Calculus Course Research Articles

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.

Exploring the dynamics of situated expectancy-value theory: A panel network analysis

Students' competence beliefs and task values are proximal psychological predictors of their achievement-related choices and academic achievement. Situated expectancy-value theory (SEVT) suggests that these beliefs are situationally sensitive and interact over short periods of time. In the present study, we explored the dynamic nature of students' situation-specific expectancy-value beliefs in five sections of an introductory calculus course across one semester (11 weeks, N = 429). Using psychometric network analysis, we examined how facets of the SEVT framework are related between persons (i.e., between-person network), within situations (i.e., within-person contemporaneous network), and from one time point to the next across one semester (i.e., within-person temporal network). Results suggested that differences existed among motivational constructs across the three networks in that costs and positively-valenced facets of motivation (i.e., competence and values) were relatively independent of each other within a given situation, but showed some significant cross-lagged effects over time. Our results suggest that interventions to support students in STEM should target positively and negatively valenced constructs (i.e., values and costs).

Observing Instructor Behaviour in an Active Learning Classroom: A Case Study of an Undergraduate Calculus Course

Active learning classrooms (ALCs) are spaces explicitly designed to encourage collaborative learning, often through the use of technology. To learn more about teaching activity in ALCs, a study was designed to observe an engineering calculus course during the winter 2020 term. A large-scale active learning classroom was selected for classroom observation using the extended Teaching Dimensions Observation Tool (TDOP+). The TDOP+ is a descriptive classroom observation protocol based on the Teaching Dimensions Observation Tool, enhanced with elements from the Active Learning Classroom Observation Tool (ALCOT). 
 This case study compares the class orchestration of different instructors teaching two different sections of the same course at a large, public university. Twenty class sessions were coded for this study: 10 for each section (5 for each instructor). The coded instructor behaviour was analyzed using a conceptual framework described by Nocera (i.e., a version of Activity Theory), focusing on mediating artifacts and instructor goals. 
 While we observed differences in the frequency and duration of active learning activities and in the type and number of tools used in each class session, the results from this case study suggest that flexible space design enables instructors with the same lesson plan (and content) to create different technological frames to achieve their varied pedagogical goals, while encouraging increased adoption of new tools.

Students’ expert-like attitudes in calculus and introductory computer science courses with active-learning pedagogy

ABSTRACT Background and Context Computer Science has traditionally had poor student retention, especially among women. Prior work has found that student attitudes are a key factor to retention, especially with “weedout” courses such as Calculus. Objective To determine how student attitudes towards CS 1 and Calculus change over active-learning courses with explicit real-world connections, and the implications for at-risk groups in CS, including women and students without prior experience in CS. Methods We use two validated instruments, the Computer Attitudes Survey (CAS) and the Mathematics Attitudes and Perceptions Survey (MAPS), both of which derive from the Colorado Learning Attitudes about Science Survey (CLASS), to compare student attitudes in Calculus I and CS 1. Our analysis includes 109 students for the CAS and 73 for the MAPS. Findings CS 1 students began the course with CAS scores higher than observed in prior work, and post-course CAS scores were even higher overall. Calculus students started the course with MAPS scores in line with prior work, but unlike prior work we find that overall MAPS scores did not decline during the semester. Women’s reported interest in math increased significantly during the semester. Students with prior computer science experience began CS 1 with higher overall CAS scores, while students with prior calculus experience began Calculus with similar overall MAPS scores but much higher reported interest. Implications Difference in student attitudes between the courses may show why Calculus acts a “weedout” course for Computer Science. This highlights the importance of instructors demonstrating the usefulness of Calculus.

Opportunity to Interpret: Infection Rates in the COVID-19 Pandemic

The COVID-19 pandemic provided students a rare opportunity to use their mathematical knowledge to make sense of a top-of-mind crisis. Based on a report in a major regional newspaper, we designed tasks that require an understanding of infection rates and an interpretation of a misleading claim made in the newspaper. Our analysis of 91 undergraduate students’ responses to one of the tasks shows that 77% of the participants used the first or second derivative to interpret the claim. While an assessment for fundamental calculus courses may include both the memorization of procedures and high-cognitive-demand tasks, the findings suggest that it is feasible and worthwhile to build assessment questions on a meaningful connection with the real world.

