The American Journal of Social Science and Education Innovations
01
https://www.theamericanjournals.com/index.php/tajssei
TYPE
Original Research
PAGE NO.
1-4
OPEN ACCESS
SUBMITED
16 October 2024
ACCEPTED
09 December 2024
PUBLISHED
01 January 2025
VOLUME
Vol.07 Issue01 2025
CITATION
Angkasa Widodo. (2025). BOOSTING CALCULUS UNDERSTANDING: THE
IMPACT OF SELF-EXPLANATION PROMPTS ON LEARNING. The
American Journal of Social Science and Education Innovations, 7(01), 1
–
4.
Retrieved from
https://www.theamericanjournals.com/index.php/tajssei/article/view/5793
COPYRIGHT
© 2025 Original content from this work may be used under the terms
of the creative commons attributes 4.0 License.
Boosting calculus
understanding: the impact
of self-explanation
prompts on learning
Angkasa Widodo
Faculty of Education, University of Sultan Ageng Tirtayasa, Indonesia
Abstract:
This study investigates the impact of self-
explanation
prompts
on
enhancing
calculus
understanding and learning outcomes. Self-explanation,
a cognitive strategy where learners generate
explanations for concepts or problem-solving steps, has
been shown to improve comprehension and retention.
In this research, we examine how the integration of self-
explanation prompts in calculus instruction influences
students' ability to grasp complex mathematical
concepts. Through a combination of pre-and post-
assessments, as well as qualitative feedback, the study
assesses how self-explanation facilitates deeper
understanding, error correction, and problem-solving
skills. The findings suggest that students who engage
with self-explanation prompts demonstrate improved
performance, stronger conceptual grasp, and greater
confidence in their ability to tackle calculus problems.
The study underscores the potential of self-explanation
prompts as an effective tool in calculus education.
Keywords:
Self-explanation, Calculus learning, Cognitive
strategies,
Learning
outcomes,
Conceptual
understanding, Problem-solving skills, Instructional
strategies,
Educational
techniques,
Student
performance.
Introduction:
Calculus, as a cornerstone of mathematics
and science, plays a pivotal role in shaping our
understanding of the physical world. It's the language of
change, enabling us to describe the rates at which
quantities vary and, consequently, to make sense of
phenomena ranging from the motion of celestial bodies
to the behavior of atoms. Yet, despite its fundamental
importance, calculus remains a challenging subject for
many students. The abstract nature of its concepts, the
intricacy of its operations, and the sheer volume of
material can overwhelm even the most dedicated
learners.
The American Journal of Social Science and Education Innovations
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The American Journal of Social Science and Education Innovations
In recent years, educators and researchers have
increasingly turned their attention to innovative
teaching methods aimed at enhancing students'
comprehension and mastery of calculus. Among these
methods, the use of self-explanation prompts has
emerged as a promising approach. Self-explanation
prompts are pedagogical tools designed to encourage
students to reflect on and clarify their thought
processes while solving problems or studying
concepts. By engaging students in active sense-making,
self-explanation prompts hold the potential to
demystify calculus, making it more accessible and
comprehensible.
This study delves into the realm of calculus education,
with a specific focus on the impact of self-explanation
prompts. Our objective is to investigate whether the
incorporation of self-explanation prompts into calculus
instruction can empower students to achieve a deeper
understanding of this complex subject, ultimately
leading to calculus mastery. We aim to explore the
effectiveness of self-explanation prompts in fostering
not only improved academic performance but also
increased engagement and enthusiasm for calculus
learning.
To achieve this, we employ a quasi-experimental
design that involves both a control group, which
adheres to traditional teaching methods, and an
experimental group, which benefits from guided self-
explanation prompts throughout their calculus
instruction. By comparing the outcomes of these two
groups, we can assess the true potential of self-
explanation prompts in calculus education.
As we embark on this exploration, it is our hope that
the findings of this study will shed light on innovative
ways to revolutionize calculus instruction. If self-
explanation prompts prove to be a valuable tool in
empowering students to conquer the challenges of
calculus, they could hold the key to unlocking greater
proficiency and confidence in this essential field of
study. Through a better understanding of calculus,
students can be better equipped to tackle complex
problems in various disciplines and contribute to
advancements
in
science,
engineering,
and
mathematics. This research journey begins with a
critical examination of self-explanation prompts and
their role in the calculus classroom, with the ultimate
aim of enhancing the calculus mastery of learners.
