Learning Calculus Research Articles

The effect of blended learning on mathematics cognitive demand and cognitive load in learning calculus of several variables at universities in Tigray, Ethiopia

The overall objective of this study was to examine the effect of blended learning on improving students’ mathematical cognitive demand and their extraneous and germane cognitive load in learning calculus of several variables. Guided by constructivist and cognitive load theories, a quasi-experimental design was conducted in three public universities. A total of 67 second-year undergraduate mathematics students participated for 4 months. The study used a mixed research method with social constructivism augmented by pragmatism. Data were analysed using analysis of co-variance procedure and thematic analysis and discussed using both quantitative and qualitative methods. The findings revealed that the treatment group students’ mathematical cognitive demand (treatment (TG1) (M = 70.9, SD = 10.8) and treatment (TG2) (M = 69.3, SD = 20.5) were significantly higher than the posttest scores of students in the comparison group in CG (M = 58.8, SD = 13.5), (p = 0.00)) with effect size of 0.25. Moreover, their germane cognitive load had improved and extraneous cognitive load reduced significantly compared to the comparison group. To conclude, mathematics cognitive demand can be improved with blended learning. These findings imply that blending mathematics instruction in higher education institutions is useful to policymakers. The finding also revealed that cognitive load was found a negative and significant predictor of mathematics cognitive demand.

Contributions to the characterization of the Schema using APOS theory: Graphing with derivative

This study contributes to Action, Process, Object, Schema (APOS) theory research by showing two approaches used by advanced mathematics students to construct relations between higher-order derivatives to solve complex problems. We show evidence of students’ ability to perform Actions on their graphing derivative Schema, that is, of its thematization. It also contributes to the literature on the learning of differential calculus by showing how advanced students use their knowledge to construct relations between concepts when facing complex situations. The work of three graduate students on transforming complex graphs and determining their properties and their relation to the domain structure is analyzed to determine their solution approaches. Their graphing derivative Schema is analyzed in depth in terms of the construction of relations among the Schema structures and assimilation and accommodation mechanisms involved in thematization in APOS theory. These findings are important in informing and developing didactic strategies to foster university students’ understanding of derivatives, which can smoothe the transition to the study of advanced mathematics courses.

Response of Prospective Mathematics Teacher Students To Learning Difficulties In Calculus Course

This study was motivated by the learning difficulties faced by prospective mathematics teacher students in calculus courses, while calculus courses studied at the college level equip prospective teacher students to teach mathematics subjects at the secondary school level. This study aims to determine students' responses to learning difficulties in calculus courses. This research used descriptive quantitative method by involving 25 students of Tadris Mathematics IAIN Kerinci as the research sample. The sampling technique used in this study was convenience sampling, which is when a researcher chooses his sample only by including people who are available. This study uses a closed questionnaire as a data collection tool that is reviewed from 7 aspects of difficulty, namely interest, motivation, talent, intelligence, facilities and infrastructure, quality, and teaching methods. The results of descriptive analysis showed that students have a high level of difficulty in learning calculus. The conclusion of this study shows that students' learning difficulties, especially in calculus courses, are strongly influenced by external factors, especially related to learning facilities and infrastructure. The results also show that prospective math teacher students at IAIN Kerinci have an unfavorable response to learning difficulties in calculus courses.

Why Isn't There an Inverse Quotient Rule?

When learning Calculus, students are taught how to undo the Chain Rule through u-Substitution and may have been introduced to Integration by Parts as a way to undo the Product Rule. This paper describes analogous integration techniques to undo the Quotient Rule and argues that the “Inverse Quotient Rule” is a worthwhile technique to teach in Integral Calculus. An appendix includes 26 textbook-style exercises for interested students.

Interventions and diversity, equity, and inclusion: Two current directions in research on the teaching and learning of calculus

Interventions and diversity, equity, and inclusion: Two current directions in research on the teaching and learning of calculus

Interactive Learning System for Learning Calculus.

IT tools has 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, calculus learning augmented reality application has limitation in promoting a human collaboration in learning. 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. 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 "Solid of Revolution" 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. The results found that both interactivities affect learning experience positively; human-human interactivity has a higher impact than the human-system interactivity. It was also found that learning performance as part of the learning experience increased from pre-test to post-test.

Enhancing Calculus Learning through Interactive VR and AR Technologies: A Study on Immersive Educational Tools

In the realm of collegiate education, calculus can be quite challenging for students. Many students struggle to visualize abstract concepts, as mathematics often moves into strict arithmetic rather than geometric understanding. Our study presents an innovative solution to this problem: an immersive, interactive VR graphing tool capable of standard 2D graphs, solids of revolution, and a series of visualizations deemed potentially useful to struggling students. This tool was developed within the Unity 3D engine, and while interaction and expression parsing rely on existing libraries, core functionalities were developed independently. As a pilot study, it includes qualitative information from a survey of students currently or previously enrolled in Calculus II/III courses, revealing its potential effectiveness. This survey primarily aims to determine the tool’s viability in future endeavors. The positive response suggests the tool’s immediate usefulness and its promising future in educational settings, prompting further exploration and consideration for adaptation into an Augmented Reality (AR) environment.

