Calculus Course Research Articles

Effects of Synchronous and Asynchronous Approaches in Geometry Learning to Stimulate Students' Critical Thinking

Geometry learning has an important role in stimulating critical thinking. During the Covid-19 pandemic, synchronous and asynchronous approaches became an alternative in geometry learning. The purpose of this study is to investigate the effectiveness of geometry learning by combining synchronous and asynchronous approaches in stimulating critical thinking. This study used a mixed design, namely quantitative and qualitative approaches. The sample was mathematics education students who had taken basic calculus and mathematical logic courses. Quantitative data collection used critical thinking worksheets and questionnaires to measure student activities and responses. Qualitative data collection through learning video recordings and researcher notes during learning. The results showed that student activity was high. Details can be explained in the discussion section.

Cognitive apprenticeship in vocational students mathematical decision making skills

Exploring the decision-making abilities of undergraduate students, including students from vocational education backgrounds, is the main priority in the achievement of mathematics learning in general and in Calculus courses particularly. Decision-making processes require cognitive guidance through activities describing in detail the systematic steps of each process. It is implicitly said as part of a cognitive apprenticeship procedure. There are claims that students with a vocational education background can develop their academic and practical potential more through a cognitive apprenticeship model. In addition, using video as visual media learning allows students to sharpen their skills. Therefore, the study aims to explore the distinction in achievement and improvement of mathematical decision-making skills between undergraduate students who learn with a Video-assisted Cognitive Apprenticeship approach (CAV), and they are who receive Cognitive Apprenticeship learning (CA) with conventional learning. A quantitative study with the Static-Group Pretest-Posttest Design was employed as a methodology in the research. Based on the research stage, there are differences in achievement and improvement of student decision-making skills with a review of the type of vocational school between undergraduate students.

Women’s Sense of Belonging in Undergraduate Calculus and the Influence of (Inter)Active Learning Opportunities

Women continue to be underrepresented in undergraduate STEM majors.<b> </b>Prior studies identify sense of belonging, or the extent to which one feels like an accepted member of an academic community, as a key contributor to women’s decisions to stick with or leave their STEM majors. Calculus can be an especially critical leak in the STEM pipeline, as is often seen as a gatekeeper course for STEM majors. Historically, Calculus instruction has been primarily lecture-based, though recently, efforts have shifted toward incorporating instruction that supports active learning. Prior studies have suggested that providing active learning opportunities may support students’ sense of belonging. However, there lacks consensus on the particular types of active learning opportunities that best support students. This mixed methods study investigates connections between women’s sense of belonging and the learning opportunities they experience during the first semester of a two-semester Calculus course designed to provide frequent active learning opportunities. Findings indicate a significant increase in sense of belonging, perceived competence, and social connectedness from Week 1 to Week 7 of the semester. Further, women overwhelmingly identified the interactive nature of group work and interactive lecture as supportive of their sense of belonging for both academic and social reasons.

SELECTION OF VIDEO CONFERENCE APPLICATION FOR MATHEMATICS LEARNING USING INTUITIONISTIC FUZZY MAX-MIN AVERAGE COMPOSITION METHOD

In this article, the Intuitionistic Fuzzy Max-Min Average Composition method is used which aims to choose the right video conferencing application for learning mathematics. The results show that the learning process in Mathematical economics, Calculus, Statistics, and Geometry courses is more appropriate using the Microsoft Teams video conferencing application than Zoom and Google Meet.

The Siren Call of Calculus A Review of Steven Strogatz’s Infinite Powers: How Calculus Reveals the Secrets of the Universe

I hate calculus. Which is a lie: I secretly love it. I enjoy teaching it, drawing intricate diagrams of where the definition of the derivative comes from, stumping my students on convoluted trigonometric integrals with solutions dependent on partial fractions, hammering mnemonics for the derivative rules—all the joys of teaching calculus. And I enjoyed learning it, too. Well, not failing it the first time, but after that. I long for my undergraduate time spent in the reading room of Rutherford South re-arranging integrals à la Fubini’s Theorem, the massive lecture halls of anxious engineering students copying every stroke of chalk from the front, and the arithmetic errors costing me scores of marks from my tests. A calculus course presents the liturgy of undergraduate mathematics: students and instructors alike gather, willfully or otherwise, to engage in the ritualistic celebration of the mysteries of the infinite.

