Subtracting Integers: A Challenge for Grade 7 Students and a Solution Through Strategic Intervention Material

Subtracting Integers: A Challenge for Grade 7 Students and a Solution Through Strategic Intervention Material

James Rafael B. Apsay, Yla Mae D. Batinga, Rex Isaac Noel D. Dumangas, Robert D. Tadeo Jr., Railyn A. Tuceno, and Leroy A. Flores*

President Ramon Magsaysay State University, Iba, Zambales, Philippines 2201

Corresponding Author*

DOI: https://dx.doi.org/10.47772/IJRISS.2025.908000161

Received: 24 July 2025; Accepted: 31 July 2025; Published: 02 September 2025

ABSTRACT

This study addresses the widespread problem of Grade 7 students encountering difficulty subtracting integers. Although this area of knowledge is considered fundamental, a significant majority of Grade 7 pupils in Iba District, Philippines, precisely 65.8%, exhibited inadequate proficiency in it. To address this challenge, a pre-experimental design was utilized. This Strategic Intervention Material (SIM) was created to facilitate a practical and experiential method of teaching the subtraction of integers. The study comprised a sample of 267 Grade 7 pupils, with a typical age of 13, who were predominantly male. These students were randomly selected from five public secondary schools in the Iba District. The students’ comprehension of integer subtraction was assessed using pre- and post-tests. Initially, students demonstrated inadequate performance in pre-tests, but significant improvement was observed in post-tests following the introduction of the SIM. While pre-tests showed no significant differences based on sex or age, post-tests revealed substantial variations by sex and moderate differences by age, indicating demographic influences on academic outcomes post-intervention. The notable increase between pre-test and post-test scores emphasizes the efficacy of the SIM in improving students’ proficiency. Recommendations include considering demographic diversity when designing interventions, integrating targeted SIMs in arithmetic instruction, and conducting continuous assessments to optimize learning outcomes. Implementing these strategies can effectively enhance mathematical skills among Grade 7 students and support their academic success in subtracting integers.

Keywords: Difficulties in Subtracting Integers, Intervention, Strategic Intervention Material, Grade 7 Students, Pre-experimental design

RATIONALE

Fundamental knowledge of the key concepts and skills involving numbers and number sense, including integers, should be mastered in the 6th grade to understand more complex mathematical principles (DepEd, 2016). However, it is uncertain whether the students will attain this when they enter high school. According to the study of Cunanan et al. (2023), it was found that 65.8% of the 284 Grade 7 students from Iba District Schools received a performance rating below 75, indicating a poor level of mastery in subtracting integers.

Integers are sets of numbers that can either be positive or negative numbers or zero (0) (Setyawati & Indiati, 2018). Integers are also described as numbers with a positive (+) and a negative (-). The negative sign can have at least three meanings in mathematics: unary, binary, and symmetric functions (Bofferding, 2014). Bofferding (2014) uses the term “minus” generically to refer to the “-” symbol, “subtraction sign” to refer to the binary meaning of the minus sign, and “negative sign” to refer to the unary meaning of the minus sign.

Many students have always misconceived and misinterpreted its concepts, especially because subtracting integers is new for 7th graders. Students’ inability to solve integer problems stems from their lack of prior exposure to negative numbers (Bofferding, 2014). Cunanan et al. (2023) stated that the teaching and learning of mathematics, particularly the concept of subtracting integers, is challenging for students as the Grade 7 students of Iba District, Zambales, cannot perform well in problems that involve the subtraction of integers. Students’ understanding of the initial negative integer idea will contradict their prior knowledge of integer arithmetic operations since it will appear abstract (Cengiz et al., 2018).

Subtracting integers requires a solid understanding of the number line, positive and negative numbers, and the rules governing their interactions. Students often need help to grasp these concepts due to their abstract nature. Traditional teaching methods, such as lectures and worksheets, may not effectively engage students or cater to their individual learning needs. Several studies have explored various models for teaching the concept of integers. However, they have found that more than counters are needed to understand integer operations and modeling (Cetin, 2019). This leads to developing Strategic Intervention Materials that offer an alternative approach by providing interactive and hands-on learning experiences.

