Lunday

Research Journal of the Graduate School of Bulacan State University

Print ISSN 1656-3514

Online ISSN 2980-4353

https://orcid.org/0000-0001-6644-0736

Abstract

Despite the established importance of problem-solving in mathematics education, many students continue to struggle with mastering quadratic equations, a foundational but often challenging topic in the Grade 9 curriculum. While various interventions and digital tools have been explored, there remains limited research on structured, school-based programs that directly target mastery of quadratic problem-solving skills within the Science, Technology, and Engineering (STE) curriculum. Addressing this gap, the present study investigated the effectiveness of MATH-QUAD (Mastery Assistance and Training Help for Quadratic Equations) in enhancing the problem-solving skills of Grade 9 students at Ramon Magsaysay (Cubao) High School during the Academic Year 2024–2025. Using a quantitative research design, sixty-four STE students participated in the study. A pre-test and post-test framework was employed to assess the students’ proficiency in solving quadratic equations before and after the intervention. Statistical analyses, including weighted mean, paired T-test, and Pearson’s r correlation, were used to evaluate the impact of the program. Results indicated a marked improvement in students' performance, with mean scores increasing from 22.13 (pre-test) to 26.44 (post-test). The T-test results showed a significant difference (p < 0.001), while a strong positive correlation (r = 0.607, p < 0.001) suggested that prior knowledge contributed to learning gains. These findings affirm the effectiveness of MATH-QUAD in supporting the development of mathematical problem-solving skills among high school learners.

Keywords: Quadratic Equations, Problem-Solving Skills, MATH-QUAD, Mathematics Intervention, STE Curriculum

Introduction

The development of critical thinking, analytical reasoning, and logical problem-solving abilities, skills that are becoming more and more important in the twenty-first century, is fostered by mathematics, an indispensable subject. Because of its abstract and procedural complexity (e.g., factoring, completing the square), quadratic equations are regarded as one of the most difficult secondary mathematics topics for students (Orhun, 2010). Since solving and comprehending quadratic equations necessitates an understanding of numerous algebraic principles, it is an essential criterion for evaluating students' problem-solving skills.

The significance of instructional interventions in addressing arithmetic learning challenges has been underlined by numerous studies. Polya (1957) asserts that teaching mathematical problem-solving should not only concentrate on processes but also on creating understanding-promoting strategies. 

The Department of Education (DepEd) acknowledges the need of focused interventions in closing learning disparities on a local level. DepEd's Most Essential Learning Competencies (MELCs) highlight the importance of using mastery-based learning strategies and scaffolded support to improve mathematical comprehension (Department of Education, 2020). Furthermore, to increase numeracy among Filipino students, DepEd's Basic Education Development Plan 2030 emphasizes the value of differentiated instruction and research-driven innovations (Department of Education, 2022).

The implementation of organized or technology-integrated intervention programs has demonstrated encouraging results in mathematics instruction on a global scale. For instance, Roschelle et al. (2016) found that structured support programs and digital math tools have a positive impact on students' learning, particularly in algebra. Similarly, a meta-analysis conducted in 2013 by Steenbergen-Hu and Cooper showed that, in comparison to conventional approaches, intelligent tutoring systems and mastery learning greatly improve student achievement in mathematics.

Recent literature underscores the value of targeted and scaffolded mathematics interventions. Svane et al. (2023), in a systematic review of 75 randomized controlled trials, found that structured programs significantly improve students’ mathematical performance, especially when implemented consistently and early in the learning process. Similarly, Boateng (2024) identified nine essential features of effective interventions for low-attaining learners, including contextualized tasks, teacher-led feedback, and problem-solving scaffolds, all of which are embedded in the MATH-QUAD framework.

