is a branch of mathematics that must be studied in school, especially at the high school level. One of the subjects in calculus is the application of integral on the volume of solid of revolution. The use of learning video as media can help students in a conceptual understanding of the volume of solid of revolution, which is one of the abstract objects in calculus. This article discusses the development of solid revolution learning videos' volume. It describes students' perception, pre-service mathematics teachers, and in-service mathematics teachers in the video. The subjects who participated in this study were 48 students in grade 12 in one state high school in Sambas Regency, West Borneo, 8 pre-service mathematics teachers of one of the universities in Yogyakarta, and 3 high school mathematics teachers in Sambas Regency. Data were collected by using a questionnaire consisting of several open questions. Through open questions, subjects were intended to express their ideas or opinions about the learning video. The finding showed that most respondents have positive perceptions of calculus learning video. 76,74% of students agree that the video is suitable for use at the beginning of learning this subject; all in-service mathematics teachers agree, and 75% of pre-service mathematics teachers also agree. This indicates that the learning video can be used as one of the teaching aids in the learning of solid revolution

Exploring Pre-Calculus (MAT133) Final Assessment Marks Between Gender Using Principal Component Analysis: A Case In UiTM Tapah

Pre-Calculus covers additional algebraic and trigonometric, where the students are encouraged to become proficient in those topics to prepare for an in-depth calculus learning. In Universiti Teknologi Mara (UiTM), practically every semester the issue of Pre-Calculus’ high failure rate is commonly reported. One of the ways to measure the students' understanding of this subject is through the final assessment performance. Besides, gender significance is one of the most notable studies in mathematics performance. Therefore, this study aims to compare the performance of part 1 diploma students who registered Pre-Calculus in UiTM Tapah in in accordance to their gender. To analyze the results, this study performed Descriptive and Principal Component Analysis using R statistical software. It was found that the students faced problems in answering Question 2, but scored more marks for Question 5. This revealed that most of the students faced difficulties in handling sketches of parabolas and circles. It was also discovered that the female students outperformed the males in this course.

Simulation as a Resource in the Calculus Solving Problem

This article is derived from the research project and developed at School of Computer Sciences of the National Polytechnic Institute of Mexico. The article reports on the problems found among engineering students with respect to their resistance to using different representation registers when solving optimization problems in the Calculus Learning Unit. Use of such registers could help the students to build mathematics knowledge and to solve calculus problems. As a didactic strategy, simulations are used in an electronic environment in order to support the students by fostering their use of tabular, graphical and algebraic representation registers. Interviews are undertaken of six of the professors who gave the calculus courses, and a diagnostic questionnaire was applied to 68 students prior to and after working with the proposal. As for the theoretical framework, the work reported by Duval and Hitt is salient in this report, particularly their emphasis of the fact that working on activities by way of one single representation system is not sufficient. From the first responses provided by the students, one can conclude that the algebraic register is preferred by the majority of students. It is however used in a mechanical fashion without affording any meaning to the content of the problem and to the process of solving it. Another conclusion reported is that implementing tasks in the classroom in which the mathematics activity requires coherent use of different representations is necessary

Effective Application of Maple Software to Reduce Student Teachers' Errors In Integral Calculus

This study explored the effective application of Maple software to reduce student teachers’ errors in Integral Calculus at Evangelical Presbyterian College of Education, Volta Region – Ghana. The study employed the quasi-experimental non-equivalent group design. Convenience and simple random sampling techniques were employed to obtain a sample of 80 students, which consisted of 40 students in the control group and 40 in the experimental group. Teacher-made Pre, -Post-Calculus Achievement Tests (CAT), and questionnaires were used to collect quantitative and qualitative data respectively. Descriptive, Independent samples t-test and paired samples t-test were used in analyzing the data. Descriptive error analysis revealed that students committed many conceptual, procedural and technical errors when solving Integral Calculus tasks. The results also indicated that there was a statistically significant difference between students of the experimental group exposed to the use of Maple software in learning integral calculus to the control group exposed to traditional methods. The researchers recommend Maple assisted instruction in the teaching and learning of Integral Calculus and also the need to employ a blended teaching approach, in which Maple software is used simultaneously with traditional teaching strategy.

Use of Maple Software to Reduce Student Teachers’ Errors in Differential Calculus

The study was conducted on the use of Maple software to reduce student teachers’ errors in Differential Calculus at Evangelical Presbyterian College of Education, Volta Region - Ghana. The research design for the study was quasi-experimental non-equivalent control group design. Convenience and simple random sampling techniques were employed to obtain a sample of 104 student teachers, which comprised 53 student teachers in the control group and 51 in the experimental group. Test items were the instruments used for data gathering. Descriptive, paired samples t-test and independent samples t-test were used in analyzing data. Descriptive content error analysis revealed that student teachers committed many conceptual, procedural and technical errors when solving tasks in the differential calculus. The results also indicated that there was a statistically significant difference between student teachers’ of the experimental group exposed to the use of Maple software in learning differential calculus to control groups exposed to traditional methods. Consequently, it was recommended that Maple assisted instruction be incorporated in the teaching and learning of differential calculus in the school; and also there is the need for the mathematics teachers in the school to employ blended teaching approaches, in which Maple software are used simultaneously to enhance teaching of mathematics concepts.

Designing Calculus Teaching Model Based on STEM for University Students: Is It Valid, Practice, and Effective?

One of the lecturers' duties apart from teaching is to develop learning products that are used to overcome various problems encountered during the learning process. For that reason, each lecturer must develop their learning model so that learning objectives can be adequately achieved. The large number of lecturers who only use ready-made teaching materials has an impact on student learning outcomes, which are still low. This can be understood because, in essence, the learning problems faced by students are different. This study aims to determine the level of validity, practicality, and effectiveness of the developed STEM-based calculus learning model in tertiary institutions. This study is part of research and development focused on the trial phase, which includes testing the validity, practicality, and effectiveness. This research was conducted at the Indonesian Christian University of Toraja, Makassar, Indonesia, with participants consisting of 5 validators/experts, two lecturers, and 20 students. Data collection was carried out using learning outcome tests, validation sheets, lecturer response questionnaires, teacher response questionnaires, and observation sheets. The data that have been collected are then analyzed using quantitative analysis techniques using SPSS version 20. The results show that the STEM-based calculus learning model that has been developed is proven to be valid, practical, and effective to improve students' learning outcomes.