https://doi.org/10.53656/math2025-3-2-saa

2025/3, стр. 257 - 283

STATISTICAL ANALYSIS OF ACADEMIC ACHIEVEMENT AND INTRINSIC MOTIVATION IN STEM STUDENTS EDUCATED THROUGH A COMPETENCYBASED APPROACH

Резюме: This study explores the impact of Competency-Based Education (CBE) on students' academic performance in selected STEM disciplines and on their intrinsic motivation. In the context of growing interest in STEM (Science, Technology, Engineering, and M athematics), the re search examines whether the implementation of CBE can enhance student achievement and foster deeper motivation. The study was conducted with two groups of students from “Hristo Botev” High School in the village of Chepintsi. To assess intrinsic motivation, questionnaires were administered before and after the CBE intervention. Academic achievement was e valuated through tests and grades. The working hypothesis suggested that CBE would positively affect both academic outcomes and intrinsic motivation. The results support this hypothesis, highlighting the potential of CBE as an effective educational approach for developing young STEM learners. The findings indi cate that CBE contributes not only to improved academic performance but also to greater interest and engagement in scientific and technological fields.

Ключови думи: competency-based education; motivation; STEM; CBE; PISA 2025

1. Introduction

Competency-based education (CBE) is an innovative constructivist approach that aims to enhance motivation and academic achievement through the development of practical skills aligned with the needs of the community and labour market (Biggs , 1996). Accordin g to White (1959), actions such as studying, learning, and problem-solving are driven by intrinsic motivation, which does not depend on rewards or punishments.

CBE encourages both intrinsic and extrinsic motivation in students, which are key factors for its successful implementation. Intrinsic motivation is associated with personal satisfaction and deep acquisition of knowledge (Deci & Ryan, 2000), knowledge retention, and greater engagement in the learning process (Zimmerman, 2000; Ryan & Deci, 2000; Pintrich & De Groot, 1990). In contrast, extrinsic motivation is based on receiving rewards or social approval and generally has a weaker effect (Leary & Baumeister, 2000).

According to Self-Determination Theory (Deci & Ryan, 1985), three fundamental psychological needs – autonomy, competence, and relatedness – are essential for fostering intrinsic motivation. Previous experience shows that when students feel competent and effective in performing tasks, their intrinsic motivation increases. In CBE these needs can be fulfilled through solving practical tasks and developing authentic assessment methods, which provide real-world context and encourage confidence (Ryan & Deci, 2000). Students see a direct connection between their efforts and results (Guskey, 2007).

In this study, a partial modification of the classical ADDIE model (Analyze, Design, Develop, Implement, Evaluate) is presented (Widyastuti 2019), as its use is recommended in an iterative and flexible format called the Successive Approximation Model (SAM) \({ }^{3}\). Each iteration includes feedback on the results achieved by the student, as well as on the difficulties encountered. This feedback is intended for both the teacher and the student and is based on quantitative and qualitative assessments of the outcomes. With each iteration, the student moves closer to the educational goal. According to Hattie (2007), timely and effective feedback is a key factor in CBE, enhancing both competence and motivation.

Students are at the center of the model, as they actively participate in the educational process and develop key competencies described in the European Qualifications Framework (EQF) \({ }^{2}\), DigComp 2.2 (Vuorikari et al., 2022), the European \({ }^{5}\) and American \({ }^{6}\) STEM frameworks, and the PISA frameworks for mathematics (OECD 2017) and natural sciences \({ }^{4}\), including competencies for both individual and team work.

Designing the study content simultaneously includes the acquisition of theoretical knowledge and the solving of practical tasks, aiming to develop skills and competencies in the natural sciences. The study materials, tasks, and resources are adapted to the students’ needs. Individual competency levels and interests are considered. The main goal of the educational process is to support students’ motivation and engagement, as well as to facilitate the experience of “flow” during learning (Csikszentmihalyi, 1990).

