THE USA JOURNALS
THE AMERICAN JOURNAL OF APPLIED SCIENCES (ISSN
–
2689-0992)
VOLUME 06 ISSUE10
27
https://www.theamericanjournals.com/index.php/tajas
PUBLISHED DATE: - 17-10-2024
https://doi.org/10.37547/tajas/Volume06Issue10-06
PAGE NO.: - 27-29
IDENTITIES. PEDAGOGICAL METHODS FOR
TEACHING SHORT MULTIPLICATION
FORMULAS
Ergasheva Fotima Erkinovna
JSPU Academic Lyceum, Mathematics teachers, Uzbekistan
Egamberdiyeva Mohinur Fahriddin qizi
JSPU Academic Lyceum, Mathematics teachers, Uzbekistan
INTRODUCTION
Algebra forms the foundation for advanced
mathematical thinking, and within algebra,
identities such as short multiplication formulas are
essential tools. These formulas, including well-
known expressions like (a+b)2=a2+2ab+b2 and
(a−b)(a+b)=a2−b2, are used extensively in
problem-solving. Despite their importance, many
students struggle to internalize and apply these
formulas effectively. This paper investigates
pedagogical methods that can enhance students'
understanding
and
retention
of
short
multiplication formulas, with a focus on the
secondary and early tertiary education levels.
The aim of this study is to identify and evaluate
effective teaching strategies, comparing traditional
methods with more interactive approaches. We
hypothesize that active learning techniques, such
as problem-based learning (PBL) and the use of
visual aids, will lead to improved comprehension
and application of these formulas.
METHODS
Study Design
This research utilized a mixed-methods approach,
combining quantitative assessments of student
performance with qualitative feedback from
RESEARCH ARTICLE
Open Access
Abstract
THE USA JOURNALS
THE AMERICAN JOURNAL OF APPLIED SCIENCES (ISSN
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2689-0992)
VOLUME 06 ISSUE06
28
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students and teachers. The study was conducted
over a 12-week period in two secondary school
classrooms, each containing approximately 30
students. One classroom followed a traditional
lecture-based teaching method, while the other
employed a combination of interactive techniques,
including problem-based learning, group work,
and visual demonstrations.
Participants
Participants were secondary school students, aged
15-17, from two comparable classrooms. Both
groups had similar academic backgrounds and
previous exposure to algebraic topics. Teachers
involved in the study had over five years of
experience teaching mathematics at the secondary
level.
Teaching Methods
•
Traditional Method: This group received
standard lecture-based instruction with the
teacher explaining short multiplication formulas
and solving examples on the blackboard.
•
Interactive Method: This group was introduced to
short multiplication formulas through a problem-
based learning approach, supplemented by visual
aids like algebra tiles and digital simulations.
Students were encouraged to work in groups and
discover the identities by solving real-world
problems.
Data Collection
Data were collected through the following
instruments:
•
Pre- and Post-Tests: Standardized tests
measuring students' understanding of short
multiplication formulas before and after the
intervention.
•
Classroom Observations: To record student
engagement, teacher-student interactions, and
overall classroom dynamics.
•
Questionnaires: Administered to both students
and teachers to gather qualitative feedback on the
effectiveness of the teaching methods.
Data Analysis
Quantitative data from the pre- and post-tests were
analyzed using paired t-tests to assess
improvement in student performance. Qualitative
data from questionnaires and classroom
observations were thematically analyzed to
identify recurring patterns and insights related to
student engagement and perception of the teaching
methods.
RESULTS
Quantitative Findings
The average score improvement in the post-test
was significantly higher for the interactive group
compared to the traditional group. The mean score
for the traditional group improved by 12%, while
the interactive group showed a 28% improvement
(p < 0.05). This suggests that students who engaged
with problem-solving and visual tools had a better
grasp of short multiplication formulas.
Qualitative Findings
Students in the interactive group reported feeling
more
engaged
and
confident
in
their
understanding of algebraic identities. They found
the
visual
aids
particularly
helpful
in
conceptualizing how the formulas worked.
Teachers also noted that group discussions helped
students clarify their doubts more effectively. In
contrast, the traditional group expressed a more
passive learning experience, with some students
struggling to retain the formulas.
Classroom Observations
In the interactive classroom, students were more
likely to ask questions and engage in peer
discussions. The traditional classroom, however,
saw fewer interactive moments, with most
students
taking
notes
without
actively
participating.
DISCUSSION
The results of this study support the hypothesis
that interactive pedagogical methods, particularly
problem-based learning and the use of visual aids,
enhance students' comprehension of short
multiplication formulas. These methods encourage
active engagement and help demystify abstract
algebraic concepts. The significant improvement in
test scores among students exposed to interactive
teaching further emphasizes the value of this
THE USA JOURNALS
THE AMERICAN JOURNAL OF APPLIED SCIENCES (ISSN
–
2689-0992)
VOLUME 06 ISSUE06
29
https://www.theamericanjournals.com/index.php/tajas
approach.
One of the main challenges of traditional methods
is their reliance on rote learning, which may hinder
long-term retention. In contrast, problem-based
learning allows students to apply the formulas in
various contexts, reinforcing their understanding.
The use of visual aids also plays a critical role in
helping students visualize the identities, making
abstract concepts more concrete.
However, the study has limitations. The sample
size was relatively small, and the study focused on
short-term performance gains. Future research
should explore the long-term effects of these
teaching methods and their applicability in
different educational settings.
CONCLUSION
This study demonstrates that interactive teaching
methods, such as problem-based learning and
visual aids, are effective tools for improving
students' understanding of short multiplication
formulas. These methods foster a more engaging
and collaborative learning environment, which
enhances students' problem-solving skills and
conceptual
grasp of algebraic identities.
Implementing these strategies in secondary and
tertiary education could significantly improve the
quality of algebra instruction, leading to better
student outcomes.
REFERENCES
1.
Baroody, A. J. (2017). "Algebraic Reasoning in
the Classroom: A Teacher's Guide to Helping
Students Understand Algebraic Concepts."
Journal of Educational Psychology, 109(3),
472-488.
2.
Hiebert, J., & Grouws, D. A. (2007). "The Effects
of Classroom Instruction on Mathematical
Understanding." In F. K. Lester (Ed.), Second
Handbook of Research on Mathematics
Teaching and Learning (pp. 371-404). National
Council of Teachers of Mathematics.
3.
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J.
M. (2019). "Elementary and Middle School
Mathematics: Teaching Developmentally."
Pearson Education.