METHOD
Our study sought to investigate the impact of self-
explanation prompts on enhancing calculus learning
and fostering mastery. To ensure the rigor and validity
of our research, we followed a structured
methodological approach consisting of participant
selection, intervention implementation, data collection,
and statistical analysis.
Participants:
We recruited a sample of 120 undergraduate students
enrolled in an introductory calculus course at a
prominent university. The participants were randomly
assigned to one of two groups: the control group (n=60)
and the experimental group (n=60). To maintain the
integrity of our study, participants were selected based
on their similar academic backgrounds and a lack of
significant prior exposure to calculus instruction beyond
basic pre-calculus courses.
Materials:
The instructional materials for both groups were
standardized and included textbooks, lecture notes, and
access to relevant online resources. Additionally, the
experimental group received a set of self-explanation
prompts, specifically designed to complement their
coursework. These prompts were meticulously crafted
to encourage students to articulate their thought
processes and reasoning while solving complex calculus
problems.
Procedures:
Pre-Test Assessment: Before the study commenced, all
participants completed a pre-test assessment consisting
of a series of calculus problems of varying difficulty
levels. This initial assessment served as a baseline
measure of their calculus proficiency.
Group Assignments: Participants were randomly
assigned to either the control group or the experimental
group. The random assignment process ensured that
both groups had comparable distributions of academic
backgrounds and initial calculus knowledge.
Instructional Phase: During the instructional phase, both
groups received identical standard calculus instruction,
which
included
lectures,
assignments,
and
examinations. However, the experimental group
received additional guided self-explanation prompts
integrated into their coursework.
Self-Explanation Prompts: The self-explanation prompts
used for the experimental group were strategically
woven into the course materials. For example, when
encountering challenging calculus problems, students in
the experimental group were prompted to elucidate
their thought processes, outline the steps they were
taking to solve the problem, and identify any difficulties
or uncertainties they encountered.
Data Collection: Data were collected during the
instructional phase, encompassing assignment scores,
examination results, and self-report surveys gauging
engagement, confidence, and perceptions of the
effectiveness of the self-explanation prompts
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The American Journal of Social Science and Education Innovations
Post-Test Assessment: Following the instructional
phase, both groups underwent a post-test assessment,
mirroring the pre-test assessment in content and
format. This enabled us to evaluate any significant
improvements in calculus proficiency.
Data Analysis: Data collected from both groups were
subjected to rigorous statistical analysis, including t-
tests and analysis of variance (ANOVA). These analyses
were conducted to assess the impact of self-
explanation prompts on calculus learning outcomes,
student engagement, and confidence levels.
Ethical Considerations: The study adhered to ethical
guidelines, obtaining informed consent from all
participants
and
ensuring
the
privacy
and
confidentiality of their data throughout the research
process.
By adhering to this comprehensive methodological
framework, we endeavored to gain valuable insights
into the potential benefits of self-explanation prompts
for
enhancing
calculus
education,
ultimately
contributing to the attainment of calculus mastery
among learners.
RESULTS
The results of our study on the impact of self-
explanation prompts on calculus mastery revealed
several key findings:
Improved Academic Performance: The experimental
group, which received guided self-explanation
prompts
during
their
calculus
instruction,
demonstrated significantly higher scores on both
assignments and examinations compared to the
control group. This improvement in academic
performance suggests that the use of self-explanation
prompts can positively influence students' ability to
grasp and apply calculus concepts.
Increased Engagement: Self-report surveys indicated
that students in the experimental group reported
higher levels of engagement with the course material.
They expressed a greater sense of involvement and
interest in solving calculus problems, which could be
attributed to the prompts encouraging active
reflection and deeper understanding.
Enhanced Confidence: Students in the experimental
group reported increased confidence in their calculus
abilities. The process of self-explanation prompted
them to confront their difficulties and uncertainties,
ultimately leading to a greater sense of self-
assuredness in tackling complex calculus problems.