First-Year Engineering Students’ Interpretations of Differentials and Definite Integrals

In this paper we focus on Norwegian first-year engineering students’ interpretations of differentials and definite integrals. Through interviews with 15 engineering students, we investigated how the students interpreted the different symbols involved in the Fundamental Theorem of Calculus (FTC), as displayed in the textbook used in their calculus course. Through the students’ reflections, we aimed to gain insight into the students’ interpretations of differentials, infinitesimals, and limits, and how these concepts were used to interpret the definite integral. Despite a rather rigorous limit-based approach to definite integrals, provided in teaching and in the students’ textbook, we observed that most students offered conceptual interpretations closer linked with an infinitesimal approach, in terms of integrals being regarded as sums of narrow bars, in line with Leibniz.

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.

The bright and dark side of autonomy: How autonomy support and thwarting relate to student motivation and academic functioning

According to Self-Determination Theory, autonomy support is essential in fostering optimal learning, growth, and functioning in students across all levels. In contrast, autonomy thwarting is associated with student malfunctioning. The purpose of the current study was to investigate the relationship between perceptions of autonomy support and thwarting, students’ autonomous and controlled motivations, and aspects of student functioning in a higher education setting. The sample consisted of 414 Norwegian university students recruited from introductory calculus courses. Structural equation modeling indicated that perceived autonomy support predicts autonomous motivation and is negatively linked to controlled motivation. Autonomy thwarting is negatively linked to autonomous motivation and positively predicts controlled motivation. We found that autonomous motivation predicts engagement, effort, and learning. Controlled motivation is negatively linked to vitality and engagement, and positively predicts effort. The results are in line with the tenets of Self-Determination Theory, and the present study highlights the importance of providing an autonomy supportive environment during higher education lectures.

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.

Comparing high-school and college instructors’ beliefs about college calculus preparation

The expectations gap – the difference between the level at which high schools prepare students and the preparation colleges expect – is believed to be accountable for hindering access to, and success in, higher education. It has been largely attributed to misalignment of priorities and lack of communication among policy makers and educators and should inform instruction at both levels. This study compared expectations of college calculus instructors and of instructors who teach calculus-preparatory courses, in college or high school, on what makes for important preparation for the first college calculus course. A total of N = 293 instructors teaching precalculus and calculus at the high school and college levels, in the United States, completed a survey that assessed participants’ beliefs on three major areas related to calculus preparation and success: the critical content prerequisites for calculus, the importance of different calculus teaching and learning elements discussed in the literature, and the ways in which college calculus instructors are willing to accommodate under-prepared students. This study confirms the existence of an expectations gap on a rather narrower issue ‘adequate preparation for college-level calculus', in terms of content and pedagogy. The significance of the finding and its implications for bridging the expectations gap are discussed.

Integral (antiderivative) learning with APOS perspective: A case study

The objective of this study is to determine students’ learning barriers in understanding integral concepts through their thinking processes with the perspective of APOS theory (Action, Process, Object-Scheme). This research applied qualitative research with a case study method. The samples of this research were 19 civil engineering students who had contracted calculus courses and who had been given a written test. The results of the written test were divided into three different categories – they are comprehension ability is high (score ), medium (60 Score < ) and low (score < 60). Deep interviews were conducted with three representative students who took the written test and met the criteria for each group. The results of the interviews showed that students in the high category still had conceptual ontogenic learning obstacle despite passing the APOS path. Students in the moderate category be able to reach the encapsulation stage but they had not been able to de-encapsulate it to the process. They had conceptual and epistemological ontogenical learning obstacles. Whereas the low category students had the tendency to only reach the action stage and had difficulty in doing initial de-encapsulation due to lack of learning experience in the prerequisite materials. The learning obstacles they experienced were psychological and conceptual-ontogenical learning obstacles. Aggregately, the students tended to experience conceptual ontogenic learning obstacle. The result of this study is expected to be used as a basis for designing a hypothetical learning trajectory in future research.