In designing the environment and tools for STEM education, geographic information systems (GIS) may also be used \({ }^{1}\). Kerski (2015) identifies 1 2 natural connections between STEM and ArcGIS, including the logical integration of the four STEM disciplines, career orientation, alignment with national science education content standards, mathematics, climate studies, investigating STEM topics with GIS , the development of critical thinkin g skills, and the belief th at learning is often most effective when it occurs outdoors, among others.

The assessment of the educational outcomes is a process based on continuous feedback from the students. It in cludes f ormative assessment (FA), which provides regular feedba ck on students’ difficulties, as well as summative assessment, which is used for the certification of competencies. Formative assessment includes self-assessment (Garov, 2013; Staribratov 2021) and feedback, while summative assessment includes peer review—also called “peer assessment” (Shotlekov, 2012) – partnership checks, or expert evaluation by a commission consisting of teachers and active professionals. To ensure a realistic assessment, the product developed during the project should be tested in a real-world environment.

2. The study

2.1.The aim of the study

To check th e effect of the application of CBE on the students’ study results in the studied STEM disciplines and on their intrinsic motivation.

2.2.Hypothesis

Hypothesis: CBE has a positive influence on students' academic achievement in the studied STEM d isciplines and enhances their intrins ic motivation.

2.3.Study methodology

In the frames of the internally institutional qualification, the pedagogical personnel passed through an education on topic CBE. For the experimental integration of CBE, a holistic approach was used for the study programs. According to it, the study content must include real-life topics that form and expand all key competencies of the students \({ }^{2}\). After coordinating the team work, a team of pedagogical specialists created a summa rized study program whose education units were projected to be taught in a team, according to the context of the topics. Main cores of the study program are in accordance with the PISA 2025 frames in natural sciences4 and DigComp 2.2 (Vuorikari et al., 2022). The main aim is the formation and development of competencies in the field of natural sciences and environment in personal, national and global context.

Study participants:

– Nine teachers, teaching: information technologies (IT), biology and health education (BHE), chemistry and environment protection (CEP), physics and astronomy (PA), mathematics (M), physical education and sport (PES), technologies and entrepreneurship (TE), geography and economics (GE) and English (E);

– 36 students (two samples of 18 students each), studying with the chosen methodology. After the preliminary test and practical task to determine the starting level before the experiment, one of the samples was categorized as the strong group and the other as the weak group. The results are presented below.

The study includes: 1) an analysis of the study results after the conducted CBE using the chosen methodology; 2) an analysis of the levels of the students’ intrinsic motivation before and after the education. The latter is included in this work.

Tools used to obtain the data:

1. A preliminary test to determine the initial level of both groups and a final test to assess the results achieved through the experimental education.

2. Results from solving practical tasks.

3. A questionnaire measuring the level of intrinsic motivation before and after the experimental education.

2.4.Conducting CBE education with the chosen methodology The joint education included the topics presented in Table 1.

Students worked in teams to develop the systems and robots shown in Table 2 and presented their projects to an audience in English.

The total duration was 32 hours (Joint education in theory and laboratory investigation work – 24 hours; Building integrated system or robot – 6 hours; Project presentation in front of the audience– 2 hours).

After the education was completed, the following were conducted: 1) a second questionnaire assessing motivation; 2) verification of academic results through a test.

3. Data analysis of the students’ achievements

3.1. Background

The selected sample consisted of 36 students from two samples (8a and 8b) of 18 students each. Sample 8a specializes in ICT and entrepreneurship, while Sample 8b focuses on natural sciences, specifically Biology and Chemistry. Both samples were tested on their preliminary and final levels of ICT knowledge and practical skills using a theoretical test and pra ctical tasks, respectively.

3.2. Test results

The first task was to compare the results achieved at the starting and final level for each sample. Therefore, tests for normality were applied to check if the data for each level of the two samples follows normal distribution or not.