Strategic Intervention Material (SIM) is an invaluable resource for supporting the educational growth of K-12 students, especially in areas where they may face difficulty. According to Bundang and Parangat (2020), the students’ least-mastered skills are developed in remedial sessions through SIM. It is a tool for learning that helps students master competency-based skills that they might not have been able to acquire in a typical classroom context. This is similar to the study by Suarez and Casinillo (2020), which concluded that SIM is a successful teaching method for raising students’ achievement levels in their least-mastered subjects. It aims to determine the methods schools employ to achieve their performance goals. SIM can assist in improving identified areas, teaching strategies, or processes to enhance students’ performance (Hernandez et al., 2019). Therefore, SIMs are instructional resources developed to address students’ learning gaps and enhance their understanding of a particular concept. It can take various forms, such as worksheets, manipulatives, games, or digital tools. They are carefully crafted to provide targeted interventions, promote active learning, and support students in developing problem-solving skills.

SIMs are designed to simplify the least-mastered skills for easy understanding and reproducibility. They ensured that the activities were aligned with the tasks or objectives, kept them concise and focused, and provided multiple activities to give students ample opportunities for skill mastery (Bahinting et al., 2022). These materials also included various activities to cater to different learning styles and ensure that the activities were suitable for the tasks or objectives at hand (Apiong, 2021).

Since SIMs may give visual representations and tangible examples that help students envision and make sense of abstract mathematical concepts and encourage active involvement and enthusiasm, utilizing them to improve students’ knowledge of the subtraction of integers offers numerous benefits. Students can better grasp the underlying concepts and methods of subtracting numbers using an interactive method like this. In addition, SIMs can be modified and customized to meet the unique needs of each student, guaranteeing that they will all be provided with the right amount of guidance and challenge. This adaptability makes the ability to adapt lessons to the specific needs of each learner possible.

Research Objectives

Educators have been exploring Strategic Intervention Materials (SIMs) as a pedagogical approach to enhance students’ understanding and proficiency in subtracting integers. This research aimed to determine the effectiveness of the SIMs developed by Cunanan et al. (2023) in secondary schools, specifically focusing on their impact on students’ learning outcomes in the Iba District, Zambales. The study sought to address the following research questions to achieve its objective:

What is the profile of the student-respondents in terms of:

Sex; and

Age?

What is the performance of the student-respondents in the pre-test and post-test involving the subtraction of integers before and after implementing the developed Strategic Intervention Material?

Is there a significant difference between the performance of the student-respondents in the pre – and post-test scores when grouped according to profile variables?

Is there a significant difference between the pre-test and post-test scores of the respondents on the assessment involving the subtraction of integers?

METHODOLOGY

Research Design

This quantitative research employed a pre-experimental design to assess students’ performance in subtracting integers and to evaluate the effectiveness of the developed Strategic Intervention Material (SIM). The pre-experimental design, characterized by its simplicity, involves observing one or more experimental groups under specific treatments without including a comparison group (Voxco, 2021). Despite the absence of a comparison group, this design is frequently used to provide preliminary evidence of the effectiveness of an intervention (Mauldin, 2020).

There are three main types of pre-experimental designs: the one-shot case study design, the one-group pre-and post-test design, and the static-group comparison (Voxco, 2021). This study utilized the one-group pre-and post-test design, where the experimental group’s performance is assessed both before and after the intervention.

Specifically, the researchers employed this one-group pre-and post-test design to evaluate the performance of Grade 7 students from five public secondary schools: Amungan National High School, Jesus F. Magsaysay High School, San Agustin Integrated School, Sta. Barbara Integrated School, and Zambales National High School. A pre-test was administered to establish the baseline characteristics of the group before the intervention, followed by a post-test to measure any improvements in the group’s performance after the implementation of the SIM.

Respondents and Location

This study was conducted in the District of Iba, Division of Zambales, for the school year 2023-2024. The study targeted five public secondary schools within Iba: Amungan National High School, Zambales National High School, Santa Barbara Integrated School, San Agustin Integrated School, and Jesus F. Magsaysay High School. The respondents were Grade 7 students from these schools, selected based on their reported lack of mastery in subtracting integers, as identified in the study by Cunanan et al. (2023). This finding contrasts with the competencies outlined by the Department of Education (2016), which state that understanding number sense, including integers, should be mastered by the 6th grade.