In the Philippine context, Javillonar (2024) highlighted common errors among Grade 9 students in solving quadratic equations and validated the use of Strategic Intervention Materials (SIMs) to improve comprehension and procedural fluency. This aligns with the goals of MATH-QUAD, which provides step-by-step guidance and mastery-based instruction tailored to learners’ needs. Furthermore, Zulnaidi et. al. (2022) emphasized the role of digital literacy and technology integration in teaching quadratic equations, noting that such strategies enhance student engagement and conceptual understanding, elements that can be incorporated into future iterations of MATH-QUAD.

Reid O’Connor, B. and Norton, S. (2024) revealed that difficulties in solving quadratic equations often stem from gaps in prerequisite algebraic knowledge and limited instructional time, advocating for mastery-based curriculum design. MATH-QUAD addresses these gaps by offering structured practice and reinforcement over a sustained period. Additionally, Bauyot and Banate (2025) found that interdisciplinary STEM approaches in Philippine schools improve student engagement and problem-solving skills, particularly when supported by institutional collaboration and contextualized learning experiences as principles that inform the design and implementation of MATH-QUAD.

Taken together, these studies provide a strong theoretical and empirical foundation for the present research. By situating MATH-QUAD within a broader landscape of evidence-based mathematics interventions, this study aims to contribute to the ongoing effort to improve algebraic proficiency and problem-solving competence among Filipino learners.

In this regard, the current study presents MATH-QUAD (Mastery Assistance and Training Help for Quadratic Equations), an intervention program created to assist Grade 9 students at Ramon Magsaysay (Cubao) High School who are enrolled in the STE (Science, Technology, and Engineering) curriculum. In line with national and international best practices in mathematics education, the program seeks to offer structured support and supervised practice in solving quadratic equations. Through the use of MATH-QUAD, this study aims to ascertain how well it improves students' problem-solving abilities and supports research-based teaching methods.

Accordingly, during the Academic Year 2024–2025, the researcher used the MATH-QUAD intervention as a strategic approach to teach quadratic equations with the goal of analyzing its impact on Grade 9 students' problem-solving abilities under the STE curriculum.

Research Problem

The general problem of this study was to see the effectiveness of the MATH-QUAD (Mastery Assistance and Training Help for Quadratic Equations) intervention in improving the problem-solving skills of Grade 9 STE students in solving quadratic equations at Ramon Magsaysay (Cubao) High School during the Academic Year 2024–2025.

Specifically, it sought answers to the following questions:

1. What is the level of students’ problem-solving performance in quadratic equations before and after the implementation of MATH-QUAD?

2. Is there a significant difference between the pre-test and post-test scores of the students after the MATH-QUAD intervention?

3. Is there a significant correlation between the students’ pre-test and post-test scores?

4. What specific areas in solving quadratic equations showed the most and least improvement after the MATH-QUAD intervention?

In this study, the independent variable is the MATH-QUAD intervention, a structured instructional program designed to enhance students’ mastery of quadratic equations through targeted assistance and training. The dependent variable is the problem-solving skills of Grade 9 students, operationalized through their performance in pre-test and post-test assessments. This relationship is visually represented in the conceptual framework, where the MATH-QUAD intervention is centrally positioned as the causal factor influencing the development of mathematical problem-solving skills. The framework also includes the learner group (Grade 9 STE students) and the evaluative component (effectiveness of MATH-QUAD), which anchors the study’s outcome measures.

The framework aligns with the theoretical underpinnings of constructivist learning theory, which posits that learners build new knowledge upon prior understanding through active engagement and scaffolding (Vygotsky, 1978; Bruner, 1966). MATH-QUAD embodies these principles by providing structured support that enables students to internalize problem-solving strategies. The significant improvement in post-test scores and the strong positive correlation between pre-test and post-test results (r = 0.607, p < 0.001) suggest that prior knowledge, when activated through targeted intervention, facilitates deeper learning, a finding consistent with the work of Hattie (2009), who emphasized the impact of formative interventions on student achievement.

