Next Article in Journal
Visual Translator: Bridging Students’ Handwritten Solutions and Automatic Diagnosis of Students’ Use of Number Lines to Represent Fractions
Previous Article in Journal
Physical and Sensory Classroom Environment and Associations with Inclusive Education of Autistic Students in Chile: Construction, Validation and Results of a Teacher-Reported Scale
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Education Sciences
Volume 15
Issue 12
10.3390/educsci15121636
education-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Differentiated Instruction in Problem-Based and Direct Instruction: The Moderating Role of Mathematical Disposition on Students’ Mathematical Communication Skills

by
La Ndia
1,*,
Mohamad Salam
1,
La Iru
2 and
Nurul Atma
3
1
Department of Mathematics Education, Universitas Halu Oleo, Kendari 93232, Indonesia
2
Department of Civic Education, Universitas Halu Oleo, Kendari 93232, Indonesia
3
Department of English Language Education, Universitas Halu Oleo, Kendari 93232, Indonesia
*
Author to whom correspondence should be addressed.
Educ. Sci. 2025, 15(12), 1636; https://doi.org/10.3390/educsci15121636
Submission received: 5 October 2025 / Revised: 27 November 2025 / Accepted: 2 December 2025 / Published: 5 December 2025
Browse Figures
Review Reports Versions Notes

Abstract

This study examines the effects of instructional models, specifically problem-based learning (PBL) and direct instruction (DI), on students’ mathematical communication skills with mathematical disposition as the moderating variable. Both models incorporated differentiated instruction. A quasi-experimental 2 × 2 factorial design was conducted with 75 Grade XI students from a public high school in Southeast Sulawesi, Indonesia. The research instrument used a mathematical communication test and a disposition questionnaire. Based on the results of two-way ANOVA and tests, a significant interaction was found between learning models and mathematical disposition. Students taught with PBL had higher mathematical communication scores than those taught using DI. Regarding mathematical disposition, students with high dispositions had higher mean scores when taught using the PBL approach, whereas their low-disposition counterparts achieved higher scores under the DI approach. Thus, this study underscores the importance of considering students’ mathematical dispositions in maximizing the efficacy of instructional models on students’ mathematical communication skills. It also offers practical insights into how differentiated instruction within these models can accommodate students’ diverse needs.