3.3. Preliminary and final test results of Sample 8a

The Kolmogorov-Smirnov test (Table 3) returned a Sig. value below 0.05, which shows that the distributi on of the test scores of Sample 8a on the preliminary test is not normal.

Consequently, the non-parametric Wilcoxon Signed Ranks test was used to verify whether there would be a statistically significant difference between the final and starting level of Sample 8a.

In Table 4 there a re 10 students (“ Positive Ranks”) whose test scores have improved after the CBE education compa red to the starting level. Additionally, the Asymp. Sig. value of 0.046 from the Wi lcoxon Signed Ranks test is below 0.05, indicating a statistically significant difference between the starting and final test results of the students in Sample 8a (Table 5).

a. Lilliefors Significance Correction a. number of students with lower scores on the final test b. number of students with higher scores on the final test c. number of students with equal scores on the final and preliminary tests a. Wilcoxon Signed Ranks Test b. Based on negative ranks.

c. Based on positive ranks.

3.4. Preliminary and final test results for Sample 8b

The Kolmogorov-Smirnov test returned a Sig. value below 0.05, which indicates a distribution that is not normal. As a result, the non-parametric Wilcoxon Signed Ranks test was applied to verify if there would be a statistically significant difference between the results from the starting and final test of Sample 8b.

*. This is a lower bound of the true significance. a. Lilliefors Significance Correction

From the ranking Table 7, it can be seen that there are 15 students given as positive ranks that improved their test scores from the start. Wilcoxon ttest, presented in Table 8, confirmed that there is a statistically significant difference between the starting and final levels of Sample 8b as it returned a Sig. value below 0.05.

a. number of students with lower scores on the final test b. number of students with higher scores on the final test c. number of students with equal scores on the final and preliminary tests a. Wilcoxon Signed Ranks Test b. Based on negative ranks.

c. Based on positive ranks.

3.5. Comparison of test results between 8a and 8b groups

The distribution of the students’ test scores in both samples was tested for normality. As can be seen from Table 9, Kolmogorov-Smirnov test returned Sig. value below 0 .05 for the Sample 8a, which means that the distribution of the results from the theoretical test for this group deviates from normal distribution.

Although Kolmogorov-Smirnov and Shapiro-Wilk tests returned Sig. value above 0.05 for Sample 8b, a non-parametric Mann-Whitney test was used to determine if there is a statistically significant difference between the results of Samples 8a and 8b.

a. Lilliefors Significance Correction

A higher mean rank equal to 23.31 can be found for Sample 8a in Table 10 compared to Sample 8b whose mean rank is 13.69. The obtained ranks confirm the results from the normality tests where the Mean value of the theoretical test scores for Sample 8a was 19.28 while that for Sample 8b was 14.11. Consequently, Sample 8a is stronger than Sample 8b. For thi s reason, Sample 8a will be categorized as the strong group and Sample 8b as the weak group.

As can be seen from T able 11 , the achieved Asymp. Sig. (2- tailed) is below 0.05, which means that the difference of 5.17 between the Mean values of the weak (8b) and the strong (8a) group is statistically significant. In other words, the students from both groups did not start from the same starting level.

The next step was to check the results of the weak (8b) group and the strong (8a) group from the test after the finish of the CBE. Firstly, normality tests were performed for both groups.

a. Grouping Variable: group b. Not corrected for ties.

As can be seen from Table 12, Kolmogorov-Smirnov returned a Sig. value below 0.05 for the weak (8b) group , which means that the data does no t follow normal distribution. Consequently, the nonparametric Mann-Whitney test for two independent samples (Table 14) can be applied to verify whether there is a statistically significant difference between the results of both groups.

*. This is a lower bound of the true significance. a. Lilliefors Significance Correction a. Grouping Variable: group b. Not corrected for ties.

Mann-Whitney test showed a Sig. value of 0.168, which is above 0 .05 indicating that there is no statistically significant difference between the mean values of the results obtained for both groups. The weak (8b) group and the strong (8a) group finish at the same level after the CBE.