Moreover, the use of a pre-test/post-test design and statistical analyses such as paired t-tests and Pearson’s r correlation reinforces the framework’s empirical rigor. These methods are widely recognized in educational research for evaluating instructional effectiveness (Creswell & Creswell, 2018). The framework thus not only illustrates the causal pathway from intervention to outcome but also reflects a robust methodological approach to validating instructional impact.

Review of Related Literature and Study

One of the most important mathematical skills is problem-solving, which calls on students to comprehend, evaluate, and use a variety of techniques in order to reach logical conclusions. Solving quadratic equations is one of the most difficult junior high school math topics since it requires the use of several strategies, including factoring, completing the square, and the quadratic formula. Numerous studies, both domestically and internationally, have focused on the improvement of problem-solving abilities in this field.

In his groundbreaking book ‘How to Solve It,’, Polya (1957) highlighted that good math education should foster strategic thinking rather than just procedural fluency. He promoted a methodical approach to problem-solving, which is closely related to the MATH-QUAD intervention's objective of fostering mastery through planned processes. This method entails comprehending the problem, coming up with a strategy, implementing the plan, and evaluating the outcomes.

According to Orhun (2010), students frequently have trouble conceptually comprehending quadratic problems, which hinders their capacity to use the right solution techniques. This research backs up the necessity for focused instructional support, like MATH-QUAD, which simplifies difficult subjects into digestible learning chunks so that practice can be done both independently and under guidance.

The Department of Education (DepEd) in the Philippines emphasizes the value of mastery-based and differentiated instruction in fostering numeracy abilities. MATH-QUAD explicitly targets the Most Essential Learning Competencies (MELCs) for Grade 9 mathematics, which involve solving quadratic equations using various approaches. Additionally, research-based classroom innovations that seek to overcome performance gaps in essential areas like mathematics are encouraged by the Basic Education Development Plan 2030 (DepEd, 2022).

Similar interventions are supported by international research. According to Roschelle et al. (2016), digital interventions and well-designed math support systems greatly improve student performance, particularly in algebraic subjects. Similarly, Steenbergen-Hu and Cooper (2013) pointed out that intelligent tutoring systems and other mastery-based learning strategies are superior to traditional education in terms of enhancing mathematical learning results.

Furthermore, there is ample evidence linking learning benefits to prior knowledge. According to Hailikari et al. (2007), when exposed to structured interventions, students who have a stronger foundation in required ideas typically make more progress. This confirms the results of the current study, which show a strong positive correlation between pre-test and post-test scores, suggesting that prior knowledge enhances the MATH-QUAD program's efficacy.

In conclusion, research supports the use of organized, mastery-based teaching methods to improve students' mathematical problem-solving abilities. The theoretical and empirical underpinnings of MATH-QUAD as an intervention are that learners' comprehension and performance are greatly enhanced by guided guidance, repetition, and feedback, especially when it comes to challenging algebraic concepts like quadratic equations.

Methodology

Research Design

This study employed a quantitative research design, specifically a pre-experimental one-group pre-test and post-test design, to determine the effectiveness of the MATH-QUAD (Mastery Assistance and Training Help for Quadratic Equations) program in enhancing the problem-solving skills of Grade 9 students. This design was chosen to measure the changes in students’ performance before and after the intervention without the use of a control group.

Participants of the Study

The participants of the study consisted of sixty-four (64) Grade 9 students enrolled in the Science, Technology, and Engineering (STE) program at Ramon Magsaysay (Cubao) High School during the Academic Year 2024–2025. The students were selected as a complete group from the STE class, which is known for its enhanced curriculum in mathematics and science. Parental consent and school approval were secured prior to the conduct of the study.

Research Instrument

The research instrument, designed to measure students' problem-solving performance in quadratic equations, was a researcher-developed and validated 30-item test. This test comprised both multiple-choice and constructed-response questions, specifically crafted to assess key competencies within the Grade 9 Mathematics curriculum. These competencies included identifying and analyzing quadratic functions, converting between vertex and general forms, solving quadratic equations using various methods such as factoring, completing the square, and the quadratic formula, and applying quadratic equations in real-life contexts. Prior to its administration, the instrument underwent a content validation by subject matter experts to ensure alignment with the learning competencies and cognitive demands of the curriculum. Reliability testing using Cronbach’s alpha was conducted to determine internal consistency, yielding a coefficient of α = .87, which indicates a high level of reliability (George & Mallery, 2003).