Unveiling interdisciplinary horizons: students’ experiences in a first-year calculus course

In the realm of higher education, the pursuit of interdisciplinarity aims to foster the exchange and integration of fragmented knowledge, yielding transformative outcomes. Employing a phenomenological method, this study delves into the interdisciplinary experience of twelve students from a first-year undergraduate calculus class. Through the analysis of written questionnaires, focus group sessions, and supplementary qualitative data, a comprehensive understanding of students’ interdisciplinary encounters is unveiled and organized into three main categories: what students think about interdisciplinarity, how they act when being involved in integrations and what external factors are involved in shaping their experience. This paper presents emergent experiential themes, shedding light on both individual and collective experiences, as students navigate and enrich their calculus learning through interdisciplinary connections.

Influence of the academic reinforcement workshop to improve the learning of integral calculation in second cycle’s students of systems engineering and computing of the faculty of sciences semester 2022-II unasam-Huaraz, 2023 [Influencia del taller de refuerzo académico para mejorar el aprendizaje del cálculo integral en estudiantes de segundo ciclo de ingeniería de sistemas y computación de la facultad de ciencias

The objective of the research is determining the influence of the Academic Reinforcement Workshop on improving the learning of integral calculus in students of the second cycle of Systems Engineering and Computer Science of the Faculty of Sciences, semester 2022-II- UNASAM -Huaraz, 2023. The research is applied type, quantitative method and pre-experimental design; Two instruments were applied: Pre test and post test validated by two experts, applied to a sample of 26 students. The variables analyzed Workshop on academic reinforcement and learning of integral calculus, in whose research an affirmative hypothesis and a null hypothesis were formulated. After analyzing the results, it is stated that there is a significant influence of the academic reinforcement workshop on the learning of integral calculus, so that the affirmative hypothesis is accepted. The verification of the hypothesis was done by applying Student's T. It is concluded that there is a significant influence of the academic reinforcement workshop on the learning of integral calculus in students of the professional career of Systems Engineering and Computer Science, semester 2022-II, UNASAM -Huaraz, 2023.

UNBOXING UNDERSTANDING: SELF-EXPLANATION PROMPTING AS A KEY TO UNLOCKING DEEP LEARNING IN CALCULUS

Deep learning in calculus often poses challenges for students, requiring a nuanced approach to foster comprehension. This study explores the efficacy of self-explanation prompting as a key strategy for enhancing deep learning in calculus. The research investigates the impact of guided self-explanation prompts on students' understanding and retention of calculus concepts. By employing a carefully designed intervention, we aim to uncover the mechanisms through which self-explanation facilitates meaningful learning in calculus. The results highlight the potential of self-explanation as a powerful tool in the educational toolkit, shedding light on how it can unlock a deeper understanding of calculus concepts and improve overall learning outcomes.

Students’ Attitudes and Academic Achievement in Learning Calculus

Students’ Attitudes and Academic Achievement in Learning Calculus

Student Engagement and Academic Achievement in Learning Calculus

Student Engagement and Academic Achievement in Learning Calculus

Analysis of Students’ Problem-Solving Ability in Solving Improper Integral Problems

This study aimed to determine the student’s problem-solving-ability using Polya stages in solving Improper Integral questions in online Integral Calculus Learning through zoom applying Student-Centered Learning. It is very rare to find the research that examines students' problem-solving abilities in solving improper integral problems. The research method used in this study was ex-post facto research. The research subjects were 14 students from class B in the third semester of the Mathematics Study Program FKIP UNIB 2020/2021 getting grades A and A- in Integral Calculus Learning. The analysis in Polya stages consisted of Understanding the Problem (P1); Devising a Plan (P2); Carrying out the Plan (P3); and Looking Back (P4. The instruments used to collect data were improper integral test sheets, analysis guide sheets, and open questionnaires. The result showed the mean score of the student’s problem-solving ability was 74.02. The mean value in each stage: P1 = 79.91; P2 = 79.46; P3 = 72.77; and P4 = 65.18. It was concluded that students already had good abilities in understanding problems and planning solutions.

Students' Perception of Mobile Application in Calculus Learning

Mathematics is a crucial subject that students learn from primary school onward. However, some students have a negative perception of mathematics, considering it difficult and tedious, especially among Generation Z, who have grown up in a world where information is readily available at their fingertips. So, traditional teaching methods may not be very effective. This study aimed to determine students’ perceptions of mobile applications in calculus learning. The study involved 35 students from a private university in Kedah. This quantitative study utilizes a survey method and employs a questionnaire as the research instrument. The perception questionnaire is divided into four categories: attractiveness, effectiveness, relevance, and motivation. Based on the research findings, this study concludes that students had a positive perception of four aspects—attractiveness, effectiveness, relevance, and motivation— when using a mobile application for calculus learning.

