Based on the above description, this study aims to enhance students’ mathematical problem-solving skills and digital literacy through the Nearpod-assisted PBL enactment within the TPACK framework. Three central research questions were formulated:

In accordance with these research questions, three hypotheses were proposed:

The participants were twelfth-grade students from two senior high schools in Bekasi, Indonesia. The schools were selected based on comparable accreditation status, curriculum implementation, student academic performance records, and socio-economic background to minimize institutional differences. To control for potential school-level confounding effects, baseline equivalence between the experimental and control groups was examined using an independent samples t-test on Initial Mathematics Ability (IMA) pretest scores. However, although the baseline test demonstrated equivalence in students' initial mathematical ability, the use of intact classes from two different schools may still allow other contextual factors—such as school academic culture, teaching quality, facilities, or overall learning environment readiness—to influence the findings. Nevertheless, this study-maintained objectivity by ensuring comparable initial academic conditions across groups. Even though the groups were located in different schools, institutional variability was minimized because both institutions implemented the same national curriculum, used comparable assessment standards, and were supervised under the same regional education authority.

The sampling procedure followed established stratified sampling principles in quasi-experimental educational research ⁷. Stratified sampling was based on students’ Initial Mathematics Ability (IMA), categorized into high, medium, and low levels using the percentile distribution of pretest scores. A total of 72 students, aged 16 to 18 years old, were selected to participate in the study. The unit of assignment was the intact classroom rather than individual students. Two existing classes were selected purposively based on schedule availability and curriculum alignment. One class was assigned to the experimental group and the other to the control group. Individual random assignment was not feasible due to institutional constraints; therefore, this study followed a quasi-experimental design rather than a true randomized experiment. During the

intervention, the experimental group consisted of 36 students who received mathematics instruction through the Nearpod-assisted PBL enactment within the TPACK framework, while the comparison group consisted of 36 students who received conventional mathematics instruction without technological integration. To ensure objectivity in the teaching experiment, the two groups were taught at different schools while following the same curriculum. Indonesian was the first language of all participants, and to minimize teacher-related variability, both groups were instructed by teachers with comparable years of teaching experience and similar academic qualifications. Prior to the intervention, both teachers were briefed on instructional objectives and research procedures to ensure consistency in curriculum coverage.

The intervention in the experimental group followed the structure of the official lesson plan (RPP) on the mode for grouped and ungrouped data and was implemented by integrating Problem-Based Learning (PBL), the TPACK framework, and Nearpod. Instructional Framework Analysis using TPACK is as follows. Content Knowledge (CK): The instructional content focused on the statistical mode for grouped data, emphasizing conceptual reconstruction of frequency relationships and symbolic equation modeling. Pedagogical Knowledge (PK): The learning process followed structured Problem-Based Learning stages incorporating scaffolding strategies such as guided questioning, collaborative reasoning prompts, and reflective evaluation. Technological Knowledge (TK): Nearpod affordances (Collaborate Board, Draw-It, interactive quizzes) were used to facilitate dynamic visualization, real-time formative feedback, and collaborative representation of statistical reasoning.

The lesson began with preliminary activities, including an introduction, readiness checks, and a Nearpod-based pretest to assess students’ prior knowledge. During the core learning phase, the five stages of PBL were implemented. The stages adopted in this study were adapted from the model proposed by Arends (2012) consisting of problem orientation, organizing students, guided investigation, presentation of solutions, and evaluation or reflection. Problem-Based Learning supports collaborative inquiry and conceptual knowledge construction (Hmelo-Silver, 2004). The instructional syntax implemented in the experimental group consisted of: (1) Problem Orientation (contextual statistical problem via Nearpod slide); (2) Problem Structuring (group identification of known and unknown variables); (3) Guided Inquiry (collaborative modeling using Draw-It and LKPD);  (4) Presentation and Discussion (solution sharing via Collaborate Board); (5) Reflection and Conceptual Reinforcement (posttest and digital reflection).