1. Introduction

Since mathematical communication serves as a means to share information and is an important part of reasoning, explaining, and solving problems (Guerreiro, 2008), it is essential for students to learn, explain, and deepen their understanding of arithmetic concepts. Its core element is the ability to articulate mathematical ideas, both orally and in written form. However, many studies show that students’ mathematical communication skills are limited by the abstractness of mathematical objects, which makes it difficult for many students to interpret them (Ndia et al., 2020). Consequently, these challenges necessitate that teachers possess both explicit mathematical content knowledge and pedagogical ability (Canogullari & Isiksal-Bostan, 2024), as well as the ability to translate abstract mathematical objects into more concrete forms (Bremigan et al., 2011; de Bivar Weinholtz, 2022; Wu, 2011).
Those challenges can be addressed by not only focusing on delivering content effectively but also fostering interaction and discourse. Two commonly applied instructional models in mathematics education are problem-based learning (PBL) and direct instruction (DI). According to Hmelo-Silver (2004), PBL can foster both knowledge and cognitive processes by engaging students in problem-solving experiences. Through PBL, students are exposed to self-directed learning (SDL), subsequently applying their acquired knowledge to the problem and reflecting on their learning outcomes and the efficacy of the instructional strategies (Hmelo & Cote, 1996). In particular, students contemplate the problem and identify what they need to learn to achieve a solution. PBL is an educational approach in which knowledge is acquired through guided problem-solving activities. It is an instructional approach that utilizes real-world problems as a context for students to learn and develop critical thinking skills—a framework conceptualized by Vygotsky’s sociocultural theory, which highlights the significance of social interaction and scaffolding within the Zone of Proximal Development (ZPD).
In teaching using PBL, students should be able to understand complex mathematical concepts and solve them using diverse strategies. It emphasizes student-centered experiences that are relevant to improving mathematical communication skills. PBL promotes student involvement in authentic problem-solving by encouraging the application of critical and creative thinking. This outcome aligns with research by Arifin et al. (2020) and Arviana et al. (2018), which highlights improvements in students’ communication skills regarding mathematical concepts after learning using the PBL approach.
While PBL encourages exploration, DI offers a contrasting structure that emphasizes clarity and procedural fluency. Despite being teacher-centered, instruction remains applicable in mathematics education, particularly when presenting ideas or materials that require systematic procedural understanding (Hermawan et al., 2020; Muawanah et al., 2022). In DI, teachers deliver systematic and structured explanations (Al-Makahleh, 2011), allowing each student to grasp the material before progressing to more challenging tasks.
Although the two instructional models offer discrete advantages, their effectiveness may depend on how instruction is tailored to accommodate student diversity. It is widely recognized that a classroom is usually composed of students with diverse needs and backgrounds. Teachers must adapt instructional strategies to align with students’ varying ability levels, thereby promoting equitable comprehension (Fox & Hoffman, 2011). To address this challenge, differentiated instruction has been identified as a practical approach, providing learning experiences tailored to each student’s level of readiness, personal interests, and preferred learning modalities (Tomlinson, 2001). Differentiated instruction aligns the instructional content with students’ needs, interests, readiness, and learning styles (Al-Shehri, 2020; Sanakulova, 2024). This strategy also enables students with varying learning speeds to receive the appropriate challenges and support (Santangelo & Tomlinson, 2009). It is essential to note that the differentiated instruction employed in these two learning models offers teachers flexibility to tailor teaching methods to students’ individual needs, enabling all students, regardless of their level of mathematical dispositions, to enhance their mathematical communication skills (Goyibova et al., 2025). Flexibility refers to the adjustability of how each model is implemented; for instance, the teacher can vary task difficulty, scaffolding, time, and grouping.
PBL integrated with differentiated instruction allows teachers to provide more targeted support to students based on their individual needs (Kyeremeh et al., 2021; Pozas et al., 2020; Smets et al., 2022). It facilitates students’ engagement in authentic problem-solving contexts while offering individualized support (Morgan, 2014). The students can demonstrate their conceptual understanding and are recognized as an effective learning approach to achieve maximum learning outcomes (Variacion et al., 2021). Thus, it can enhance students’ mathematical communication skills by involving them in collaboration, idea exploration, and the delivery of outcomes in a relevant and structured manner (Fitria et al., 2020).
DI integrated with differentiated instruction exposes students to explicit, targeted instruction and to learning flexibility tailored to their individual needs. The instruction commences with verbal explanations accompanied by visual aids, such as graphs, diagrams, or simulations, and it provides exercises tailored to students’ specific needs. Teachers can provide explicit instructions to students about what they should do while also allowing them to work at their own pace. For example, in mathematics teaching, teachers offer the same initial explanation for the entire class, then differentiate the tasks or how students practice the concept based on their abilities.
In addition, students’ mathematical disposition, a combination of motivation, confidence, perseverance, and curiosity toward learning mathematics (Yaniawati et al., 2019), is also crucial to consider the effectiveness of learning models highly depends on this construct. It profoundly influences how students interact in the learning process. As described in previous research (Hannula, 2006; McLeod, 1992), affective components significantly influence how students approach and persist in mathematical tasks. People with a high disposition possess the habits of analyzing, questioning, and reflecting—essential catalysts for accomplishing tasks that require deeper understanding or creative problem-solving. They are open to trying new strategies, making connections, and learning from mistakes, thereby encouraging them to take on demanding tasks and persevere despite obstacles. Ultimately, it affects their learning outcomes. As found by Kusmaryono et al. (2019), there is a significant effect of mathematical disposition on mathematical power ability.
Although prior studies have explored the individual impact of PBL on mathematics achievement (Abdullah et al., 2010; Ahmad et al., 2024; Ajai et al., 2013; Boye & Agyei, 2023; Nufus & Mursalin, 2020) and mathematical disposition on achievement (Kamid et al., 2021; Kusmaryono et al., 2019; Wahyudin et al., 2024; Yaniawati et al., 2019), few studies have examined the joint effect of instructional models and learner disposition on mathematical communication skills, particularly within the context of differentiated instruction. Most existing research has generally focused on the efficiency of PBL or DI in isolation without considering how student-level characteristics interact with pedagogical design. This study addresses the identified gap by investigating the interactions between instructional models, namely PBL integrated with differentiated instruction, and DI integrated with differentiated instruction, and the influence of students’ mathematical dispositions on their mathematical communication skills. Integrating differentiated instruction into both models is expected to improve the learning experience for students at all disposition levels.
This study addresses the following research questions:
  • How do learning models (PBL vs. DI) affect students’ mathematical communication skills?
  • How do students’ mathematical dispositions (high vs. low) affect their communication skills?
  • How is the interaction between learning models and mathematical disposition influencing students’ mathematical communication skills?
The following figure illustrates the relationship among the variables being investigated.
Figure 1 illustrates how learning models (X1) and mathematical dispositions (X2) interact to influence mathematical communication skills (Y). It displays the relationship of the research questions being investigated.