USE OF FLIPPED CLASSROOM IN THE TEACHING-LEARNING PROCESS ON DESCRIPTIVE STATISTICS

Educational institutions seek to transform the teaching-learning conditions through the use of new pedagogical and technological models. The aim of this quantitative research is to analyze the use of flipped classroom in the teaching-learning process on descriptive statistics through data science. The participants are 49 students who took the Basic Statistics course during the 2017 school year. This study used a single group quasi-experiment to examine the research hypotheses about Flipped classroom. In the Basic Statistics course, the students have difficulties to assimilate the knowledge about mean, mode, median, range and quartiles. Therefore, this research proposes the consultation of YouTube videos before the class, use of the Mathportal application collaboratively during the class and use of the Mathportal application individually after the class. The Mathportal application is a web tool that allows checking the results of the exercises on the mean, mode, median, range and quartiles at any time. The results of machine learning (linear regression) indicate that flipped classroom positively influences the teaching-learning process on descriptive statistics. On the other hand, data science allows the identification of 3 predictive models about the consultation of the YouTube videos and use of the Mathportal application through the decision tree technique. This research recommends the use of the Mathportal application for the teaching-learning process on statistics. Even, this web application can be used in the courses of differential calculus, geometry, algebra and financial mathematics. The implications of this research are the transformation of the educational context through the use of flipped classroom and incorporation of technological tools before, during and after the face-to-face classes. Finally, flipped classroom is a pedagogical model that is transforming the organization and implementation of school activities through the use of technology inside and outside the classroom.

Flipped Classroom and Peer Learning: A New Approach to the Educational Process at University

In this paper, a new flipped classroom model at the university emerged. The innovation of the model lies in the combination of two methods of the students' learning process: students work together in small groups before the class (cooperative learning) and also conduct presentations in groups within the class (group peer tutoring). Indeed, during the semester students alternate in the roles of the tutor and the tutee in the classroom process. The teaching experiment was carried out at the Department of Business Administration of the University of Patras in the context of the Calculus course of the 1st semester. Of the 344 participating students, 179 chose to follow the procedure of the flipped classroom while 165 the traditional lecture. It was revealed that the proposed model of the flipped classroom induces the students’ academic performance of the students. In addition, this level of academic performance is maintained even after the semester in mathematics and in courses in different cognitive subjects. The proposed flipped classroom model that emerged, can offer benefits to the educational process and the students in terms of both traditional and distance learning environments.

Integrating Workbook-Making in Learning Calculus during the Pandemic: A Phenomenological Study

Calculus is one of the courses considered frustrating and difficult by most learners. This frustration, along with difficulty encountered, is coupled with the challenges brought about by the paradigm shift to online learning. In an effort to address some of these challenges, the teacher-researcher employed project-based learning through workbook-making in hopes of improving students' learning. The study used a phenomenological approach to investigate the second year Bachelor of Secondary Education- Mathematics students’ lived experiences in workbook-making during the pandemic. The study utilized simple random sampling among the students who were taking Calculus course during the second semester of the school year 2020-2021. Eleven (11) students responded and were subjected to semi-structured interview questions. Using thematic analysis, three themes emerged: (1) Difficulties and Challenges in making Calculus workbook during the Pandemic, (2) Strategies employed to make Calculus workbook during the Pandemic, and (3) Workbook-making as a tool in learning Calculus. The result of the study may be a springboard for other Mathematics educators to devise learning interventions or apply project-based learning, specifically workbook-making, in enhancing students’ learning, not only in Calculus but Mathematics in general, during the pandemic. It can also serve as a baseline in conducting related studies in other fields and levels.

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.

What Knowledge Do Teachers Need to Predict the Mathematical Behavior of Students?

The aim of this study was to explore the specialized knowledge of five mathematics teachers who participated in a continuing training project. Teachers were asked to formulate conjectures about the type of mathematical work that students enrolled in a calculus course would develop when approaching the graphical representation of functions as an introductory activity to the calculation of the volume of solids of revolution. The data collected was analyzed using the categories of the MTSK (Mathematics Teacher’s Specialized Knowledge) model. The results report how knowledge of topics and the knowledge of features of learning mathematics, particularly in relation to the knowledge of strengths and difficulties, served as fundamental pillars for the formulation of the conjectures about students’ mathematical behavior.