First, students were oriented to a contextual problem presented through interactive slides. Next, they were organized into heterogeneous small groups and guided to identify problem-solving strategies using LKPD designed according to PBL-TPACK principles. Inquiry activities were supported by Nearpod tools such as Collaborate Board, Draw-It, and digital LKPD, enabling students to explore information, discuss solution ideas, and articulate reasoning collaboratively. Students then presented their group solutions, which were evaluated using the performance rubric. The lesson concluded with consolidation of key concepts, a Nearpod-based posttest, and a digital reflection using the Open-Ended Response feature and a digital literacy questionnaire. Formative assessment was conducted throughout the intervention using Nearpod’s real-time response system, including interactive quizzes, open-ended responses, and collaborative board submissions. Immediate feedback was provided to guide conceptual refinement during inquiry stages.

This intervention aligned PBL stages, digital pedagogy, and the procedural steps outlined in the lesson plan, enabling students to engage in structured problem-solving supported by interactive technology. Meanwhile, the comparison group received instruction through direct teaching. Before the intervention, students in both groups completed a test assessing their initial problem-solving

skills. The intervention is depicted in Table 1. It was conducted over four sessions, beginning with an introduction to the research procedures, followed by PBL-based learning activities embedded in Nearpod, and ending with a post-test. Each session lasted 90 minutes and was held during regular course study hours.

The research instruments developed included data-collection instruments and learning materials. These instruments comprised the students’ Initial Mathematical Ability (IMA) test, a pretest–posttest measuring mathematical problem-solving skills, digital learning activity sheets, and a digital literacy questionnaire. All instruments were designed to assess improvements in students’ mathematical problem-solving skills and digital literacy after participating in PBL-TPACK learning supported by Nearpod, across three initial ability levels: high, medium, and low. The data-collection procedure followed three stages: pre-intervention testing, implementation of the learning intervention, and post-intervention assessment.

Mathematical problem-solving skills

Because the participants were 12th-grade senior high school students, all test items focused on statistical content. The IMA test was designed to assess students’ initial understanding of data representation and consisted of four items. These items evaluated students’ comprehension of graphical, bar-chart, and pie-chart representations, including skills such as decision-making, identifying true–false statements, and selecting statements consistent with the given data, as illustrated in Figure 1.

Based on Figure 1, the IMA test instrument not only measures basic mathematical skills but also assesses students’ problem-solving abilities, particularly in identifying essential information from graphs on harvested land area and rice production, analyzing month-to-month changes—including increases, decreases, and production patterns—and evaluating data-based statements in which students must determine the validity of statements using logical reasoning rather than merely reading the graph accurately. Through Agree–Disagree-type items, the instrument requires students to employ multistep reasoning, such as calculating differences in data, comparing rates of change, and interpreting trends. Thus, the IMA test illustrates the extent to which students can apply fundamental mathematical concepts in real-world contexts and connect them to more complex problem-solving processes. The IMA test was administered to participants for approximately 40 minutes.

Furthermore, the mathematical problem-solving items were developed based on predetermined indicators, namely:

The example questions from the pre-test and post-test are specified in Figure 2.

This type of problem was used to assess students' logical reasoning, recognition of structural information (equalities among variables), and ability to identify numerical patterns. The use of integer constraints and range relationships was intentionally designed to stimulate reasoning beyond direct computation. The student worksheet (LKPD) used in this study was systematically designed to integrate the phases of Problem-Based Learning (PBL) with the TPACK framework and Nearpod’s interactive features. Each component of the LKPD was designed to support the development of mathematical problem-solving and to enhance digital literacy through structured inquiry and technology-mediated collaboration. Figure 3 presents an example of the student worksheet (LKPD) used in the statistics lesson during the implementation of the Nearpod-assisted PBL enactment within the TPACK framework.

The LKPD begins with a non-routine contextual problem involving the mode of grouped data with an unknown frequency, intentionally creating cognitive conflict to prompt students to identify relevant information, construct mathematical models, and devise solution strategies. Presented digitally via Nearpod, the problem allows students to highlight key data, pose questions, and discuss ideas online, thereby strengthening their Digital Skills and Digital Ethics.