To determine the sample size for data collection, the researchers applied Slovin’s Formula to the total population of 802 Grade 7 students in Iba, resulting in a computed sample size of 267 students. The respondents were then selected through a random sampling method to ensure a representative sample.

Instruments

The Strategic Intervention Material (SIM) developed by Cunanan et al. (2023) was provided to the students in the schools mentioned above. This SIM comprises five components: the guide card, activity card, assessment card, enrichment card, and reference card. It served as a remediation tool for students struggling with the subtraction of integers. Researchers developed pre- and post-tests based on the subject matter to evaluate the SIM’s effectiveness.

The pre-and post-tests included a demographic profile section and a 30-item test. The pre-test assessed the student’s prior understanding of integer subtraction, while the post-test measured the knowledge gained after the intervention.

To ensure the quality and accuracy of the research instruments, they underwent a validity test. Content validity was evaluated by the Mathematics instructors from President Ramon Magsaysay State University, ensuring the appropriateness of the assessment content for the student-respondents. Additionally,. a pilot test was conducted with twenty (20) Grade 7 students from the Laboratory High School of President Ramon Magsaysay State University to test the instrument’s reliability

Data Collection

The assessment test was reproduced upon thorough examination and validation, and exact copies were distributed to all respondents. The results from these assessments served as the primary data for analysis and interpretation.

To conduct the study, a letter of request was sent to the school division superintendent and the respective school principals seeking permission to carry out the research. Additionally, the researchers requested assistance from the mathematics teachers at each school to help manage the distribution and administration of the instruments.

The researchers administered the tests through face-to-face interactions during scheduled class times as the principals or subject teachers arranged, ensuring that all Grade 7 students participated in the assessment process.

Data Analysis

Collected data were treated with statistical analysis, employing descriptive statistical tools like frequency, percentage, and mean to describe the results. The pre-and post-test scores were transformed into ratings using the transmutation table the Department of Education provided to assess student respondents’ proficiency in subtracting integers. To test the hypotheses of the study, the following nonparametric tests were used after the data (pre- and post-test scores) were tested not normally distributed (p-values = 0.000 < 0.05): Mann-Whitney U Test, Kruskal-Wallis H Test, and Wilcoxon Signed-Rank Test. The research data and findings were analyzed and interpreted to benefit those who will read the study, particularly the students, teachers, and future researchers.

RESULTS AND DISCUSSIONS

Profile of the Grade 7 Student-Respondents

Table 1 shows the frequency and percentage distribution of the Grade 7 student respondents’ profile regarding age and sex.

Table 1 Profile of the Grade 7 Student-Respondents

The demographic profile of the 267 Grade 7 student-respondents indicates a predominance of male students, who comprise 56.55% of the sample, compared to 43.45% female students. This was also the case during the study of Baye et al. (2016), where males had a higher frequency than females at the 7th-grade levels.

The age distribution shows that the mean age of the students is approximately 12.85 years, with the majority being 13 years old (60.67%). A significant portion is also 12 years old (30.71%), while smaller percentages are 14 years old (6.37%), 15 years old (1.50%), and rare cases of 16 and 26 years old, each at 0.37%. This suggests that most students are within the typical age range for Grade 7, though there are a few outliers. This is similar to the study of the National Center for Education Statistics (NCES) on the age distribution of students, which found that the modal age for 7th-grade students is 13 years old, with the majority of students falling within the 12-14 age range (NCES, 2020). This aligns with the high percentage of 13-year-old respondents observed in the table.

Grade 7 Students’ Performance in the Pre-test and Post-test Involving the Subtraction of Integers Before and After Implementing the Developed Strategic Intervention Material

Table 2 presents the frequency distributions, percentage distributions, and mean values of the pre-test and post-test performance ratings of Grade 7 student-respondents in subtracting integers before and after implementing the developed Strategic Intervention Material.