The complex and integrated nature of a mathematics lecturer’s specialized knowledge

Knowledge required to teach mathematics at the university level is a current and relevant research topic in Mathematics Education. Thus, the case study presented in this article pertains to one mathematics lecturer whose knowledge is examined focusing on his delivery of a Multivariable Calculus course. The data required were gathered via classroom observations and a semi-structured interview and were subsequently analyzed through the lens of the Mathematics Teacher’s Specialized Knowledge model. The interactions among different components of the lecturer’s specialized knowledge that were identified in terms of intra-domain and inter-domain relationships provide empirical support for the complex and integrated nature of the mathematics lecturer’s knowledge.

THE ROLE OF BELIEF MATHEMATICS ON STUDENTS' LEARNING OUTCOMES IN DIFFERENTIAL CALCULUS COURSES

The subjects in this study were second semester students of 2020/2021 mathematics education study program, Universitas Muhammadiyah Tangerang. The purpose of this study was to find out how big the role of mathematical belief in student learning outcomes in the differential calculus course which was held in the even semester of 2020/2021. The research method is a survey method with a descriptive correlation analysis technique with instruments in the form of questionnaires and tests. The data were analyzed by regression analysis using SPSS statistic 20 software. The results showed that based on the results of the analysis and discussion, conclusions could be drawn including the role of mathematical belief in giving a significant influence on student learning outcomes in the differential calculus course. The results of the study using SPSS 20 showed that the value of the close relationship between mathematical beliefs and learning outcomes was 0.89, this indicates that there is a very strong relationship between mathematical beliefs and learning outcomes. The results show that the belief in mathematics on the learning outcomes of the differential calculus course contributes 79.2%. Analysis of the Significance Test of the Role of Mathematics Belief on Learning Outcomes for Differential Calculus Courses shows that an increase in the mathematical belief score in the Differential Calculus course will give an increase of 0.830

SELF-EFFICACY MATHEMATICS EDUCATION STUDENTS IN DIFFERENTIAL CALCULUS COURSES

Self-efficacy is one of the important soft skills for students because it affects success in solving a problem. This study aims to: (1) describe the self-efficacy of Mathematics Education students in the differential calculus course; (2) analyze the effect of the self-efficacy of Mathematics Education students on learning outcomes in the differential calculus course. This research is a survey research with a descriptive quantitative approach. In taking the sample, the researcher used a purposive sampling technique, namely class C differential calculus with a sample of 22 students. The instruments used in this study were test questions and self-efficacy questionnaires. The results showed that in general students self-efficacy was in the moderate category, with details of 18% in the high category (H), 59% in the medium category (M), and 23% in the low category (L). In addition, self-efficacy has a positive effect on student learning outcomes by 57.3%.

Improving Students’ Mathematical Problem-Solving Ability Using M-APOS Approach to Derivative Material

This research is quasi-experimental research that aims to see the improvement of students' mathematical problem-solving abilities on derived material using M-APOS learning. Data analysis using statistical tests on the pretest, post-test, and normalized gain data. Data analysis was carried out with the help of Microsoft Office Excel and SPSS 24 software. The research sample was 66 people who took the differential calculus course. The research instrument is a mathematical problem-solving ability test in the form of a description of four items. This study concludes that there are differences in the increase in mathematical problem-solving abilities of students who receive M-APOS learning with students who receive expository learning. Furthermore, students gave a positive response to M-APOS learning.

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.

SELF-EFFICACY MATHEMATICS EDUCATION STUDENTS IN DIFFERENTIAL CALCULUS COURSES

Self-efficacy is one of the important soft skills for students because it affects success in solving a problem. This study aims to: (1) describe the self-efficacy of Mathematics Education students in the differential calculus course; (2) analyze the effect of the self-efficacy of Mathematics Education students on learning outcomes in the differential calculus course. This research is a survey research with a descriptive quantitative approach. In taking the sample, the researcher used a purposive sampling technique, namely class C differential calculus with a sample of 22 students. The instruments used in this study were test questions and self-efficacy questionnaires. The results showed that in general students self-efficacy was in the moderate category, with details of 18% in the high category (H), 59% in the medium category (M), and 23% in the low category (L). In addition, self-efficacy has a positive effect on student learning outcomes by 57.3%.