The inquiry section guides students in analyzing the frequency table, applying the mode formula, and articulating their reasoning in a structured way. This process is reinforced by Nearpod tools—such as Draw-It, Collaborate Board, and Open-Ended Response—that support data visualization, argument construction, and digital comparison of solutions across groups. These

activities sharpen problem-solving skills in representation, planning, and evaluation while fostering Digital Culture through collaborative digital interaction.

In the final stage, the LKPD requires students to develop group conclusions and complete a digital reflection in Nearpod. This reflection prompts students to evaluate the effectiveness of their strategies, identify errors, and reflect on their digital behaviors, thereby supporting metacognitive growth and Digital Safety awareness.

Overall, the LKPD serves as an integrated pedagogical instrument that promotes conceptual exploration, higher-order problem solving, and comprehensive digital literacy within a technology-enhanced PBL learning environment aligned with TPACK principles. Afterward, they completed a posttest parallel to the pretest and submitted a Nearpod-based reflection to document their learning experiences.

Digital literacy questionnaire

Students’ digital literacy was assessed using a Likert-scale questionnaire developed from Indonesia’s National Digital Literacy Framework, which comprises four pillars: Digital Skills, Digital Ethics, Digital Culture, and Digital Safety. Digital competence frameworks emphasize structured domains, including information literacy, communication, content creation, safety, and problem-solving (⁵; ³⁴). The instrument was adapted from established theoretical models of digital literacy (¹²; ¹⁴; ²⁰; ²⁷; ³¹; ³⁵) and aligned with the competencies outlined by Kominfo and Kemdikbud (⁵; ⁴⁰). The questionnaire consisted of 20 items distributed across four dimensions, show in Table 2: (1) Digital Skills (5 items) (2) Digital Ethics (5 items): (3) Digital Culture (5 items): and (4) Digital Safety (5 items).

Digital literacy was measured using a Likert-scale questionnaire and digital tasks aligned with the four national literacy pillars (Digital Skills, Digital Ethics, Digital Culture, and Digital Safety), supplemented by observational data of students’ digital behaviors. The data provided a comprehensive overview of students’ development in problem-solving and digital literacy.

Data analysis was conducted to evaluate the proposed research hypotheses. Statistical conclusions were drawn using independent samples t-tests and two-way ANOVA at a significance level of . Effect sizes (Cohen’s d and partial eta-squared) were calculated to assess the magnitude of the observed effects. Students’ improvement in mathematical problem-solving skills was measured using gain scores, calculated as the difference between posttest and pretest scores

. The intervention was considered effective if:

To address the research hypotheses, a four-phase data analysis procedure was used as follows

Phase 1: Testing IMA score differences between the experimental and control groups

The first stage of the analysis assessed whether IMA scores differed between the experimental and control groups using either an independent-samples t-test or the Mann–Whitney test. Before conducting the difference test, both datasets were examined for normality and homogeneity. Normality was tested using the Shapiro–Wilk test, and homogeneity of variance was assessed using Levene’s test, each at a significance level of . When both datasets met the assumptions of normality and homogeneity ( .05 \end{document} ]]>), the difference in IMA scores was evaluated using the t-test. Conversely, if either assumption was violated , the test was employed to analyze the difference between groups. The hypotheses tested were as follows:

H₀: There is no significant difference in IMA scores between experimental and control groups.

H₁: There is a significant difference in IMA scores between the experimental and control groups.

If the resulting significance value from either the t-test or Mann–Whitney test exceeded , H₀ was retained; otherwise, H₀ was rejected in favor of H₁.

Phase 2: Testing differences in gain scores between experimental and control groups

The second stage of the analysis aimed to determine whether there was a significant difference in students’ improvement in mathematical problem-solving skills between those taught through Nearpod-assisted PBL within the TPACK framework and those taught through direct instruction. Students’ gain scores were calculated by subtracting pretest scores from posttest scores. Before conducting the difference test, gain scores in both groups were assessed for normality using the Shapiro–Wilk test and for homogeneity of variance using Levene’s test at . When assumptions were satisfied, an independent samples t-test was conducted to compare gain scores between the experimental and control groups. If assumptions were violated, the Mann–Whitney test was employed. The hypotheses tested were:

H₀: There is no significant difference in gain scores between the experimental and control groups.

H₁: There is a significant difference in gain scores between the two groups.