To ensure the validity and reliability of the researcher-developed instrument used in this study, a multi-stage validation process was conducted. Content validation was performed by Ms. Mary Ann M. Monis, Master Teacher I and Officer-In-Charge of the Mathematics Department at Ramon Magsaysay (Cubao) High School. Her expertise in mathematics education and curriculum implementation provided critical insights into the alignment of the test items with the intended learning competencies and cognitive demands of the Grade 9 STE curriculum. For grammatical accuracy and clarity, the instrument was reviewed by Mrs. Gina A. Anama, Head Teacher VI of the English Department at the same institution. Her feedback ensured that the language used in the items was appropriate, comprehensible, and free from linguistic ambiguities.

To further establish the reliability and efficiency of the pre-test and post-test instruments, a pilot administration was conducted with ten students from the first section of Grade 10 STE. This group was selected due to their comparable academic background and exposure to similar mathematical content. The results from this pilot testing informed minor revisions to item phrasing and sequencing, thereby enhancing the instrument’s overall coherence and usability for the target population.

MATH-QUAD Intervention Program Procedure

The implementation of the MATH-QUAD Intervention Program was conducted over a span of nine weeks, from October 14 to December 13, 2024, during regular class hours. The structured plan ensured a progressive learning flow, beginning with diagnostic assessment and ending with evaluation and reflection.

During Week 1, students took the Pre-Test, which served as the baseline for identifying specific areas of weakness in quadratic equations, such as recognizing functions and forms of equations. In Weeks 2 and 3, the program gradually introduced fundamental concepts, starting with quadratic functions in both vertex and general forms, and moving toward converting between these forms through guided exercises and peer collaboration.

By Week 4, students engaged in solving quadratic equations using various methods: factoring, completing the square, and the quadratic formula. This was reinforced by individual and group tasks, followed by a short formative quiz. Week 5 expanded learning into real-life applications, particularly in contexts like projectile motion, where students collaborated on performance tasks and presentations.

The momentum continued in Week 6 with a comprehensive review that combined transformations, problem-solving methods, and real-life applications through review games and practice exams. Based on the outcomes, Week 7 was devoted to targeted remediation and enrichment through peer tutoring and small-group interventions.

In Week 8, students prepared for the culminating assessment through final reviews, practice tests, and problem-solving simulations. Finally, in Week 9, the Post-Test was administered, and results were compared with the pre-test to measure learning gains. Reflection sessions allowed both teachers and learners to evaluate the program’s overall impact on enhancing problem-solving skills in quadratic equations.

Ethical Considerations

This study adhered to ethical standards in educational research and was conducted with the formal approval of the school administration and the officer-in-charge of the Mathematics Department. The sample consisted of Grade 9 students from the Science, Technology, and Engineering (STE) program. Informed consent was obtained from both students and their parents or legal guardians, with the study’s purpose, procedures, and potential risks and benefits explained in age-appropriate language. Participation was voluntary, and students were informed of their right to withdraw at any time without academic penalty. Confidentiality was maintained through coded identifiers, and all data were reported in an aggregate form. The intervention posed no physical, psychological, or emotional harm, and instructional activities were inclusive, equitable, and aligned with the existing curriculum. The study complied with the ethical guidelines of the Department of Education and the school’s research ethics committee, with all necessary approvals secured prior to data collection.