The Effect of Teaching Mathematics Supported by e-learning platforms on the Students’ Mathematical Skills in a College Course in Jordan

Exploring the impact of e-learning on a student's math skills was the main objective of this study. The experimental design was applied in this study to 80 students from the calculus course from the first semester in the 2021-2022 academic year at The Hashemite University, where they were divided into two groups, a control group and a experimental group. Three modules of calculus textbook (function, ends, graph curves) were adopted, the traditional whiteboard was used in the teaching of the control group, while e-learning platforms were used to teach the experimental group. A tribal test dish to measure sports skills and a distance test on students. Use SPSS to assess the effects. The experimental group showed superiority over the control group by analyzing the results from the tests applied. Teaching on e-learning platforms (Modal, E-Learning, zoom) has shown effective consequences for the student's sports skills. These results correspond to a set of previous studies that will be presented in this research.

Reforming the Teaching and Learning of Foundational Mathematics Courses: An Investigation into the Status Quo of Teaching, Feedback Delivery, and Assessment in a First-Year Calculus Course

Several universities are witnessing an increase in students’ enrolment in mathematics-intensive programmes over the last decades. This increase has come with the price of high failure rates in foundational mathematics courses, which poses challenges to mathematics teaching and learning in higher education. It is therefore inevitable, for some universities, to transform the teaching and learning of mathematics to more student-centred approaches that engage the students mathematically and enhance their success rates. We approach this transformative effort by investigating students’ perception of teaching, feedback, and assessment as a first step in reforming the teaching of a first-year mathematics course at a Norwegian university. The results of both quantitative and qualitative analyses of the data generated using a questionnaire from 107 (80 men) engineering students show that the status quo of teachings offers little support for learning. The teaching is dominated by teacher-led instruction, note-taking, and large pieces of proof which make learning difficult for students during class activities. The results also show that the current structure of the course offers limited formative feedback to students and that the assessment tasks require restructuring to capture students’ time and effort. We discuss the implications of these findings and make some recommendations for improvement.

Competence and autonomous motivation as motivational predictors of college students’ mathematics achievement: from the perspective of self-determination theory

BackgroundApplied Calculus courses serve hundreds of thousands of undergraduates as quantitative preparation and gatekeepers across diverse fields of study. The current study investigated how motivational factors are associated with students’ learning outcomes in Applied Calculus courses from the perspective of self-determination theory—a sound comprehensive motivation theory that has been supported by considerable research in psychology and education. In order to have a nuanced understanding of students’ motivation and learning in Applied Calculus courses, we used three different types of learning measures to investigate students’ mathematics achievement, including course grades, a standardized knowledge exam, and students’ perceived knowledge transferability.ResultsWe tested the relationships between motivational factors and learning outcomes with a multi-semester sample of 3226 undergraduates from 188 Applied Calculus classrooms. To increase the precision of our analysis, we controlled for three demographic variables that are suggested to be relevant to mathematics achievement: gender, minority group status, and socioeconomic status. With a series of multilevel modeling analyses, the results reveal that: (1) competence satisfaction predicts college students’ mathematics achievement over and above the satisfaction of needs for autonomy and relatedness; and (2) autonomous motivation is a more powerful predictor of college students’ mathematics achievement than controlled motivation and amotivation. These findings are consistent across different types of learning outcomes.ConclusionsSelf-determination theory provides an effective framework for understanding college students’ motivation and learning in Applied Calculus courses. This study extends self-determination theory in the field of mathematics education and contributes to the dialogue on advancing undergraduate science, technology, engineering, and mathematics (STEM) education by providing evidence to understand how motivational factors are associated with students’ learning outcomes in undergraduate mathematics courses.

Analysis of a teaching learning process of the derivative with the use of ICT oriented to engineering students in Chile

This work aims to analyze the responses of a group of engineering students related to problems about tangents in a teaching learning process of derivative in a differential calculus course. The methodological design, oriented to a group of 161 students from two Chilean universities, considers different onto-semiotic configurations in problem-situations about tangents. The methodology implemented integrates information and communication technologies in differentiated activities, favoring the use of languages and progressive approach to the meaning of the derivative. The exploratory-type analysis was carried out applying some tools of the onto-semiotic Approach of mathematical knowledge and instruction. Difficulties were found in the concept of function and the Euclidean conception of the tangent line, which brings with it a weak interpretation of the derivative function and its geometric representation. It is concluded that the implementation of the geometric interpretation through information and communication technologies makes it possible to improve the teaching of the derivative.