H₀ was rejected when . Effect size was calculated using Cohen’s d to determine the magnitude of the improvement difference.

Phase 3: Testing the main and interaction effect of learning model and IMA level on gain scores

The third stage examined whether students’ improvement in mathematical problem-solving skills differed by learning model (experimental and control), IMA level (low, medium, high), and the interaction between these two factors. Before conducting inferential analyses, gain scores were assessed for normality and homogeneity of variance. All datasets met the assumptions of normality and homogeneity (p > .05), indicating that the data were suitable for two-way ANOVA analysis. A two-way ANOVA was conducted with learning model (experimental and control) and IMA level (low, moderate, high) as independent variables. The hypotheses tested were:

Main Effect of Learning Model

H₀: There is no significant difference in gain scores between learning models.

H₁: There is a significant difference in gain scores between learning models.

Main Effect of IMA Level

H₀: There is no significant difference in gain scores among IMA levels.

H₁: There is a significant difference in gain scores among IMA levels.

Interaction Effect

H₀: There is no interaction effect between learning model and IMA level on gain scores.

H₁: There is a significant interaction effect between learning model and IMA level on gain scores.

H₀ was rejected when . When significant interaction effects were detected, post hoc comparisons (Tukey HSD) were conducted. Effect sizes were reported using Partial Eta Squared .

Phase 4: Testing differences in digital literacy scores between the experimental and control groups

The fourth phase of the analysis examined whether a significant difference in digital literacy emerged between students who received PBL-TPACK instruction supported by Nearpod and those taught through direct instruction. To address this objective, two sequential tests were conducted: (1) testing the normality and homogeneity of digital literacy scores in both the experimental and control groups, and (2) testing the difference in digital literacy scores between the two groups.

The first test followed the same procedures used in Phase 1, whereas the second analysis used either an independent-samples t-test or the Mann–Whitney test, depending on the results of the normality and homogeneity assessments. The hypotheses for assessing differences in digital literacy scores were as follows:

H₀:There is no significant difference in digital literacy scores between the experimental and control groups.

H₁: There is a significant difference in digital literacy scores between the experimental and control groups.

H₀ was accepted when the significance value exceeded ; conversely, H₀ was rejected when the significance value was below , indicating that a significant difference in digital literacy scores exists between the experimental and control groups.

Prior to hypothesis testing, assumption tests were conducted for all datasets. The Shapiro–Wilk test indicated that all variables, including Initial Mathematics Ability (IMA), gain scores, and digital literacy scores, were normally distributed  .05) \end{document} ]]>. Levene’s test also confirmed homogeneity of variance across groups  .05) \end{document} ]]>. Therefore, parametric statistical analyses, including independent samples t-tests and two-way ANOVA, were considered appropriate.

Before the instructional experiment was conducted, an analysis of students’ initial mathematics ability (IMA) in both the experimental and control groups was conducted to ensure that the two groups were equivalent at baseline. This step aimed to minimize the influence of external

variables—other than the instructional approaches such as imbalances in IMA across groups, on the improvement of mathematical problem-solving skills and digital literacy. Therefore, an IMA test was administered to all participating students prior to the implementation of the learning intervention. The descriptive statistics for IMA scores in both groups are presented in Figure 4.

Based on Figure 4, both groups showed similar IMA scores. This is evident in comparable Min–Max ranges across categories, small differences in mean scores, and low, uniform standard deviations, indicating stable score dispersion. For example, the mean scores of students with high IMA in the experimental group (Exp-High) and the control group (Ctrl-High) were nearly identical, namely and , respectively.

Inferential statistical testing was then conducted to strengthen confidence in these findings. The Shapiro–Wilk normality test showed that the experimental group obtained , while the control group obtained . Additionally, Levene’s test for equality of variances confirmed that the IMA data were homogeneous, . Thus, the use of parametric statistical techniques, such as the independent samples t-test and two-way ANOVA on gain scores, was deemed appropriate. An independent samples t-test was subsequently conducted to examine whether there was a significant difference in IMA scores between the experimental and control groups. The results indicated that there was no statistically significant difference between the two groups,  .05, Cohen′s d = .44 \end{document} ]]>. Therefore, both groups were considered equivalent at baseline prior to the intervention.