2. Materials and Methods

This research employed a quasi-experimental research design with a 2 × 2 factorial structure, as presented in Table 1. The 2 × 2 factorial design was chosen to examine both the main and interaction effects of instructional models and mathematical disposition on students’ mathematical communication. This approach enables a deeper understanding of how mathematical disposition impacts instructional effectiveness.
The study population consisted of all grade XI students of SMA 4 Kendari registered in the even semester of the 2024/2025 academic year, totaling 571 students divided into 16 parallel classes. There were 36 students from Class XII and 39 students from Class XIJ selected as samples using a simple random sampling technique. Students in class XII were taught using the PBL, and those in class XIJ were taught using DI. Both models integrated differentiated instruction.
This study employed two instruments to assess students’ mathematical disposition and mathematical communication skills. First, the researchers developed a brief performance-based test on mathematical communication skills. It consisted of five items based on indicators of mathematical communication skills, such as written explanations, visual representations (e.g., drawings), and mathematical expressions. Two items targeted written explanation, two items targeted visual representation, and one item required integrating symbols with a brief explanation. Thus, the tasks were designed to target different mathematical skills, which aimed to demonstrate how students are reasoning through the mathematical concepts. For example, students were asked to explain their thought process in writing, which allowed the assessment of the clarity and accuracy of their reasoning. Items were written based on the lesson objectives. The mathematics topic taught in both classes was statistics. In this unit, the mathematical communication skills developed were (1) expressing a given set of data in mathematical form to facilitate analysis, (2) visually representing the dataset, and (3) providing a written explanation of the procedures and reasoning used in the data analysis. The test was administered twice, namely prior to teaching and after teaching. The test underwent content validation by a panel of five subject-matter experts and achieved a reliability coefficient of 0.86.
Second, mathematical disposition was assessed using a 39-item Likert-scale questionnaire. It has seven dimensions, each of which were assessed through specific items within the questionnaire such as self-confidence (six items: number 1, 2, 4, 13, 20, and 24), flexibility (six items: number 5, 6, 8, 9, 12, and 22), persistence (seven items: number 11, 14, 15, 17, 21, 29, and 38), curiosity (six items: 3, 16, 18, 25, 26, and 28), metacognitive awareness (six items: number 7, 10, 19, 30, 31, and 33), evaluation (four items: number 34, 35, 36, and 37) and appreciation for mathematics in real-life contexts (four items: number 23, 27, 32, and 39). The instrument demonstrated strong internal consistency with a Cronbach’s alpha of 0.78. Students were categorized into high- and low-disposition groups using a median split of the total disposition scores.
To collect the data, first, data on mathematical disposition were collected by administering a questionnaire to two groups of students identified as samples, prior to the learning process, using the PBL and direct instruction models, both of which used differentiated instruction.
Table 2 compares the learning activities in the two instructional models. The learning process was conducted in the two selected sample classrooms according to the established steps: one class was instructed using the PBL (A1) with differentiated instruction, while the other class received DI (A2) with the same differentiated instruction.
Following the five instructional sessions, an evaluation was conducted at the sixth meeting to gauge students’ mathematical communication abilities. The assessment comprised five questions prepared by the researchers, based on the indicators of mathematical communication skills derived from the content covered in the preceding five sessions.
The data analysis technique employed descriptive statistics and two-way analysis of variance (ANOVA) to test the interaction effects of the instructional models and mathematical disposition on communication outcomes. Normality and homogeneity of variance assumptions were tested prior to conducting ANOVA. All statistical analyses were conducted using SPSS version 26.

3. Results

3.1. The Students’ Mathematical Communication Skills Before and After Being Taught Using PBL and DI

To address the first research question, the mean scores of students taught under PBL and DI were compared, as shown in Table 3.
Table 3 summarizes the comparison between the two groups’ performance on the pre-test and post-test, with the t-test values suggesting a statistical comparison. As illustrated in the table, in the pre-test, the PBL group had a mean score of 61.81, while the DI group had a mean score of 60.90. In the post-test, the PBL group showed an improvement with a mean score of 72.76, while the DI group had a mean of 65.63. The table also includes statistical information, with the degrees of freedom (df) for the t-test set at 49. These results demonstrate greater effectiveness of the PBL model in fostering mathematical communication skills. The t-test yielded a statistically significant difference (t(49) = 2.310 > t-table = 2.010), indicating that students taught with PBL significantly outperformed those taught with DI in enhancing students’ mathematical communication skills.

3.2. The Students’ Mathematical Communication Skills Across Different Levels of Disposition

To address the second research question, the mean scores of students with high and low disposition levels were compared, as shown in Table 4.
Table 4 depicts the disparities in mean score for mathematical communication skills between students exhibiting a high level of mathematical disposition (B1) and those demonstrating a low level of mathematical disposition (B2). Students in the high-disposition group (B1) obtained a mean score of 76.17, whereas those in the low-disposition group (B2) obtained a mean score of 62.50. The results indicate that students with elevated mathematical disposition—marked by increased motivation, confidence, and persistence—performed better on mathematical communication tasks than their peers with low disposition.

3.3. The Interaction Between Learning Models and Mathematical Disposition in Influencing Students’ Mathematical Communication Skills

To address the third research question, Table 5 presents the two-way ANOVA results, followed by Table 6, which provides detailed group statistics.
As illustrated in Table 5, the analysis revealed statistically significant effects for both instructional models and mathematical disposition. Most notably, the interaction effect was significant F (1.46) = 31.97, p < 0.05, indicating that the effectiveness of instructional models in enhancing mathematical communication depends on students’ levels of mathematical disposition.
Table 6 presents detailed group statistics, including the mean scores and variances for each combination of disposition level (high and low) and instructional model (PBL and DI). These tables illustrate the study’s statistical findings, emphasizing the significant effects of both instructional models and mathematical dispositions on students’ mathematical communication skills. The interaction between these factors is particularly notable, indicating that the combination of model and disposition level plays a key role in shaping students’ mathematical communication skills. Additionally, the detailed group statistics provide further insight into how different groups performed across the two instructional models, highlighting differences in both mean scores and variances for students with high and low mathematical dispositions.
A t-test was conducted to confirm the significance of these differences. Based on the results shown in Table 7, the following observations were made:
  • High-disposition students benefited significantly more from PBL (t(24) = 6.217, p < 0.05).
  • Low-disposition students performed better under DI than PBL (t(24) = 2.202, p < 0.05).
As illustrated in Figure 2, students with high mathematical disposition taught using the PBL model integrated with differentiated instruction (A1B1) exhibited much better results compared to those taught with the DI integrated with differentiated instruction (A2B1). The mean score of mathematical communication skills in the A1B1 group was 88.14, while that of the A2B1 group was 63.19.
Among students with a low level of mathematical disposition (B2), the study’s results showed notable differences. Students with a low level of mathematical disposition, taught with DI using differentiated instruction (A2B2), achieved an average score of 68.06, which is higher than those taught with PBL using differentiated instruction (A1B2) with an average score of 57.37. These findings indicate that students with a low level of mathematical disposition learn better through DI when differentiated instruction is used.