3.6. Preliminary and final task scores for the strong (8a) group Both Kolmogorov-Smirnov and Shapiro-Wilk tests returned a Sig. value below 0.05, thus, the distributions of the task scores obtained for both samples are not normal (Table 15). Consequently, the nonparametric Wilcoxon Signed Ranks test was used to verify whether there is a statistically significant difference between the scores obtained from the preliminary and final task. Table 16 shows 17 positive ranks, i.e. 17 students from the strong (8a) group have obtained higher scores on the final task compared to the preliminary task. In addition, Wilcoxon Signed Ranks Test (Table 17) returned a Sig. value below 0.05 indicating a statistically significant difference between the scores obtained on the final and preliminary tasks.

(8a) group on the preliminary and final tasks

a. Lilliefors Significance Correction a. number of students with lower scores on the final task b. number of students with higher scores on the final task c. number of students with equal scores on the final and preliminary tasks

between the students’ scores of the strong (8a) group from the preliminary and final tasks

a. Wilcoxon Signed Ranks Test b. Based on negative ranks.

3.7.Preliminary and final task scores for the weak (8b) group Shapiro-Wilk test returned a Sig. value below 0.05 for both samples, which means that the distribution of the scores on the preliminary and final tasks is not normal.

(8b) group on the preliminary and final tasks

a. Lilliefors Significance Correction

For this reason, the nonparametric Wilcoxon Signed Ranks test was used to verify whether there is a statistical difference between the scores of the weak group (8b) on the preliminary and final tasks.

As can be seen from Table 19, there are 18 positive ranks, i.e. all students achieved higher scores on the final task in comparison with the preliminary task. Wilcoxon test (Table 20) returned a Sig. value below 0.05, which also confirmed that the difference between the scores on the final and preliminary tasks is statistically significant.

a. number of students with lower scores on the final task
b. number of students with higher scores on the final task
c. number of students with equal scores on the final and preliminary tasks

a. Wilcoxon Signed Ranks Test b. Based on negative ranks.

3.8.Comparison of task scores between the strong (8a) and weak (8b) group

Preliminary level

Kolmogorov-Smirnov and Shapiro-Wilk tests ( Table 21 ) returned Sig. values below 0 .05 indicating that the distribution of the results from t he practical task for both groups is not normal.

The non-parametric Mann-Whitney test was applied to verify if there is a statistically significant difference between the results from the practical task obtained for the weak (8b) group and the strong (8a) group.

As can be seen from the test statistics, the Mann-Whitney test (Table 23) returned a Sig. value of 0.407, which is above 0.05, leading to the conclusion that there is not statistically significant difference in the starting practice levels of the students from both groups.

a. Lilliefors Significance Correction

a. Grouping Variable: group b. Not corrected for ties.

Final level

The results for both groups from the practice were tested for normality.

As can be seen from Table 24 , Shapiro -Wilk test returns a Sig. value below 0 .05 for the weak (8b) group and the strong (8a) group , which is sufficient to conclude that the distributions of the results from the practice are not normal. For this reason, the nonMollov, D. Stoitsov-, G. Stoitsovparametric Mann-Whitney test was selected to find if there is significant difference between the results from both groups.

a. Lilliefors Significance Correction

a. Grouping Variable: group b. Not corrected for ties.

Based on the Asymp. Sig. (2-tailed) value, which is above 0.05 (Table 26), it can be concluded that there is not a statistically significant difference between the results of the weak 8b group and the strong (8a) group. Consequently, both groups finished the CBE education at the same levels of practice.

