ABSTRACT
This study was conducted to determine the Effectiveness of Concrete-Pictorial-Abstract (CPA) Approach to Improve Number Sense of Grade 2 Learners in Dr. H. Serafica Elementary School, in Brgy. Bayog, Elementary School. The findings of the study were the bases for the proposed Enhancement Plan. This study employed a quantitative research design, specifically a quasi-experimental pretest-posttest control group design, to determine the effectiveness of the Concrete-Pictorial-Abstract (CPA) approach on the number sense of Grade 2 learners. The design was suitable because it allowed for the comparison of learning outcomes between students exposed to the CPA approach (experimental group) and those taught using traditional methods (control group), while assessing the impact of the intervention over time. In this design, the independent variable was the instructional approach, represented by the use of the CPA method, while the dependent variable was the number sense of the learners, measured through their performance on pretests and posttests. By administering a pretest, the researcher established a baseline for each group and controlled for pre-existing differences in mathematical ability.
The posttest, administered after the intervention, measured the improvement in learners’ number sense, allowing for a clear evaluation of CPA’s effectiveness. The experimental group received mathematics instruction using the CPA approach, beginning with concrete manipulatives, followed by pictorial representations, and culminating in abstract numerical problems. The control group followed the regular mathematics curriculum without the structured CPA intervention. This comparison ensured that any observed differences in learning outcomes could be attributed to the CPA approach rather than external factors.
The Test of Difference Between Pre-Test and Post-Test Scores of Learners shows the comparison of learners’ performance before and after the instructional intervention. The table provides information on pre-test and post-test results, the computed statistical value, the critical value, the decision regarding the null hypothesis, and the interpretation of the findings. It is designed to evaluate the effectiveness of the instructional approach in improving learners’ comprehension and overall academic performance. As reflected in the table, learners initially demonstrated a moderate level of readiness, with many requiring review and reinforcement before the intervention. After the implementation of the instructional strategy, the post-test results showed a significant increase, indicating that learners achieved mastery of the content.
The noticeable improvement between pre-test and post-test performance demonstrates that the intervention effectively enhanced learners’ skills and understanding, highlighting the positive impact of structured teaching approaches on academic outcomes. The statistical analysis indicated that the difference between pre-test and post-test performance was significant, leading to the rejection of the null hypothesis. This confirms that the improvement in learners’ performance was not due to chance. The interpretation clearly indicates a significant improvement in learners’ performance, validating that the instructional strategy successfully addressed learning gaps and strengthened comprehension abilities. The results imply that the instructional intervention had a meaningful and positive effect on learners’ academic performance. The overall average rating in the post-test reflects a marked improvement from the initial assessment, suggesting that the intervention successfully elevated learners’ readiness and mastery of the content. The result implies that the teaching strategy effectively enhanced learners’ understanding, problem-solving skills, and overall confidence in applying learned concepts.
Keywords: Effectiveness, Concrete-pictorial-abstract approach, Number Sense, Grade 2
INTRODUCTION
The Concrete-Pictorial-Abstract (CPA) approach is an instructional strategy that sequentially guides learners from hands-on, tangible experiences to visual representations, and finally to abstract mathematical symbols and operations. In relation to the development of number sense, this approach is particularly effective because it allows learners to build a deep understanding of numbers and their relationships rather than relying on rote memorization. At the concrete stage, learners manipulate physical objects such as base-ten blocks, counters, or unifix cubes, enabling them to internalize concepts such as place value, addition, and subtraction. The pictorial stage then bridges the concrete and abstract by encouraging learners to draw diagrams, use number lines, or create ten frames, helping them visualize mathematical relationships. Finally, in the abstract stage, learners apply conventional mathematical symbols and algorithms with confidence, as they have a strong conceptual foundation. This progression fosters flexibility, estimation skills, and relational understanding, which are key components of number sense, allowing learners to not only perform calculations but also understand the “why” behind the operations.
Qi Lin (2022) investigated the effect of distributed leadership and teacher autonomy on professional collaboration, emphasizing how clear communication and structured guidance enhance understanding and productivity in learners. While this study focused on leadership in schools, the findings resonate with the CPA approach in mathematics education, as structured, step-by-step scaffolding enhances learners’ ability to internalize concepts and apply knowledge effectively. Lin found that progressive, scaffolded guidance enabled learners to develop autonomy and confidence, which parallels how the CPA approach builds strong number sense: starting with manipulatives, progressing to visual models, and culminating in abstract reasoning. This literature underscores the importance of deliberate, structured approaches in teaching, whether in leadership or mathematics, to improve performance and conceptual understanding (Lin, 2022).
From the researcher’s perspective, several strategies can enhance the development of number sense, including manipulatives, visual aids, mental math exercises, and problem-solving tasks. Among these, the CPA approach stands out as it integrates all these strategies within a sequential framework that aligns with learners’ cognitive development. Concrete experiences with physical objects anchor understanding, pictorial representations enhance visualization and internalization, and abstract symbols allow learners to generalize concepts and perform operations efficiently. The researcher observes that students taught through CPA demonstrate higher engagement, better conceptual understanding, and increased confidence in mathematics compared to students taught using traditional, abstract-first methods.
Despite its effectiveness, implementing the CPA approach is not without challenges, which can affect learners’ academic performance in mathematics. Time constraints pose a significant difficulty, as concrete and pictorial activities require more classroom time than traditional methods. Limited resources, such as insufficient manipulatives, create barriers to hands-on learning. Additionally, some learners initially resist the CPA approach, perceiving manipulatives as “play” rather than real mathematics, which can hinder engagement and understanding. Teacher preparedness is also critical; educators without proper training may fail to facilitate the transitions between concrete, pictorial, and abstract stages, leading to misconceptions or incomplete understanding. Parental skepticism can further complicate the process, as parents accustomed to traditional methods may undervalue the hands-on activities essential to building number sense.
Pursuing this study on the CPA approach is essential to address the gaps in learners’ number sense and mathematics achievement. By examining how sequential, scaffolded instruction impacts conceptual understanding and problem-solving skills, the study aims to provide empirical evidence supporting effective teaching strategies. It also seeks to inform educators, school administrators, and policymakers about best practices in mathematics instruction, ultimately contributing to improved student engagement, academic performance, and long-term mathematical fluency. The findings of this study will help bridge the gap between abstract mathematical instruction and meaningful, intuitive understanding, reinforcing the importance of the CPA approach as a cornerstone of effective mathematics education.
This study was conducted to determine the Effectiveness of Concrete-Pictorial-Abstract (CPA) Approach to Improve Number Sense of Grade 2 Learners in Dr. H. Serafica Elementary School, in Brgy. Bayog, Elementary School. The findings of the study were the bases for the proposed Enhancement Plan.
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