The results in Table 1 show that two canonical functions were evaluated. The first canonical function (function 1) obtained a value of 0.99398 with p = 0.000, indicating a highly significant relationship. Function 1 for "Eigenvalue" obtained a value of 82.31551, indicating that this function explains 99.95% of the cumulative variation in the data. Canonical correlation function 2 obtained a value of 0.19708 with p = 0.345, indicating statistical insignificance. Therefore, the first function can be used for further interpretation, while the second function is irrelevant in the context of this analysis. The Wilks' Lambda results support this condition, with the canonical function producing an F value of 91.41359 with a significance of p = 0.000. Therefore, the first canonical function can explain the two sets of variables, while the second function cannot.

Table 2 shows that the results of the Pillai's Trace, Hotellings's Trace, Wilks' Lambda, and Roy's Largest Root statistical tests are statistically significant with a p- value of <0.05. This analysis indicates a relationship between the independent and dependent variables in the canonical model structure. For example, an indication that the variance explained by the canonical function is significant is obtained from the F value = 12.13427 and p = 0.000 by Pillai's Trace value (1.02684). Then, Wilks' Lambda gives a value of 0.01154 with an approximate F = 91.41359 and p = 0.000, which indicates that most variables can be explained significantly, and this is one of the leading indicators in canonical analysis. For Hotelling's Trace, the value of 82.35592, F = 432.36860, and p = 0.000 is obtained, and the relationship between variables is firm in the canonical model. Finally, to get a value of 0.9880, Roy's largest root with F = significant at p = 0.000, the most considerable canonical function is substantial and contributory. Thus, this finding supports that both canonical functions can be considered in the further analysis because they have a significant relationship simultaneously.

Table 3 shows that the contribution of each variable is different in the canonical model. Based on the results of the "standardized canonical coefficients for DEPENDENT variables" in the second function, the physical organic chemistry variable (Y2) has a high correlation value of 0.87444, meaning that Y2 is dominantly contributory to the second canonical function. On the other hand, the more minor contribution to the second function is the variable Y1, with a coefficient value of 0.14341. This finding confirms that the second canonical function represents the relationship involving the variable Y2 more than Y1. On the other hand, for the independent variable, X2 (general chemistry) has a value of 0.85133 based on the standardized canonical coefficient. This value indicates that the function contributes very strongly. In contrast, X1 has a lower coefficient value of -1.31622, meaning that the contribution given is very small or negative with the first function. A higher contribution is provided by X2 with a coefficient value of 1.00385 on the second function compared to -0.00594 from X1.

Thus, Table 3 shows that variable X2 (general chemistry) significantly influences the first canonical function. In contrast, variable Y2 (physical organic chemistry) significantly impacts the second function more. The indication is that each variable has a specific relationship to each canonical function. Therefore, this finding can be the focus of subsequent interpretations to explain the relationship between sets of independent and dependent variables.

Table 4 results from the canonical loading calculation related to strengthening the relationship between variable data. The results show that the independent and dependent variables strongly correlate with a higher canonical value on variable X2 (general chemistry) of 0.9999 in the table "Correlation between Covariates and Canonical Variables". This finding confirms that X2 contributes most to the second canonical function, while variable X1 = 0.64679 has a lower contribution. In terms of dependent variables in the table, both variables have a high correlation to the second canonical function, such as Y2 (physical organic chemistry), which is highly correlated with a value of 0.99725 and followed by a value of 0.89227 from organic chemistry (Y1). Both dependent variables have a close relationship in the second canonical function, with the most dominant contribution being Y2. Thus, student success in basic chemistry courses can be a predictor of their success during advanced material lectures.

Prerequisite courses and advanced courses have a significant relationship based on statistical analysis. The first canonical correlation was 0.99398 for function 1, with a significance level of <0.05 (p=0.000, individually substantial). This correlation confirms that introductory chemistry courses (X2) support sustainable learning, particularly in physical organic chemistry (Y2). This value indicates that basic chemistry material substantially prepares students for advanced material. The conceptual nature of introductory chemistry provides a solid foundation for students to delve deeper into other, more advanced chemistry materials. This contribution is evident in the canonical coefficient of 0.85133 (Standardised canonical coefficients for COVARIATES CAN. VAR.). This aligns with mastering fundamental chemistry concepts as a foundation for higher-order thinking in higher education. In chemistry education, learning based on the representational level is the primary foundation for building scientific mental models(Barke et al., 2012).