During the learning process, the experimental group received instruction through Nearpod-assisted PBL within the TPACK framework, whereas the control group received direct instruction. Students’ mathematical problem-solving skills were assessed using pretest and posttest instruments focused on statistical problem-solving tasks. Descriptive statistics for pretest and posttest scores are presented in Table 3.

Although descriptive results show improvements in both groups, the primary analysis focused on gain scores (Posttest − Pretest) to directly measure students’ improvement. Before the inferential analysis, gain scores in both groups were examined for normality and homogeneity. The Shapiro–Wilk test indicated that gain scores were normally distributed in both groups (experimental: ; control: ). Furthermore, Levene’s test demonstrated that the variances of the gain scores were equal across groups, . These findings confirm that the assumptions of normality and homogeneity were met .05) \end{document} ]]>, justifying the application of an independent samples t-test. Therefore, an independent samples t-test was conducted to compare the gain score between the experimental and control groups.

The experimental group demonstrated higher gain scores  compared to the control group  An independent samples t-test confirmed that this difference was statistically significant, . Students who received instruction through the Nearpod-assisted PBL enactment within the TPACK framework demonstrated significantly greater improvement in mathematical problem-solving skills than those who received direct instruction.

As shown in Table 4, gain scores across all IMA levels were consistently higher in the experimental group than in the control group. This pattern suggests that the Nearpod-assisted PBL enactment within the TPACK framework contributed more substantially to students’ improvement on statistical problem-solving tasks. These findings indicate that the instructional approach had a meaningful impact on students’ mathematical problem-solving development.

To further examine whether students’ improvement in mathematical problem-solving skills differed by learning model and initial mathematics ability (IMA), a two-way ANOVA was conducted on gain scores, with learning model (experimental vs. control) and IMA level (low, moderate, high) as the independent variables. The analysis revealed a significant main effect of learning model, , indicating that students in the experimental group demonstrated greater improvement than those in the control group.

A significant main effect of IMA level was also observed, , suggesting that improvement differed across students with low, moderate, and high initial mathematics ability. Importantly, a significant interaction effect between the learning model and IMA level was found, , indicating that the effectiveness of the instructional model varied depending on students’ initial ability levels.

Tukey HSD post hoc analysis indicated that students in the experimental group with moderate IMA achieved significantly higher gain scores than those in the control group (mean difference= ). Similarly, students with high IMA in the experimental group outperformed their counterparts . However, for students in the low IMA category, the difference in gain scores between the experimental and control groups did not reach statistical significance .081) \end{document} ]]>.Although descriptively, the experimental group showed greater improvement.

Figure 5 shows the interaction between the learning model and the IMA level on the gain scores. The non-parallel slopes indicate that the magnitude of improvement varied across IMA categories. Although all IMA groups benefited from the Nearpod-assisted PBL enactment within the TPACK framework, the increase in gain scores was more pronounced among students with moderate or high initial mathematics ability than among those in the low-IMA category.

The fourth analysis examined whether a significant difference in digital literacy scores emerged between students taught through Nearpod-assisted PBL enactment within the TPACK framework and those taught through direct instruction. Prior to hypothesis testing, assumption checks were conducted. The Shapiro–Wilk test indicated that digital literacy scores were normally distributed in both groups (experimental: (; control ). Levene’s test confirmed homogeneity of variance . Overall, the data met the assumptions of normality and homogeneity (p > .05), supporting the use of parametric testing. Therefore, an independent samples t-test was performed.

The results revealed a statistically significant difference between the experimental and control groups, , with Cohen’s , indicating a large effect size. Students in the experimental group obtained a higher overall mean digital literacy score compared to the control group (M = 3.50). Descriptive analysis across the four pillars showed consistently higher scores in the experimental group, as presented in Table 5.

A shown in Figure 6, these findings indicate that the structured implementation of PBL within the TPACK framework, supported by Nearpod, significantly contributed to students’ digital literacy development across all national literacy dimensions. Digital literacy was analyzed at the group level because the study did not hypothesize differential effects across initial mathematics ability categories.