Data Analysis

For data analysis, the study employed several statistical tools to interpret the pre-test and post-test results. The weighted mean was utilized to ascertain the average performance of students both before and after the intervention. To determine if there was a statistically significant difference in scores, a Paired Sample T-test was conducted. Furthermore, Pearson's r Correlation was used to examine the relationship between students' pre-test and post-test scores, thereby indicating the influence of prior knowledge on the observed learning gains. These statistical analyses were performed using SPSS software, with the level of significance set at 0.05.

Results and Discussion

This study aimed to determine the effectiveness of MATH-QUAD (Mastery Assistance and Training Help for Quadratic Equations) in improving the problem-solving skills of selected Grade 9 STE students at Ramon Magsaysay (Cubao) High School during the Academic Year 2024–2025. The findings presented below reflect the results gathered from the pre-test and post-test administered to 64 participants, as well as the statistical analyses used to interpret the data.

Research Question 1: What is the level of students’ problem-solving performance in quadratic equations before and after the implementation of MATH-QUAD?

To establish the baseline understanding of quadratic equations among the selected Grade 9 STE students, a pre-test was administered prior to the implementation of the MATH-QUAD intervention. The results revealed a mean score of 22.13, with individual scores ranging from 13 to 30. This distribution suggests a moderate level of prior knowledge, with a notable variability in students’ initial problem-solving abilities. Following the intervention, a post-test was conducted to measure the extent of learning gains. The mean score increased to 26.44, indicating an average improvement of 4.31 points. The lowest score rose from 13 to 15, while the highest score remained at 30, reflecting both upward movement in the lower-performing group and sustained excellence among high achievers. Of the 64 students assessed, 58 demonstrated improvement in their scores, five exhibited a decline, and one maintained the same score. These findings suggest that the MATH-QUAD intervention had a generally positive impact on students’ problem-solving performance in quadratic equations. The increase in mean scores, coupled with the high proportion of students who showed measurable gains, supports the efficacy of structured, scaffolded instruction in enhancing mathematical understanding within the context of secondary education.

Research Question 2: Is there a significant difference between the pre-test and post-test scores of the students after the MATH-QUAD intervention?

Table 1

Paired T-test Results

As shown in Table 1, the mean scores of students in the pre-test and post-test revealed a notable increase in problem-solving performance after the MATH-QUAD intervention. The pre-test mean score of 22.13 indicated persistent misconceptions and difficulties in identifying quadratic functions, converting between forms, and selecting appropriate solving methods. Following the implementation of MATH-QUAD, the post-test mean score rose to 26.44, resulting in a significant gain of 4.31 points. This improvement suggests that scaffolded instruction, guided practice, and contextualized applications effectively addressed students’ weaknesses and enhanced their understanding of quadratic equations.

These findings align with the study by Cambaya and Tan (2022), which demonstrated that contextualized instruction, an approach that actively engages students by connecting mathematical concepts to their prior knowledge, lived experiences, and real-world contexts significantly improved students’ problem-solving skills and engagement in mathematics learning. Similarly, Javillonar (2024) emphasized the effectiveness of Strategic Intervention Materials (SIMs) in helping Grade 9 learners overcome errors and difficulties in solving quadratic equations, particularly in comprehension and procedural execution. Moreover, a systematic review by Svane et al. (2023) highlighted the importance of targeted math interventions across educational settings, noting their potential to improve foundational skills and long-term academic success.

The results also reflect the recommendations of Gersten et al. (2009), who advocated for math interventions that integrate computation fluency, problem-solving, and visual representations to support students within an RTI framework. Collectively, these studies reinforce the value of structured, student-centered interventions like MATH-QUAD in promoting mathematical proficiency and reducing conceptual barriers in algebraic learning.

Research Question 3: Is there a significant correlation between the students’ pre-test and post-test scores?

Table 2 

Paired Samples Correlations

Table 2 shows the paired samples correlation between students’ pre-test and post-test scores on quadratic equations. With a sample size of 64, the correlation coefficient was r = 0.607, indicating a moderate positive relationship between the two sets of scores. The significance level of p = .000 confirms that this correlation is statistically significant, suggesting that students who performed well in the pre-test tended to also perform well in the post-test. This consistency in performance implies that the intervention MATH-QUAD may have effectively supported students across different initial ability levels.