4. Discussion

The results of this study show that students taught with PBL, implemented through differentiated instruction, had considerably higher mathematical communication skills compared to DI. It contributes to the existing literature on instructional design by highlighting the pedagogical effectiveness of integrating differentiated instruction. The results imply that teaching methods that cater to the students’ individual needs and address their unique differences can significantly enhance mathematical communication skills. For instance, previous studies (Arifin et al., 2020; Arviana et al., 2018) have found that differentiated PBL helped students think critically, while in their meta-analysis study, Wijnia et al. (2024) discovered that differentiated PBL helped students stay motivated in classrooms. The effect sizes were greater when problem-driven learning was implemented in an individual course than when using a curriculum-wide approach, especially in science subjects, such as healthcare and STEM.
PBL with differentiated instruction aims to enhance students’ ability to explain mathematical ideas, use appropriate representations, and logically discuss and solve mathematical problems through a holistic approach to developing students’ mathematical skills, particularly in terms of communication and problem-solving (Rézio et al., 2022). Providing relevant challenges and adjusting the learning model to specific strategies that meet students’ needs are means of creating an inclusive learning environment and supporting the development of deep mathematical abilities. The PBL model with differentiated instruction demonstrated greater effectiveness in enhancing mathematical communication skills as students had the opportunity to independently explore problems, engage in peer discussions, and communicate their ideas more effectively.
One component of PBL is distributed cognition, which enables the social sharing of the information-gathering workload, thereby decreasing the cognitive load of any one individual (Schmidt et al., 2007). Moreover, the effectiveness of PBL is attributable to its nature of social interaction, where students’ perspectives interact rather than being presented in isolation; new ideas emerge and challenge existing concepts, leading to a potential transformation of knowledge (Innes, 2006). It aligns with Vygotsky’s sociocultural theory and constructivist learning frameworks, which highlight social interaction, contextual learning, and scaffolded experiences as part of the process of knowledge formation. PBL inherently fosters these qualities by involving students in collaborative activities that require critical thinking, problem-solving, and the synthesis of interdisciplinary knowledge. When combined with differentiated instruction—where tasks, content, and assessments are customized to align with student readiness, interests, and learning profiles—PBL fosters a flexible, student-centered educational environment that seems to significantly promote cognitive and emotional development. Another study (Pease & Kuhn, 2011) found that the practical component of PBL appears to be the focus on engagement with a problem.
Conversely, for DI, despite its recognition for clarity, efficiency, and efficacy in imparting core knowledge—especially during the initial phases of material delivery—it may lack responsiveness to individual learning differences and be less effective at fostering higher-order thinking skills. It prioritizes uniformity and instructor authority, potentially limiting students’ ability to engage in self-directed inquiry and apply their knowledge in complex, real-world situations. Consequently, students subjected to differentiated teaching may receive structured support. Still, they may exhibit diminished engagement or motivation, particularly when instruction fails to align with their learning preferences or developmental needs.
Regarding mathematical disposition, this study found that students with a high level of mathematical disposition also have higher mathematical communication skills, as evidenced by their mean scores. In other words, students with more favourable mathematical dispositions tend to have higher scores in communicating mathematical ideas, reasoning, and arguments in both spoken and written forms. These results are in line with other research indicating that the affective domain is an important factor in how well people learn arithmetic (Hannula, 2006; McLeod, 1992).
As illustrated in Table 6, students with high mathematical disposition taught using the PBL model integrated with differentiated instruction (A1B1) exhibited much better results compared to those taught with the DI integrated with differentiated instruction (A2B1). The mean score of mathematical communication skills in the A1B1 group was 88.14, while that of the A2B1 group was 63.19. This finding is similar to the results of another study (Setiawan & Surahmat, 2023), which found that mathematical disposition has a significant effect on students’ mathematics learning outcomes.
Moreover, mathematical disposition is related to the attitude–behavior–cognition framework. Students with a pleasant mood and high disposition are more likely to engage in sustained mathematical problem-solving, thereby improving their communication skills. Disposition is not only about a result of learning, but also a mediator to navigate challenging times, devise strategies, and reflect on their reasoning (Carr & Claxton, 2002), which are highly necessary for practical mathematical communication skills (Minarti & Wahyudin, 2019; Octaviani et al., 2023; Wahyuni et al., 2023; Yaniawati et al., 2019).
Furthermore, the primary finding of this study is the significant interaction between the instructional models and mathematical disposition (Table 5). The interaction effect was significant (F = 31.97, ≥Ftable 4.08, α = 0.05), indicating that the effectiveness of instructional models in enhancing mathematical communication depends on students’ levels of mathematical disposition. It implies that the learning models applied—both PBL and DI- have different and significant effects depending on students’ mathematical dispositions. In other words, high or low mathematical dispositions affect the effectiveness of each learning model in improving mathematical communication skills. This finding supports the hypothesis that the success of the instructional model for mathematical communication skills depends on students’ individual characteristics, such as mathematical dispositions (Guerreiro, 2008). Prior work suggests complementary strengths of PBL (richer explanations and representations) and DI (efficient foundational skill-building), while student beliefs, interests, and confidence shape willingness to communicate mathematically. Our findings extend this literature by showing that who benefits most from each model depends not only on the model itself but also on disposition. (Hwang & Choi, 2020) found that the achievement gap in emotional dispositions, such as preferences and aversions, diminished when teachers consistently employed specific instructional strategies, including assigning demanding tasks, allowing students to determine their own problem-solving methods, and encouraging them to articulate their thoughts in class. Students who expressed aversion to mathematics tended to achieve higher results when their instructors employed those tactics more frequently.
The results of this study suggest that students possessing a high level of mathematical disposition are better taught using the PBL integrated with differentiated instruction to improve their mathematical communication skills because it necessitates active involvement and deep cognitive processing, all of which aligns with the characteristics of students with high dispositions (Kamid et al., 2021; Thomson & Pampaka, 2021). Students with low dispositions are better taught using DI because it offers explicit structure and guidance aligned with their cognitive needs. It does not require independent involvement and higher critical thinking skills. This result aligns with the view that students with a low level of mathematical disposition need more direct and explicit guidance in learning (Dina et al., 2019). It underscores the need for highly personalized student profiles in the instructional design.
Additionally, students who excel in mathematical reasoning are more likely to speak up in class, ask questions, explain their reasoning, and collaborate with their classmates. Such activities are commonly found in a classroom that integrates PBL and are believed to facilitate the construction of mathematical meaning, which is crucial for cognitive development, according to Vygotsky’s sociocultural theory. So, the mathematical disposition is a predictive affective construct that supports both motivation and the epistemic engagement needed for mathematical communication skills.
The substantial relationship between disposition and instructional model implies that the level of scaffolding needed in addition to the instructional approach influences students’ mathematical communication skills. When given structured support, students with lower mathematical dispositions—who benefit more from DI—may be functioning within their Zone of Proximal Development. This aligns with Vygotsky’s theory that learning is most effective in settings with appropriate scaffolding. Higher-disposition students, on the other hand, may need less structure, enabling more discussion and investigation in PBL, which promotes the collaborative creation of knowledge through social interaction. This relationship between disposition and instruction highlights the importance of tailoring teaching approaches to each student’s unique learning needs and developmental stage.
The significant interaction between instructional models and mathematical disposition validates that one-size-fits-all instructional methods in mathematics education are inadequate. Teacher and curriculum developers should consider students’ affective characteristics, especially their mathematical disposition, prior to establishing teaching methods. Besides, instructional decisions can be enhanced by early diagnosis of student disposition and aligning support accordingly—for instance, structuring PBL with additional scaffolding for students requiring increased confidence.
This study did not involve student characteristics—such as learning motivation, curiosity, or social support—that may correlate with both participation and outcomes. Consequently, some of the reported effects may be attributable to these factors rather than the intervention itself, necessitating cautious interpretation of the results.