By possessing basic knowledge and representational competence, students have an easier time understanding and interpreting phenomena from the macro to the symbolic level (Cheng & Gilbert, 2009)(Keiner & Graulich, 2021)(Taber, 2001), whereas previous studies tended to focus on submicroscopic applications. Specifically, introductory chemistry demonstrates a dominant contribution compared to school chemistry. This is because introductory chemistry studies many fundamental concepts, such as atomic structure, chemical bonding, fundamental chemical laws, stoichiometry, reaction mechanisms, and reaction rates, which serve as the primary basis for studying organic chemistry as a process of building mental models. (Taber, 2012) emphasised that effective mental structures and models are constructed from mastery of fundamental chemical concepts. Improving mental models also plays an essential role in helping students gain a deep understanding of chemistry and its application in society (Barke et al., 2009)(Barke et al., 2012)(Mezirow, 1997). This dominance indicates that mastery of pure chemistry content learned and obtained from introductory courses influences students' success in understanding advanced material.

In contrast, school chemistry 1 (X1) contributed less, which needs to be considered and addressed in the teaching context. One possible reason is that this course emphasises pedagogical approaches, lesson planning, and delivery methods rather than reinforcing in-depth chemistry concepts. School chemistry is designed to provide students with pedagogical insight and competency as future teachers. The experience of studying school chemistry 1 offers theoretical and practical literacy to prepare students to master chemistry concepts, analyse learning difficulties in specific chemistry topics, and understand chemistry learning design based on the needs of secondary-level students. This demonstrates the potential for strengthening the structure of school chemistry learning so that it focuses not only on teaching strategies but also on deepening conceptual understanding contextually. Integration of content and pedagogy is crucial to support continuous learning and build solid mental models, in line with Klafki's didactic framework, which emphasises the importance of the interconnectedness of "what," "why," and "how" in lesson planning.

Following Wolfgang Klafki's (1980) didactic framework, for content analysis (what), the results show that introductory chemistry (X2) significantly contributes to basic organic chemistry (Y1) and physical organic chemistry (Y2) courses. This finding confirms that introductory chemistry has a substantial weight in supporting students' understanding of advanced concepts with high complexity. Therefore, introductory chemistry is key for students in building scientific mental models and supporting continuous learning. For didactic analysis (why and how), this context highlights the school chemistry course (X1). The canonical test shows that X1 contributes less than X2, thus concluding that the focus of X1 should be building integration between students' conceptual understanding and pedagogical skills. In Klafki's thinking, this finding emphasises the importance of considering learning strategies to accommodate students' conceptual understanding and teaching skills. Although statistically, school chemistry contributes less than introductory chemistry, its presence has a very crucial role in building students' mental models, considering that learning science, such as chemistry, requires various approaches to understand chemical materials, especially at the submicroscopic level (Keiner & Graulich, 2021); (Schwedler & Kaldewey, 2020); (Widing et al., 2023) .

This study confirms that students with a strong foundation in chemistry are better prepared for advanced material and can handle cognitive load and analytical thinking. This finding is relevant to the literature, which states that students' difficulties in understanding advanced concepts are often rooted in a weak understanding of introductory chemistry and submicroscopic representations. For example, to practice problem-solving skills, these skills tend to be trained using representational concepts through graphs, writing, reaction stages, arrow notation, and other methods (Bruce et al., 2022)(Hunter et al., 2021)(Shabrina et al., 2023)(Watts et al., 2020). However, these concepts have not fully trained students' elaboration skills in understanding concepts at the specific level (Dood & Watts, 2022). Some instructors have not intended to practice representational concepts because they believe it could disrupt the duration of class material completion (Popova & Jones, 2021). Therefore, training or understanding the level of representation is not enough without knowing the students' needs, but a more relevant approach is needed to address the problem.