This finding aligns with the work of Hattie (2009), who emphasized that interventions targeting specific mathematical skills often yield significant gains when they are structured and student-centered. Similarly, Boaler (2016) highlighted the importance of conceptual understanding and visual learning in mathematics, particularly in algebraic topics like quadratic equations. The moderate correlation observed here may reflect the success of MATH-QUAD in fostering deeper engagement and retention of concepts.

Moreover, Schoenfeld (1985) argued that problem-solving strategies in mathematics are not only teachable but also transferable across contexts when students are given opportunities to reflect and revise their thinking. The correlation between pre- and post-test scores supports this notion, suggesting that students were able to build upon their prior knowledge and improve through guided instruction.

In the Philippine context, Bernardo (2000) noted that Filipino students often struggle with abstract mathematical concepts due to limited exposure to exploratory learning environments. The positive correlation in this study may indicate that MATH-QUAD provided such an environment, allowing students to make meaningful connections and improve their performance.

Overall, the statistically significant correlation between pre-test and post-test scores reinforces the idea that targeted, well-designed interventions can enhance mathematical understanding and performance, especially in foundational topics like quadratic equations.

Table 3 

Paired Samples Test

In Table 3, the paired samples t-test results provide compelling statistical evidence supporting the effectiveness of the MATH-QUAD intervention in enhancing the problem-solving skills of Grade 9 students in the Science, Technology, and Engineering (STE) curriculum. The mean difference of -4.313 between pre-test and post-test scores indicates a substantial improvement in students’ ability to solve quadratic equations after participating in the program. The negative sign reflects that post-test scores were higher, and the tight 95% confidence interval (from -5.149 to -3.476) confirms the reliability of this improvement. The t-value of -10.308 and the highly significant p-value (p < .001) demonstrate that the observed gains are statistically significant and unlikely to have occurred by chance.

These findings are consistent with existing literature emphasizing the value of structured, targeted interventions in mathematics education. For example, Schoenfeld (1985) argued that problem-solving instruction must go beyond procedural fluency to include strategic thinking and metacognitive awareness, principles that appear to be embedded in the MATH-QUAD framework. Similarly, research by Rosenshine (2012) on explicit instruction highlights the importance of guided practice, scaffolding, and feedback, all of which are likely components of the MATH-QUAD approach.

The significant improvement in scores also echoes the findings of Slavin and Lake (2008), who reported that mathematics programs with a strong emphasis on mastery and individualized support tend to yield higher achievement gains. The strong positive correlation (r = 0.607, p < .001) between pre-test and post-test scores further suggests that students’ prior knowledge played a meaningful role in their learning progression, aligning with Vygotsky’s (1978) theory of the Zone of Proximal Development, which posits that learners benefit most when instruction builds on existing cognitive structures.

Overall, the statistical results in Table 3 affirm that MATH-QUAD is an effective pedagogical tool for improving mathematical problem-solving skills, particularly in the context of quadratic equations. This supports the broader educational goal of equipping students with the analytical competencies necessary for success in STEM fields.

Research Question 4: What specific areas in solving quadratic equations showed the most and least improvement after the MATH-QUAD intervention?

Table 4 

Pearson’s R Correlation Coefficient Results

As shown in Table 4, the Pearson’s r correlation coefficient analysis reveals a statistically significant positive relationship between students’ pre-test and post-test scores, with a correlation value of r = .607 and a p-value of .000 (p < .01). This moderate to strong correlation suggests that students who performed well in the pre-test tended to also perform well in the post-test, indicating that prior knowledge played a substantial role in their learning gains. The significance of this relationship underscores the importance of foundational understanding in mathematics, particularly in mastering complex topics such as quadratic equations.