Table 2 Pre-test and Post-test Performace of the Grade 7 Student-Respondents in Subtracting Integers Before and After Implementing the SIM

Out of 267 respondents, 23 students, or 8.61%, achieved a performance rating range of 90-100 (Outstanding); 12 students, or 4.49%, received a performance rating range of 85-89 (Very Satisfactory); and 8 students, or 3.00%, fell within the performance rating ranges of 80-84 (Satisfactory) and 75-79 (Fairly Satisfactory). The remaining 216 students, or 80.90%, obtained a performance rating below 75 (Did Not Meet Expectations). The pre-test result indicates that the majority of the student respondents scored below 75, followed sequentially by those scoring 90-100, 85-89, 75-79, and 80-84. The 267 student-respondents yielded a mean performance score of 71.54, classified as Failed or Did Not Meet Expectations. This suggests a poor level of mastery among the respondents regarding the subtraction of integers. These findings corroborate various studies highlighting students’ persistent conceptual and procedural difficulties with negative numbers and integer operations (Bofferding, 2014; Hefendehl-Hebeker, 2016).

After the implementation of the developed Strategic Intervention Material, the performance ratings showed considerable improvement. Out of 267 respondents, 57 students, or 21.35%, achieved a performance rating range of 90-100 (Outstanding); 37 students, or 13.86%, received a performance rating range of 85-89 (Very Satisfactory); 24 students, or 8.99%, fell within the 80-84 (Satisfactory) range; and 62 students, or 23.22%, achieved ratings in the 75-79 (Fairly Satisfactory) range. The remaining 87 students, or 32.58%, scored below 75 (Did Not Meet Expectations).

This post-intervention distribution indicates that while a significant portion of students still scored below 75, there was a noticeable increase in higher performance ratings, with the largest group falling within the 75-79 range, followed by 90-100, 85-89, and 80-84. The overall mean performance score improved to 80.25, which is classified as satisfactory. This implies that the student-respondents demonstrated considerable improvement in solving the subtraction of integers after the intervention.

These results align with findings from Johnson et al. (2018), who investigated the effectiveness of a strategic intervention program in enhancing students’ performance in integer subtraction, revealing significant improvements in post-test scores following the intervention. Furthermore, a meta-analysis by Ghosh and Sharma (2022) synthesized findings from multiple studies on the impact of strategic interventions on students’ performance in integer operations.

Test of Significant Difference Between the Performance of the Student-respondents in the Pre – and Post-test Ratings When Grouped According to Profile Variables

Table 3 presents the statistical tests used to compare the significant difference in student respondents’ performance in pre- and post-test ratings, categorized by profile variables such as sex and age.

Table 3 Difference Between the Performance of the Student-respondents in the Pre- and Post-test Ratings When Grouped According to Profile Variables

For the pre-test ratings, the Mann-Whitney U Test was employed to evaluate differences based on sex, yielding a U statistic of 8688.5 and a p-value of 0.911. The result led to the acceptance of the null hypothesis, indicating no significant difference in pre-test ratings between male and female students. This finding aligns with a study by Brown and Harris (2021), which found no significant gender differences in initial mathematical performance, including basic arithmetic skills such as subtraction. Similarly, the Kruskal-Wallis H Test was used to assess differences based on age, with an H statistic of 6.356 and a p-value of 0.273. This also resulted in the acceptance of the null hypothesis, suggesting no significant differences in pre-test ratings across different age groups. These results are consistent with research by Lee and Kim (2020), which reported no significant age-related differences in baseline subtraction skills among students.

In contrast, the post-test ratings revealed significant differences. The Mann-Whitney U Test for sex differences produced a U statistic of 7059.5 and a p-value of 0.007, leading to the rejection of the null hypothesis. This indicates a highly significant difference in post-test ratings between male and female students. Similar findings were reported by Jones and Smith (2022), who observed significant gender differences in post-intervention performance in the subtraction of integers, suggesting that males and females may benefit differently from specific teaching strategies. Additionally, the Kruskal-Wallis H Test for age differences yielded an H statistic of 11.306 and a p-value of 0.046, leading to the rejection of the null hypothesis. This finding shows a significant difference in post-test ratings among different age groups. This is supported by the work of Garcia and Martinez (2021), who found that age can significantly influence learning outcomes and post-test performance in arithmetic tasks, potentially due to varying cognitive development and learning experiences.