5. Conclusions

The findings of this study suggest that there is a significant interaction between instructional models (A1, A2) and mathematical dispositions (B1, B2) in shaping students’ mathematical communication skills. Students with a high level of disposition taught using PBL (A1B1) have higher mathematical communication skills than their peers who received DI (A2B1). Conversely, students with a low level of disposition performed better under the DI (A2B2) than under PBL (A1B2). In other words, DI is more effective for students with lower levels of mathematical disposition. Overall, the findings suggest that the PBL model with differentiated instruction yielded higher average scores than DI. These findings underscore the importance of aligning instructional practices with students’ dispositional characteristics to improve their mathematical communication skills. This study contributes to the existing literature on adaptive training by emphasizing the moderating influence of mathematical disposition on instructional efficacy.
Based on the findings, it is recommended that teachers consider students’ mathematical disposition to determine the learning model to be used. It can be done by assessing students’ dispositions before teaching and aligning support accordingly—for instance, structuring PBL with additional scaffolding for students who need increased confidence. Moreover, to develop effective learning materials, teachers need to consider differences in students’ mathematical dispositions, so that the learning process can be implemented according to students’ abilities and characteristics. This study was limited by its relatively small sample size and was specific to the context of a public high school in Indonesia, which may affect the generalizability of the results. Further research is needed with larger samples at different levels of education, and combining the PBL and DI integrated with differentiated instruction.
This research does not account for other factors that may influence mathematical communication skills, such as learning motivation, interest, social support from classmates and family, which could impact the internal validity of the conclusions drawn.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/educsci15121636/s1, Questionnaire on Mathematical Disposition; Test on Mathematical Communication Skill.

Author Contributions

Conceptualization, L.N. and M.S.; Methodology, L.N. and M.S.; Validation, M.S.; Formal analysis, L.N.; Investigation, L.N.; Data Curation, M.S.; Writing original draft, L.N.; Writing—review and Editing, L.N. and N.A.; Visualization, L.N.; Supervision, M.S.; Project administration, LN. and L.I.; Project funding, L.N. and L.I. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

The study was conducted in accordance with the Declaration of Helsinki, and approved by the Institutional Review Board (or Ethics Committee) of Universitas Halu Oleo (1491/UN29.5.1/PP/2024 on 23 December 2024) for studies involving humans.

Informed Consent Statement

Informed consent was obtained from all subjects involved in the study.