4. Data analysis of the students’ intrinsic motivation

4.1. In the strong (8a) group

*. This is a lower bound of the true significance. a. Lilliefors Significance Correction

The results for the levels of the intrinsic students’ motivation in the strong 8a group before and after the app lication of CBE were tested for normality. According to the Kolmogorov -Smirnov and Shapiro-Wilk tests, the data for the levels of the intrinsic students’ motivation before CBE is normally distributed. Correspondingly, both Kolmogorov-Smirnov and Shapiro-Wilk tests returned Sig. value > 0. value \( \gt 0.05\) (Table 27).

The Kolmogorov-Smirnov and Shapiro-Wilk tests (Table 27) showed similar results for the distribution of the data on the level of intrinsic students’ motivation in the strong (8a) group after CBE.

Therefore, the parametric paired samples t-test was used to check if there is a statistically significant difference between the mean values of the two samples.

The paired samples t-test returned Sig. value of 0.244, which is above the critical significance level of 0.05. Consequently, there is no statistically significant difference between the starting and final level of the students’ intrinsic motivation in the strong (8a) group.

4.2.in the weak (8b) group

The results for the levels of the intrinsic students’ motivation in the weak

8b group before and after the application of CBE were tested for normality.

According to the Kolmogorov-Smirnov and Shapiro-Wilk tests, the data for the levels of the intrinsic students’ motivation before CBE is not normally distributed. Correspondingly, both Kolmogorov-Smirnov and Shapiro-Wilk tests returned Sig. value < 0.05 (Table 29).

Therefore, the non-parametric Wilcoxon Signed Ranks Test was used to check if there is a statistically significant difference between the mean values of both samples.

Table 30 shows that there are 18 positive ranks that correspond to the total number of the students in the weak (8b) group whose motivation was enhanced after the conducted CBE education. Consequently, the Wilcoxon Signed Ranks Test returned a Sig. value below 0.05 indicating that there is a statistically significant difference between the st arting and fin al level of students’ intrinsic motivation in the weak (8b) group. The results are shown on Table 31. The Kolmogorov-Smirnov and Shapiro-Wilk tests showed opposite results for the distribution of the data for the level of the intrinsic students’ motivation in the weak (8b) group after CBE.

*. This is a lower bound of the true significance. a. Lilliefors Significance Correction

a. number of students with lower intrinsic motivation after CBE b. number of students with higher intrinsic motivation after CBE c. number of students with unchanged intrinsic motivation after CBE

a. Wilcoxon Signed Ranks Test b. Based on negative ranks.

4.3.Comparative analysis of the starting and final levels of students’ intrinsic motivation in both groups

Firstly, it was interesting to verify if the difference between the starting levels of students’ intrinsic motivation in both groups is statistically significant. Based on the fact that the data for the starting level of students’ intrinsic motivation in the weak (8b) group is not normally distributed compared to that in the strong (8a) group, the non-parametric Mann Whitney significance test was applied (Table 33).

As can be seen from Table 32, the mean rank for the strong (8a) group is higher than that for the weak (8b) group, which means that the starting level of intrinsic motivation is higher for the students from the strong (8a) group. The Mann-Whitney test (Table 33) returned a Sig. value of 0.024, which is below 0.05 proving that the higher starting level of students’ intrinsic motivation in the strong 8a group is statistically different than that in the weak (8b) group.

a. Grouping Variable: group b. Not corrected for ties.

The next step was to verify if there is a statistical difference between the final levels of students’ intrinsic motivation in both groups. Because the data in both cases is normally distributed then the parametric independent samples t-test was applied to assess the difference between the final level of students’ intrinsic motivation in both groups.

Levene’s test returned a Sig. value \( \gt 0.05\), thus, equal variances can be assumed for both groups. For this reason, an attention should be paid on the first row of the t-test where the returned Si g. value is also > 0.05. value is also \( \gt 0.05\).

Consequently, there is no statistically significant difference between the final levels of students’ intrinsic motivation in both groups. In other words, the students from both groups started with different levels of intrinsic motivation but after the CBE education the students from the weak (8b) group managed to reach the level of intrinsic motivation of the students from the strong 8a group.