In summary, while the pre-test ratings showed no significant differences based on sex or age, the post-test ratings indicated significant variations, with highly significant differences observed between male and female students and significant differences across different age groups. These results are corroborated by recent studies, suggesting that demographic factors like sex and age can significantly impact academic performance following instructional interventions in solving subtraction of integers.

Test of Significant Difference Between the Pre-test and Post-test Scores of the Student-respondents on the Assessment Involving the Subtraction of Integers

Table 4 presents the results of the Wilcoxon Signed Ranks Test, which was used to assess the difference in performance of student-respondents in pre- and post-test ratings before and after implementing the Strategic Intervention Material (SIM) for solving subtraction of integers.

The analysis shows there were 16 negative ranks, where post-test scores were lower than pre-test scores, with a mean rank of 45.53. Conversely, there were 226 positive ranks, where post-test scores were higher than pre-test scores, with a mean rank of 126.88. Additionally, 25 students had tied ranks, where their post-test scores were equal to their pre-test scores. The Wilcoxon Signed Ranks Test yielded a test statistic of -12.824 and a significance (p-value) of 0.000, leading to the rejection of the null hypothesis. This result indicates a highly significant difference between the pre-test and post-test scores, suggesting that the Strategic Intervention Material substantially impacted the Grade 7 student’s ability to solve subtraction of integers.

Table 4 Difference Between the Performance of the Student-respondents in the Pre- and Post-test Ratings Before and After Implementing the Strategic Intervention Material

Post-Test Rate < Pre-Test Rate Post-Test Rate > Pre-Test Rate Post-Test Rate = Pre-Test Rate

Both local and international studies support this finding. Locally, Cruz and Santos (2023) demonstrated similar improvements in student performance with the use of targeted intervention materials in mathematics, highlighting the effectiveness of such strategies in enhancing arithmetic skills. Internationally, the study by Smith and Jones (2022) corroborates these results, showing significant gains in mathematical proficiency among students exposed to strategic interventions designed explicitly for integer operations. These studies collectively emphasize the efficacy of strategic interventions in improving students’ mathematical abilities, particularly in operations involving integers.

Thus, the significant difference observed between the pre-test and post-test scores of the students, as evidenced by the Wilcoxon Signed Ranks Test, indicates that implementing the Strategic Intervention Material markedly improved the Grade 7 student’s performance in solving subtraction of integers.

CONCLUSIONS

Based on the findings of this study involving Grade 7 students, several key conclusions emerge. First, the student cohort predominantly comprises young male adolescents. Second, before implementing the Strategic Intervention Material (SIM), students exhibited inadequate performance in the pre-test assessing the subtraction of integers; however, following the implementation of the SIM, their performance significantly improved in the post-test. Third, initial assessments showed no significant differences in performance based on sex or age, whereas subsequent evaluations revealed substantial differences in post-test scores based on sex and moderate differences based on age. These findings suggest the influence of demographic variables on academic outcomes following educational interventions targeting subtraction skills. Lastly, the substantial increase observed between pre-test and post-test scores indicates the effectiveness of the SIM in enhancing Grade 7 students’ proficiency in subtracting integers, highlighting the importance of targeted instructional strategies in improving mathematical skills at this educational level.

RECOMMENDATIONS

Based on the findings of this study involving Grade 7 students, several recommendations can be made to enhance educational practices and improve student outcomes. First, it is essential to consider the demographic composition of student groups, particularly the prevalence of young male adolescents, when designing and implementing educational interventions. Understanding demographic characteristics can help tailor interventions to better meet the needs of specific student populations.

Second, the implementation of Strategic Intervention Materials (SIM), as evidenced by this study, proves effective in enhancing students’ proficiency in the subtraction of integers. Therefore, educators and curriculum developers are encouraged to incorporate similar targeted interventions that focus on fundamental arithmetic skills into their teaching practices.

Third, ongoing assessment and evaluation should be conducted to monitor the effectiveness of educational interventions over time, particularly concerning how demographic factors such as sex and age influence academic performance. This will provide insights into where adjustments may be needed to optimize learning outcomes across diverse student groups.

By adopting these recommendations, educators can better equip Grade 7 students with the necessary mathematical skills and support their academic success in subtracting integers.

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