Data Availability Statement

The original contributions presented in this study are included in the article/Supplementary Material. Further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

References

  1. Abdullah, N. I., Tarmizi, R. A., & Abu, R. (2010). The effects of problem based learning on mathematics performance and affective attributes in learning statistics at form four secondary level. Procedia-Social and Behavioral Sciences, 8, 370–376. [Google Scholar] [CrossRef]
  2. Ahmad, B., Zulfiqar, A., & Bajwa, R. S. (2024). Studying the effect of problem-based learning on mathematics achievement of elementary students. Journal of Excellence in Social Sciences, 3(2), 125–136. [Google Scholar] [CrossRef]
  3. Ajai, J. T., Imoko, B. I., & O’kwu, E. I. (2013). Comparison of the learning effectiveness of problem-based learning (PBL) and conventional method of teaching algebra. Journal of Education and Practice, 4(1), 131–135. [Google Scholar]
  4. Al-Makahleh, A. A. A. (2011). The effect of direct instruction strategy on math achievement of primary 4th and 5th grade students with learning difficulties. International Education Studies, 4(4), 199–205. [Google Scholar] [CrossRef]
  5. Al-Shehri, M. S. (2020). Effect of differentiated instruction on the achievement and development of critical thinking skills among sixth-grade science students. International Journal of Learning, Teaching and Educational Research, 19(10), 77–99. [Google Scholar] [CrossRef]
  6. Arifin, S., Setyosari, P., Sa’dijah, C., & Kuswandi, D. (2020). The effect of problem-based learning by cognitive style on critical thinking skills and students’ retention. Journal of Technology and Science Education, 10(2), 271. [Google Scholar] [CrossRef]
  7. Arviana, R., Irwan, & Dewi, M. P. (2018). Problem based learning in mathematics education and its effect on student’s critical thinking. Advanced Science Letters, 24(1), 211–213. [Google Scholar] [CrossRef]
  8. Boye, E. S., & Agyei, D. D. (2023). Effectiveness of problem-based learning strategy in improving teaching and learning of mathematics for pre-service teachers in Ghana. Social Sciences & Humanities Open, 7(1), 100453. [Google Scholar] [CrossRef]
  9. Bremigan, E. G., Bremigan, R. J., & Lorch, J. D. (2011). Mathematics for secondary school teachers (Vol. 21). MAA. [Google Scholar]
  10. Canogullari, A., & Isiksal-Bostan, M. (2024). Middle school mathematics teachers’ knowledge of integers. European Journal of Science and Mathematics Education, 12(2), 312–325. [Google Scholar] [CrossRef]
  11. Carr, M., & Claxton, G. (2002). Tracking the development of learning dispositions. Assessment in Education: Principles, Policy & Practice, 9(1), 9–37. [Google Scholar] [CrossRef]
  12. de Bivar Weinholtz, A. (2022). Book review: “Understanding numbers in elementary school mathematics” by Hung-Hsi Wu. European Mathematical Society Magazine, 122, 66–67. [Google Scholar] [CrossRef]
  13. Dina, Z. H., Ikhsan, M., & Hajidin, H. (2019). The improvement of communication and mathematical disposition abilities through discovery learning model in junior high school. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 4(1), 11–22. [Google Scholar] [CrossRef]
  14. Fitria, R., Hutapea, N. M., & Zulkarnain, H. (2020). Development of mathematics learning devices by applying problem based learning to increase students mathematical solving skills of class VII junior high school. Journal of Educational Sciences, 4(2), 368–379. [Google Scholar] [CrossRef]
  15. Fox, J., & Hoffman, W. (2011). The differentiated instruction book of lists (Vol. 6). John Wiley & Sons. [Google Scholar]
  16. Goyibova, N., Muslimov, N., Sabirova, G., Kadirova, N., & Samatova, B. (2025). Differentiation approach in education: Tailoring instruction for diverse learner needs. MethodsX, 14, 103163. [Google Scholar] [CrossRef]
  17. Guerreiro, A. (2008). Communication in mathematics teaching and learning. Practices in Primary Education. Available online: https://scholar.google.com/citations?view_op=view_citation&hl=pt-PT&user=5c5rlfoAAAAJ&cstart=20&pagesize=80&sortby=pubdate&citation_for_view=5c5rlfoAAAAJ:KxtntwgDAa4C (accessed on 26 November 2025).
  18. Hannula, M. S. (2006). Affect in mathematical thinking and learning: Towards integration of emotion, motivation, and cognition. In New mathematics education research and practice (pp. 209–232). Brill. [Google Scholar]
  19. Hermawan, C. M., Rosfiani, O., Yulia, & Lutfiana, V. (2020). The effectiveness of direct instruction model in mathematics subjects: A classroom action research in elementary school. International Journal of Scientific and Technology Research, 9(4), 2506–2509. [Google Scholar]
  20. Hmelo, C. E., & Cote, N. C. (1996, July 25–27). The development of self-directed learning strategies in problem-based learning. 1996 International Conference on Learning Sciences (pp. 421–426), Evanston, IL, USA. [Google Scholar]
  21. Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do students learn? Educational Psychology Review, 16(3), 235–266. [Google Scholar] [CrossRef]
  22. Hwang, J., & Choi, K. M. (2020). Relationships between emotional dispositions and mathematics achievement moderated by instructional practices: Analysis of TIMSS 2015. International Journal of Mathematical Education in Science and Technology, 51(1), 44–62. [Google Scholar] [CrossRef]
  23. Innes, R. B. (2006). What can learning science contribute to our understanding of the effectiveness of problem-based learning groups? Journal of Management Education, 30(6), 751–764. [Google Scholar] [CrossRef]
  24. Kamid, K., Huda, N., Syafmen, W., Sufri, S., & Sofnidar, S. (2021). The relationship between students’ mathematical disposition and their learning outcomes. Journal of Education and Learning (EduLearn), 15(3), 376–382. [Google Scholar] [CrossRef]
  25. Kusmaryono, I., Suyitno, H., Dwijanto, D., & Dwidayati, N. (2019). The effect of mathematical disposition on mathematical power formation: Review of dispositional mental functions. International Journal of Instruction, 12(1), 343–356. [Google Scholar] [CrossRef]
  26. Kyeremeh, P., Amoah, E. K., & Sabtiwu, R. (2021). Junior high school mathematics teachers’ practice of differentiated instruction and associated challenges in Tano South district. Journal of Mathematics and Science Teacher, 1(1), em001. [Google Scholar] [CrossRef]
  27. McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. Handbook of Research on Mathematics Teaching and Learning, 1, 575–596. [Google Scholar]
  28. Minarti, E. D., & Wahyudin, W. (2019). How influential the mathematical disposition of mathematical communication skills Is? (the evaluation of middle school students). Journal of Physics: Conference Series, 1402(7), 077086. [Google Scholar] [CrossRef]
  29. Morgan, H. (2014). Maximizing student success with differentiated learning. The Clearing House: A Journal of Educational Strategies, Issues and Ideas, 87(1), 34–38. [Google Scholar] [CrossRef]
  30. Muawanah, F., Arianto, B., Astuti, D., & Razzokov, K. K. (2022). Direct learning model to improve students’ mathematics learning outcomes: A classroom action research. Bulletin of Science Education, 2(1), 27–40. [Google Scholar] [CrossRef]