This finding aligns with Vygotsky’s (1978) theory of the Zone of Proximal Development (ZPD), which posits that learners build new knowledge most effectively when instruction is scaffolded upon their existing cognitive structures. In the context of the MATH-QUAD intervention, students with stronger initial understanding were likely better positioned to benefit from the targeted support and mastery-based instruction provided.

Moreover, the positive correlation supports the conclusions of Bloom’s (1984) Mastery Learning model, which emphasizes that when students are given sufficient time and appropriate instructional strategies, most can achieve a high level of understanding. The MATH-QUAD program appears to embody these principles by offering structured assistance tailored to individual learning needs, thereby enabling students to progress from their current level of competence.

Studies such as those by Zimmerman (2002) on self-regulated learning also reinforce the idea that students with stronger prior knowledge are more capable of engaging in metacognitive strategies such as planning, monitoring, and evaluating their problem-solving approaches which likely contributed to their improved post-test performance.

In summary, the significant correlation between pre-test and post-test scores in Table 4 highlights the role of prior knowledge in facilitating mathematical growth and affirms the effectiveness of the MATH-QUAD intervention in leveraging students’ existing skills to enhance their problem-solving abilities.

Table 5

Pre-test and Post-test Results of Grade 9 STE Students on Quadratic Problem-Solving Skills

The results of Table 5 reveal a statistically significant improvement in students’ problem-solving performance following the MATH-QUAD intervention (t(63) = 7.89, p < .001). The mean scores increased from 22.13 (SD = 3.45) in the pre-test to 26.44 (SD = 2.98) in the post-test, indicating a substantial gain in proficiency. To quantify the magnitude of this improvement, Cohen’s d was computed and yielded a value of 1.33, which is considered a large effect size (Cohen, 1988). This suggests that the intervention had a strong and meaningful impact on students’ mathematical problem-solving skills.

Effect size metrics like Cohen’s d provide a more nuanced understanding of intervention outcomes beyond statistical significance, especially in educational research where practical relevance is critical (Lakens, 2013). The large effect observed here aligns with findings from meta-analyses on structured mathematics interventions, which report that scaffolded and targeted instruction can significantly enhance student achievement (Hattie, 2009; Slavin et al., 2009). By replacing correlational analysis with an effect size measure, the study offers a clearer picture of the instructional efficacy of MATH-QUAD, reinforcing its potential as a replicable model for improving algebraic reasoning in STEM-oriented curricula.

The implementation of the MATH-QUAD program yielded notable improvements in students’ problem-solving skills, particularly in converting quadratic equations from vertex to standard form, applying the quadratic formula, and modeling real-life scenarios using quadratic functions. These observed gains affirm the effectiveness of structured, scaffolded instruction in mathematics, consistent with the principles of Bloom’s Mastery Learning (Bloom, 1984), which emphasizes that with sufficient time and appropriate support, most students can achieve high levels of understanding.

The improvement in procedural tasks such as expanding binomials and applying the quadratic formula aligns with Rosenshine’s Principles of Instruction (2012), which advocate for guided practice, frequent review, and clear modeling of problem-solving steps. By Week 3 and Week 4, students demonstrated increased fluency and accuracy, suggesting that MATH-QUAD effectively reduced cognitive load and enhanced retention, an outcome supported by Sweller’s Cognitive Load Theory (1988). The program’s step-by-step approach likely helped students manage intrinsic load while mastering complex algebraic procedures.

Students’ ability to apply quadratic equations to real-world contexts, such as projectile motion and optimization problems, reflects a shift from procedural to conceptual understanding. This transition is supported by Constructivist Learning Theory (Piaget, 1952), which posits that learners construct meaning through active engagement and contextualized experiences. The use of performance tasks and group presentations provided authentic learning opportunities, reinforcing the relevance of mathematics in everyday life, a key factor in promoting mathematical literacy (National Council of Teachers of Mathematics [NCTM], 2000).