Analysis of Difficulty Understanding Student Mathematica by Using Online Learning Model

This research is based on the low understanding of students’ mathematics. One of the causes for the low understanding of students’ mathematics is a factor in the students themselves in the form of student difficulties in solving problems related to the material in the Differential Calculus course. The purpose of this study was to describe the difficulties of students’ mathematical understanding in solving problems in the Differential Calculus Course using the online learning model. This type of research uses a qualitative approach and is descriptive in nature. The subjects of this study were first semester students taking Differential Calculus courses in the Mathematics Education study program, Muhammadiyah University of Tapanuli Selatan, Academic Year 2020/2021. The instrument used in this study was an interview. The results showed that the difficulties of students’ mathematical understanding in solving problems in the Differential Calculus course using the online learning model were related to technical difficulties, adaptation difficulties and internal difficulties for each individual student. To overcome these difficulties, it is necessary to have a more varied strategy for using online learning media.
 Keywords: Online learning; mathematic; media

Exploring problem-solving through the intervention of technology and Realistic Mathematics Education in the Calculus content course

In Thai mathematics classrooms, there is a lack of attention to support students’ mathematical problem-solving skills by working from real-world contexts that make sense to students. This study aimed to investigate how pre-service mathematics teachers’ problem solving can be explored in their content course, intervening with technology and Realistic Mathematics Education (RME) through the Mean Value Theorem (MVT) lesson. The study included nine pre-service mathematics teachers purposively selected from a public university in Thailand who attended a Calculus course. Data was collected from classroom artifacts, observation notes, and interviews. It was found in this study that the intervention of technology and RME in pre-service mathematics teachers’ content courses has the potential to build pre-service mathematics teachers’ problem-solving abilities. It was also discussed that the intervention could use RME to conceptualize mathematics theorem and cultivate Polya’s problem-solving steps. The findings provide light on the efficacy of using technology and RME in enhancing problem-solving skills among other content courses and could be used to inform the creation of mathematics curricula and instructional strategies in undergraduate content courses for mathematics education programs.

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.

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.

Student mathematics understanding through blended learning approach

This study aims to describe students' understanding of the concept of calculus by using a blended learning approach, namely online learning, face-to-face learning, and individualized learning. The subject are students of mathematics education STKIP PGRI Sumenep who has taken calculus course I representative of three categories, namely the category of students with high, medium, and low levels of ability. The data collection technique used a test in the form of five essay questions on indeterminate integral material, interviews to explore student responses using unstructured interview guidelines, and observation to determine student activity in the process of learning activities in calculus courses. The data analysis technique consists of three stages, namely data reduction, data presentation and drawing conclusions. The results show that students are only able to re-state concepts that have been studied before, but students have not been able to provide examples and non-examples as a form of understanding integral concepts and students in relating concepts are still not appropriate and in accordance with the procedure for solving integral problems.

Teaching Undergraduate Calculus at an Urban HBCU through a Global Pandemic

Over the last decade, there has been a national effort to prepare a more diverse student population for success in science, technology, engineering, and mathematics (STEM) careers. While there are a variety of best teaching practices in undergraduate STEM education, student engagement has been widely used to improve student learning. Specifically, it is important for students to have opportunities to practice or apply the theory they have learned in courses to real-world problems. Implementing active learning is one model that can be used to achieve this objective. However, due to the COVID-19 pandemic, professors have had to offer courses in online formats and determine how to continue to implement effective teaching strategies during this unprecedented time. Professors are anticipating the possibility of the need to continue offering courses in fully online and hybrid formats even in the future. With an emphasis on a STEM gateway course sequence, the aim of this paper is to highlight pre-COVID-19 research studies in online STEM education at Historically Black Colleges and Universities (HBCUs), explore how COVID-19 impacted students, teaching, and learning in undergraduate calculus courses, and outline opportunities for continuing to implement teaching techniques that work effectively for in-person and online calculus instruction.

Teaching and Learning of Vertex Coloring Using an Inquiry-Based Approach

Traditional lecturing is the dominant method of teaching mathematics in undergraduate mathematical courses in many countries, whereas active student-centered approaches such as inquiry-based learning have been shown in some instances to be more effective. Most teaching resources (inquiry-based tasks) available at the tertiary level are related to calculus, linear algebra, and differential equations courses. In this paper, we focus on using an inquiry-based approach to explore the teaching and learning of vertex coloring, a common topic in graph theory and undergraduate discrete mathematical courses. We designed seven inquiry-based tasks related to vertex coloring to teach vertex coloring in an undergraduate graph theory course to students majoring in mathematics. In sharing these tasks, describing students’ engagement with them, and discussing how these tasks were perceived by the students and lecturer, we hope to promote using inquiry-based tasks in undergraduate discrete mathematical courses.

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.