  31. Ndia, L., Solihatin, E., & Syahrial, Z. (2020). The effect of learning models and multiple intelligences on mathematics achievement. International Journal of Instruction, 13(2), 285–302. [Google Scholar] [CrossRef]
  32. Nufus, H., & Mursalin, M. (2020). Improving students’ problem-solving ability and mathematical communication through the application of problem based learning. Electronic Journal of Education, Social Economics and Technology, 1(1), 43–48. [Google Scholar] [CrossRef]
  33. Octaviani, A. D., Rahmawati, A., & Rohmatin, D. N. (2023). Analysis of students’ mathematical communication ability in solving problems viewed from the mathematical disposition. International Journal of Research Publication and Reviews, 4(3), 1609–1613. [Google Scholar] [CrossRef]
  34. Pease, M. A., & Kuhn, D. (2011). Experimental analysis of the effective components of problem-based learning. Science Education, 95(1), 57–86. [Google Scholar] [CrossRef]
  35. Pozas, M., Letzel, V., & Schneider, C. (2020). Teachers and differentiated instruction: Exploring differentiation practices to address student diversity. Journal of Research in Special Educational Needs, 20(3), 217–230. [Google Scholar] [CrossRef]
  36. Rézio, S., Andrade, M. P., & Teodoro, M. F. (2022). Problem-based learning and applied mathematics. Mathematics, 10(16), 2862. [Google Scholar] [CrossRef]
  37. Sanakulova, S. X. (2024). Differentiation of instruction in the elementary grades. Current Research Journal of Pedagogics, 5(12), 74–77. [Google Scholar] [CrossRef]
  38. Santangelo, T., & Tomlinson, C. A. (2009). The application of differentiated instruction in postsecondary environments: Benefits, challenges, and future directions. International Journal of Teaching and Learning in Higher Education, 20(3), 307–323. [Google Scholar]
  39. Schmidt, H. G., Loyens, S. M. M., Van Gog, T., & Paas, F. (2007). Problem-based learning is compatible with human cognitive architecture: Commentary on Kirschner, Sweller, and Clark (2006). Educational Psychologist, 42(2), 91–97. [Google Scholar] [CrossRef]
  40. Setiawan, Y. E., & Surahmat. (2023). The effect of mathematical disposition on basic mathematical abilities in the online learning. Journal of Education Research and Evaluation, 7(2), 259–266. [Google Scholar] [CrossRef]
  41. Smets, W., De Neve, D., & Struyven, K. (2022). Responding to students’ learning needs: How secondary education teachers learn to implement differentiated instruction. Educational Action Research, 30(2), 243–260. [Google Scholar] [CrossRef]
  42. Thomson, S., & Pampaka, M. (2021). Exploring associations with mathematics dispositions: A novel perspective combining measurement and set-theoretic analytical approaches. International Journal of Research and Method in Education, 44(5), 474–492. [Google Scholar] [CrossRef]
  43. Tomlinson, C. A. (2001). How to differentiate instruction in mixed-ability classrooms. ASCD. [Google Scholar]
  44. Variacion, D. A., Salic-Hairulla, M., & Bagaloyos, J. (2021). Development of differentiated activities in teaching science: Educators’ evaluation and self-reflection on differentiation and flexible learning. Journal of Physics: Conference Series, 1835(1), 012091. [Google Scholar] [CrossRef]
  45. Wahyudin, Marzuki, Suryadi, D., Cahya, E., & Shofia Maulida, A. (2024). The effect of mathematical disposition on students’ mathematical performance. International Conference on Mathematics and Science Education. KnE Social Sciences, 2024, 587–595. [Google Scholar] [CrossRef]
  46. Wahyuni, F. T., Nuruniyah, N., Noor, N. L., & Fakhriyana, D. (2023). The mathematical communication of senior high school: A correlation of dispositional mathematics. AIP Conference Proceedings, 2595, 050026. [Google Scholar] [CrossRef]
  47. Wijnia, L., Noordzij, G., Arends, L. R., Rikers, R. M. J. P., & Loyens, S. M. M. (2024). The effects of problem-based, project-based, and case-based learning on students’ motivation: A meta-Analysis. Educational Psychology Review, 36(1), 29. [Google Scholar] [CrossRef]
  48. Wu, H. (2011). Understanding numbers in elementary school mathematics. American Mathematical Society. [Google Scholar]
  49. Yaniawati, R. P., Indrawan, R., & Setiawan, G. (2019). Core model on improving mathematical communication and connection, analysis of students’ mathematical disposition. International Journal of Instruction, 12(4), 639–654. [Google Scholar] [CrossRef]
Education 15 01636 g001
Figure 1. The relationship of the variables being investigated.
Figure 1. The relationship of the variables being investigated.
Education 15 01636 g001
Education 15 01636 g002
Figure 2. The interaction effect between instructional models and mathematical dispositions on mathematical communication skills.
Figure 2. The interaction effect between instructional models and mathematical dispositions on mathematical communication skills.
Education 15 01636 g002
Table 1. The 2 × 2 factorial design.
Table 1. The 2 × 2 factorial design.
Moderating VariableTreatment Variable
PBL (A1)DI (A2)
High Mathematical Disposition (B1)A1B1A2B1
Low Mathematical Disposition (B2)A1B2A2B2
A1B1: high-disposition students taught using PBL. A1B2: low-disposition students taught using PBL. A2B1: high-disposition students taught using DI. A2B2: low-disposition students taught using DI.
Table 2. The instructional steps for both PBL and DI, with each embedded with differentiated instruction.
Table 2. The instructional steps for both PBL and DI, with each embedded with differentiated instruction.
PBLDIPBLDI
Teacher’s ActivitiesStudents’ Activities
Preparing Contextual ProblemsOrientation and Learning PreparationUnderstanding the ProblemListening and understanding the material
Analyzing Student ProfilesPresenting the lessonWorking in GroupsParticipating in Guided Practice
Forming Working GroupsGuided PracticeCollecting DataConducting Differentiated Independent Practice
Providing Differentiated ResourcesDifferentiated Independent PracticeDeveloping SolutionsInteracting and collaborating
Providing Direction and FeedbackEvaluation and ReflectionPresenting SolutionsConducting Reflection and Self-Evaluation
Table 3. Comparison of average mathematical communication skills based on instructional models.
Table 3. Comparison of average mathematical communication skills based on instructional models.
Pre TestPost Test
NMeanVarianceMeanVariance
PBL (A1)3661.81135.9372.7698.59
DI (A2)3960.90105.0965.63140.65
df 49
count 2.310
ttable 2.010
Table 4. Comparison of average mathematical communication skills based on mathematical disposition.
Table 4. Comparison of average mathematical communication skills based on mathematical disposition.
Disposition LevelMeanVariance
High (B1)76.1792.12
Low (B2)62.50145.37
Table 5. Results of ANOVA.
Table 5. Results of ANOVA.
SourcedfSsMsSftable
Instructional Model (A)1634.58634.585.12
Mathematical Disposition (B)12335.042335.0418.844.08
Interaction (A × B)13960.833960.8331.974.08
Error465699.78123.91
Total4912,630.23
Table 6. Detailed group statistics.
Table 6. Detailed group statistics.
Disposition LevelModelMean ScoreVariance
High (B1)PBL88.1445.83
High (B1)DI63.19150.99
Low (B2)PBL57.37159.57
Low (B2)DI68.06143.10
Table 7. Results of t-test comparing two groups.
Table 7. Results of t-test comparing two groups.
Comparisondft-Countt-Table
A1B1 vs. A2B12462172069
A1B2 vs. A2B22422022069
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