5. Interpretation of the results

1. A pedagogical study was conducted with a representative sample of 36 students from “Hristo Botev” High School in the village of

Chepintsi. The aim was to examine changes in both the students’ academic performance and their intrinsic motivation following the implementation of CBE in selected STEM disciplines from the curriculum.

2. The obtained results were assessed with the SPSS software of IBM for analysis of study results by using parametric and nonparametric tests in dependence of the type of distribution for rejecting the random character of the results.

3. On the base of the abovementioned actions and obtained results, the following conclusions for the starting level can be made:

3.1. The analysis of the results from the preliminary test on academic achievement, conducted before the implementation of the specialized education, re vealed a statisticall y significant difference between the initial performance levels of the two samples, with 8a outperforming 8b. Consequently, sample 8a was categorized as the strong group and 8b as the weak group.

3.2. The results from the performance of the preliminary practical task showed statistically insignificant difference between the strong group and the weak group.

3.3. The initial intrinsic motivation of the strong group was higher than that of the weak group.

4. The processing of the final results showed:

4.1. Statistically significant difference between preliminary and final test level for each group individually, which confirms the positive influence of the applied methodology on the study results of the students. Same result was observed for the practical tasks in both groups. The intergroup comparison showed statistically insignificant difference between the preliminary results and after that also between the final results from their solving.

4.2. The intergroup comparison showed that the weak group has a lower result at the preliminary test in comparison with the strong group, however, at the final the results from the test were statistically indistinguishable, which means that the methodology has a higher positive effect on the study results of the weak group.

4.3. Statistically insignificant difference between prelimina ry and final level of intrinsic motivat ion in the strong group. In contrast, the weak group enhanced their intrinsic motivation. The intergroup comparison showed that the initial intrinsic motivation of the strong group is higher compared to that of the weak group.

The main hypothesis of the pedagogical study stating that CBE influences positively the obtained study results from the education in the studied STEM disciplines and enhances the students’ intrinsic motivation was confirmed by the results from the conducted pedagogical experiment.

6. Conclusion

The proposed variant for the practical implementation of the joint CBE concept involves a specific group of study subjects, though it is not the only possible configuration. When considering a design-thinking approach in education, projects can be selected that aim to improve the lives and social environments of citizens. For example, techno logical solutions for people with disabilities and innovations to enhance community services can be developed. Additionally, projects focused on sustainable energy, smart health-protection devices, ecological innovations, and platforms for social engagement align with various disciplines, including psychology, civic education, natural sciences, and information technologies. By using such an approach, students not on ly acquire in terdisciplinary knowledge, but also develop social responsibility and awareness of the real needs of their communities. This approach adds variety and emphasizes the integration of multiple disciplines.

Acknowledgements

The work on the article is supported by the MUPD-FMI-010 project of the National Program “Young Scientists and Postdoctoral Researchers” – 2.

NOTES

1. ArcGIS, https://www.arcgis.com/index.html, last visited 11.03.2025

2. European-qualifications-framework, https://europa.eu/europass/bg/european-qualifications-framework-eqf, last visited 11.03.2025

3. Oana, C., 2022. ADDIE Model: What It Is and How to Apply It, https://venngage.com/blog/addie-model/, last visited11.03.2025

4. PISA 2025 SCIENCE FRAMEWORK (DRAFT) May 2023, https://pisa-framework.oecd.org/science-2025/assets/docs/PISA_2025_Science_Framework.pdf, last visited 11.03.2025

5. Tasiopoulou et al., 2022. European Integrated STEM Teaching Framework. October 2022, European Schoolnet, Brussels. https://files.eun.org/STEAMIT/STE(A)M-IT-Framework-Digital.pdf, last visited 11.03.2025

6. The Global STEM Alliance (GSA) STEM Education Framework, https://www.nyas.org/wp-content/uploads/2024/02/ gsa_stem_education_framework_dec2016.pdf, last visited 11.03.2025

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