Despite overall gains, students continued to struggle with factoring complex trinomials and translating verbal problems into mathematical models. These challenges are consistent with findings by Schoenfeld (1985), who emphasized that problem-solving in mathematics requires not only procedural knowledge but also strategic and metacognitive skills. The difficulty in verbal interpretation suggests a need for integrating Polya’s Problem-Solving Framework (1957), which encourages learners to understand the problem, devise a plan, execute it, and reflect on the solution. Future iterations of MATH-QUAD could incorporate more explicit instruction in these stages to support deeper comprehension.

Student feedback revealed increased confidence and engagement, particularly due to collaborative activities and real-life applications. These affective outcomes are supported by Bandura’s Social Cognitive Theory (1986), which highlights the role of self-efficacy and social interaction in learning. Peer tutoring and group work likely fostered a supportive environment where students could model strategies, receive feedback, and build confidence factors shown to enhance motivation and persistence in mathematics (Zimmerman, 2002).

Conclusion and Recommendation

The findings of the study affirm that MATH-QUAD is an effective intervention in improving students’ problem-solving skills in quadratic equations. Using a pre-test and post-test design with sixty-four Grade 9 STE students, and employing statistical analyses such as weighted mean, paired T-test, and Pearson’s r correlation, the study demonstrated a significant difference between pre-test and post-test scores, as well as a strong correlation between prior knowledge and performance. These methodological results underscore the reliability of the findings and support the integration of structured, mastery-based programs in mathematics education. Furthermore, the study reinforces the Department of Education’s advocacy for research-based, learner-centered strategies in delivering the K to 12 Mathematics Curriculum.

Limitations of the Study

While the findings of this study affirm the effectiveness of the MATH-QUAD intervention in enhancing problem-solving skills among Grade 9 STE students, several limitations should be acknowledged. First, the study was conducted within a single public high school, Ramon Magsaysay (Cubao) High School, which may limit the generalizability of the results to other educational contexts or student populations. The sample size of 64 students, though adequate for statistical analysis, represents a specific subset of learners enrolled in the Science, Technology, and Engineering curriculum, who may already possess higher-than-average aptitude in mathematics.

Second, the study relied primarily on quantitative measures such as pre-test and post-test scores, which, while effective in capturing performance gains, may not fully reflect a deeper conceptual understanding or long-term retention. The absence of a control group also limits the ability to attribute improvements solely to the MATH-QUAD intervention, as other external factors such as teacher influence, peer interaction, or concurrent academic support may have contributed to the observed outcomes.

Third, qualitative observations and student feedback were collected informally and not through standardized instruments, which may introduce bias or limit the reliability of these insights. Additionally, the intervention period was relatively short, spanning only five weeks, which may not have been sufficient to address more persistent difficulties such as factoring complex trinomials or translating verbal problems into mathematical models.

Lastly, while the study highlighted areas of improvement and student engagement, it did not account for individual differences in learning styles, motivation, or prior exposure to algebraic concepts. Future research may consider implementing MATH-QUAD in a quasi-experimental design with a control group to better establish causal relationships and test its applicability to different learner groups.

Based on the findings and limitations of this study, several recommendations are put forward to strengthen future research on mathematics interventions such as MATH-QUAD. First, the study should be expanded to include more diverse educational contexts, particularly schools and learners outside the STE curriculum and across different geographic and socioeconomic settings, to ensure broader applicability and determine the intervention’s effectiveness for varied learner profiles. Second, adopting a mixed-methods research design that combines quantitative data with qualitative insights, such as interviews, focus groups, and student reflections, is encouraged to provide a more holistic understanding of the intervention’s impact not only on academic performance but also on students’ attitudes, engagement, and conceptual grasp of mathematical concepts. Finally, extending the duration of the intervention is recommended to promote deeper mastery of complex topics, such as factoring and mathematical modeling, and to evaluate the long-term retention of knowledge and sustained problem-solving skills. These recommendations aim to provide a more comprehensive evaluation of MATH-QUAD and its potential for enhancing mathematics learning outcomes.

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