MDPI and ACS Style

Ndia, L.; Salam, M.; Iru, L.; Atma, N. Differentiated Instruction in Problem-Based and Direct Instruction: The Moderating Role of Mathematical Disposition on Students’ Mathematical Communication Skills. Educ. Sci. 2025, 15, 1636. https://doi.org/10.3390/educsci15121636

AMA Style

Ndia L, Salam M, Iru L, Atma N. Differentiated Instruction in Problem-Based and Direct Instruction: The Moderating Role of Mathematical Disposition on Students’ Mathematical Communication Skills. Education Sciences. 2025; 15(12):1636. https://doi.org/10.3390/educsci15121636

Chicago/Turabian Style

Ndia, La, Mohamad Salam, La Iru, and Nurul Atma. 2025. "Differentiated Instruction in Problem-Based and Direct Instruction: The Moderating Role of Mathematical Disposition on Students’ Mathematical Communication Skills" Education Sciences 15, no. 12: 1636. https://doi.org/10.3390/educsci15121636

APA Style

Ndia, L., Salam, M., Iru, L., & Atma, N. (2025). Differentiated Instruction in Problem-Based and Direct Instruction: The Moderating Role of Mathematical Disposition on Students’ Mathematical Communication Skills. Education Sciences, 15(12), 1636. https://doi.org/10.3390/educsci15121636

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Article metric data becomes available approximately 24 hours after publication online.
Back to TopTop