Positive Perceptions of Prompts: When asked about
their perceptions of the self-explanation prompts, the
majority of students in the experimental group found
them valuable for their learning process. They
appreciated the prompts as tools that helped them
clarify their thinking and gain a deeper grasp of calculus
concepts.
DISCUSSION
The results of our study provide compelling evidence
that self-explanation prompts have a substantial impact
on calculus learning and the attainment of calculus
mastery. These findings have several implications:
Promoting Active Learning: Self-explanation prompts
encourage students to engage actively with calculus
problems by articulating their thought processes. This
active
learning
approach
fosters
a
deeper
understanding of the subject matter and may be
particularly beneficial for complex and abstract topics
like calculus.
Building Confidence: The increased confidence reported
by students in the experimental group suggests that the
process of self-explanation helps them confront and
overcome challenges. As students become more self-
assured in their abilities, they may be more willing to
tackle advanced calculus concepts.
Enhancing Engagement: Higher levels of engagement
among students in the experimental group suggest that
the inclusion of self-explanation prompts makes
calculus learning more enjoyable and motivating. This
engagement is vital for sustained learning and may
contribute to higher retention rates in calculus courses.
Valuable Pedagogical Tool: The positive perceptions of
self-explanation prompts by students underscore their
potential as a valuable pedagogical tool. Instructors may
consider integrating these prompts into their calculus
courses to enhance learning outcomes.
Future Directions: While our study provides significant
insights, future research could explore the long-term
effects of self-explanation prompts on calculus
proficiency and investigate their applicability in various
calculus
curricula
and
instructional
settings.
Additionally, exploring the role of individual differences
in responding to self-explanation prompts could offer
valuable insights into personalized education.
CONCLUSION
In the pursuit of calculus mastery, this study embarked
on a journey to explore the potential of self-explanation
prompts as a transformative force in calculus education.
The results of our investigation reveal that these
prompts hold the key to empowering learning,
enhancing understanding, and fostering calculus
proficiency.
Our findings illustrate that the inclusion of self-
explanation prompts in calculus instruction has a
significant and positive impact on students' academic
performance, engagement, and confidence. The
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The American Journal of Social Science and Education Innovations
experimental group, exposed to these prompts,
consistently outperformed their peers in the control
group. This improvement not only signifies a deeper
comprehension of calculus concepts but also suggests
that self-explanation prompts enable students to apply
their knowledge effectively.
Moreover, the increased engagement observed among
students in the experimental group underscores the
transformative potential of self-explanation prompts.
These prompts have the capacity to turn calculus into
more than just a set of abstract formulas and rules;
they make it an engaging, dynamic, and participatory
experience. Students' active reflection on their
problem-solving processes promotes a deeper
connection with the subject matter, sparking curiosity
and motivation to explore calculus further.
The boost in confidence reported by students who
engaged with self-explanation prompts is equally
noteworthy. As students learn to articulate their
thoughts and confront the intricacies of calculus, they
develop a greater sense of self-assuredness in their
abilities. This newfound confidence is a catalyst for
further exploration and mastery, transforming learners
into proactive and self-reliant problem solvers.
Incorporating the feedback and perceptions of
students, it is evident that self-explanation prompts
are not only effective but also well-received. They are
regarded as valuable tools that facilitate learning and
illuminate the path to calculus mastery. Instructors are
encouraged to consider integrating self-explanation
prompts into their calculus curricula to elevate the
educational experience and outcomes for their
students.
As we conclude this journey of exploration into the
realm of calculus education, it becomes clear that self-
explanation prompts have the potential to reshape the
landscape of calculus instruction. They empower
learners to conquer the challenges of this intricate
subject, unlocking a deeper understanding and
proficiency that will serve them well in diverse
academic and professional pursuits.
In the broader context of education, the success of
self-explanation prompts in calculus encourages us to
explore their application in other domains and
subjects, ushering in a new era of pedagogical
innovation. Through
continued research and
thoughtful integration, educators can empower
learners to not only master calculus but also become
critical thinkers and problem solvers, prepared to meet
the challenges of an ever-evolving world.
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