Regarding methodological contribution (how to teach), the use of canonical correlation adds value to this study. This method allows for the analysis of simultaneous relationships between sets of variables, which cannot be accommodated by simple correlation analysis or linear regression. Its application in the context of chemistry education, particularly the exploration of the relationship between prerequisite courses and advanced achievement, makes this study crucial for providing instructors with additional insights into chemistry learning development strategies relevant to 21st-century learning (Prastikawati et al., 2024). This study also confirms that optimal academic performance at a high level can be enhanced by meeting performance in foundational-level courses. In cognitive load theory, students with optimal mastery and understanding of introductory chemistry are more likely to reduce cognitive load when facing more complex problems. A strong foundation of understanding can allocate students' cognitive resources to analyse advanced concepts (Anmarkrud et al., 2019)(Mayer & Moreno, 2003)(Paas et al., 2016)(Nooijen et al., 2024).

This study has practical implications for the design of chemistry learning, even at the curriculum level, where previous studies have shown that canonical chemistry is widely used in various engineering and industrial fields (Alrawashdeh et al., 2024); (Kudraszow et al., 2025); (Yang et al., 2025); (Zheng et al., 2025). In education, the context of its use is not in the analysis of simultaneous relationships between materials, but rather in perceptions, personalities, teaching practices, behaviours, etc. (Elmore & Ellett, 1978); (Holland & Piper, 2016); (Mukherjee et al., 2009). Therefore, it is necessary to strengthen the conceptual content in introductory chemistry and innovation in school chemistry learning so that it not only trains pedagogical aspects but also supports the in-depth understanding needed in advanced chemistry courses. These findings also support the development of 21st-century skills, such as critical thinking, creativity, problem-solving, collaboration, and digital literacy, which are essential for prospective chemistry teachers to face various global challenges (Kain et al., 2024); (Hidayat et al., 2025); (Ødegård et al., 2025); (Vlachopoulos & Makri, 2024)

Thus, this study provides a theoretical contribution by explaining the relationship between prerequisite and advanced courses, as well as a practical contribution by supporting learning renewal, curriculum strengthening, and continuous learning, as well as strengthening students' readiness as future adaptive and transformative professional educators.

Although the results of this study are considered significant, particularly the analysis of the relationship between basic and advanced chemistry courses, several limitations still require consideration. First, this study used a correlational approach, so causal conclusions cannot be drawn directly between the independent and dependent variables. Second, the sample size does not fully represent the entire population of chemistry education students. Therefore, further investigation with a larger sample size is highly recommended in future studies. Third, aspects of the lecturer's teaching style or learning strategies were not included as pedagogical variables, as these factors significantly influence student academic performance. Longitudinal or experimental designs are highly recommended for further study to explore causal relationships and consider broader contextual factors in chemistry learning.

The results of this study need to be interpreted very carefully, considering the study's design, which is limited to one study program and the use of a solely quantitative approach. Furthermore, although all quotes and paraphrases in this article have been compiled with efforts to maintain the accuracy of the source's meaning, readers are still advised to read the primary sources directly to gain a more comprehensive understanding and avoid potential distortion of interpretation. These findings are expected to be a starting point for further studies with a broader sample scope and a more varied approach.

The canonical correlation test has demonstrated a significant relationship between basic and advanced chemistry courses. It allows instructors and curriculum developers to design learning innovations in higher education settings. For example, integrating problem-solving-based learning, needs-based learning, and applying multiple representations can facilitate the construction of student structures and mental models, thereby achieving a deeper understanding of chemistry material. This integration can potentially train students to solve problems, especially when experiencing more complex learning in advanced courses.

Overall, the practical implications of the study results are improved quality of content-based programs and curricula, which are also aligned with student needs. This approach can strengthen student competencies in the local context while contributing to global challenges. Continuous chemistry learning can be adopted in various universities, considering that analytical and synthetic skills are key elements for students to adapt to the diverse challenges of the international workplace. Therefore, integrating collaboration, problem-solving, inclusiveness, and adaptive skills into learning is a strategic step in preparing students for 21st-century learning. Integration goes beyond simply understanding chemistry content conceptually; it also fosters the ability to implement it practically and innovatively in the real world.