Relationship of Critical Thinking with Competencebased Approach in Learning Calculus

In this article, an analysis of a topical problem for university didactics concerning the formation of critical thinking (CT) in students in the process of modernization of higher education has been made. A comparison is drawn between properties of both ordinary and critical thinking. Special attention is given to the relationship between CT and competence-based approach in learning Calculus. A model of CT formation in students has been presented and detailed consideration given to pedagogic and didactic conditions for CT formation.

Analyzing Common Errors in Differentiating and Integrating Functions as Basis for Supplemental Calculus Learning Tool

Calculus is one of the most interesting fields of Mathematics yet difficult to pass. In this study, the common errors committed by the students were analyzed and categorized based on Newman’s error analysis guide. Using the quantitative research method, 10 Bachelor of Secondary Education major in Mathematics students enrolled in Calculus I and II were purposively chosen. The study hypothesized that no significant effects of the errors committed when classified according to types of errors and math fields to the overall performances in Calculus I and II of the students. Data collected were analyzed and interpreted using Mean Percentage Scores and Structural Equation Modelling. Based on the results, students commit errors mostly in differentiating functions involving logarithms. In terms of integration, students commit errors more on algebraic functions. Based on Newman’s error analysis, errors committed by mathematics major students are categorized into comprehension in both differentiation and integration processes. The result reveals that while students are equipped with the necessary skills needed for the transformation, process, and encoding, comprehension of the pre-requisite concepts should be strengthened and given attention specifically in algebraic and logarithmic functions. Finally, an instructional material addressing the identified common errors was developed.

The Effects of Online Mathematics Homework on Learning, Attitude, and Efficacy in a College Calculus Class – A Case Study

This case study examines how online mathematics homework impacts student learning, attitude, and efficacy in a college Calculus I class. This research is important because it provides data on student perceptions for how to effectively implement online homework. Participants for this study completed homework using a blend of online and paper formats. We use a mixed methods approach to analyze quantitative survey data and qualitative data collected in focus groups and interviews. Our findings indicate students benefited from using a combination of paper homework and online homework. Recommendations are made for how instructors can utilize the benefits of both approaches to support student learning, attitude, and efficacy.

Impact of learning environments on students’ achievements in Calculus contents before and during COVID-19 crises

ABSTRACT In this research, the students’ achievements in learning Calculus, before and during COVID-19 crisis, are analyzed and compared. Two groups of students, the experimental and the control one, were monitored. Both groups worked in three corresponding subgroups (traditional, hybrid and online) in the frame of different learning environment. The distance learning was applied with the students in the experimental group, in autumn 2020, during COVID-19 crisis, while the control group students learned in autumn 2019, before COVID-19 crisis. The new teaching material was prepared for the students in the experimental group. The comparison between these two groups and their subgroups is described in this paper. It turned out that the students from the experimental group, who used new teaching material for distance learning, had better results than the students in the control group.

Improving high school students' performance in basic calculus using the Enhancing Mastery & Expertise in Mathematics supplementary material


 Preparing K-12 students to gear up for higher mathematics and sciences, and to be more mathematically college-ready, teachers were given the essential role in bridging the learning gaps. One way to address this was the utilization of modules. The researcher developed Enhancing Mastery & Expertise in Mathematics (EM&EM) module in Basic Calculus. The objective of this quasi-experimental research was to evaluate the effectiveness of the EM&EM module in improving students' performance about the theorems of differentiation. The experimental and comparison groups comprised forty-six (46) Grade 11 students who used the EM&EM module and the DepEd module, respectively. The instruments used in the study were the pretest, formative tests, and posttest found in the EM&EM module. Mean and standard deviation were used to describe student performance in these assessments. To see if a significant difference existed, the formative test and posttest scores between the two groups were analyzed using an independent t-test, while the pretest and posttest scores within each group were analyzed using a paired sample t-test. The findings showed that the experimental and comparison groups' formative tests and posttest scores did not differ significantly, although the former generally performed better when their mean scores were compared. However, there was a significant difference between the two groups' pretest and posttest scores, and that had a large positive effect on their improvement. Therefore, just like the DepEd module, the EM&EM module was effective in facilitating the learning process. Overall, the EM&EM module significantly and substantially enhanced students' learning of Basic Calculus.

Assessing Productive Meanings in Calculus

We offer an analysis of calculus assessment items that highlights ways to evaluate students’ application of important meanings and support their engagement in generative ways of reasoning. Our central aim is to identify characteristics of items that require students to apply their understanding of key ideas. We coordinate this analysis of assessment items with a discussion of relevant findings from research on the teaching and learning of calculus, emphasizing the importance of promoting students’ engagement in quantitative and covariational reasoning. We conclude with a broader commentary on the importance of instructors attending to students’ meanings in their teaching, and offer suggestions for flexibly introducing these items as part of formative assessments throughout the life of a calculus course.