Introduction

Chemical stoichiometry is a fundamental concept in chemistry concerned with the quantitative relationships between reactants and products in chemical reactions (Giunta, 2016). It provides the foundational understanding necessary for predicting the outcomes of chemical reactions, enabling chemists to determine optimal conditions for achieving desired yields. However, stoichiometry is widely recognized as a challenging topic for students, particularly due to its abstract nature and the complex mathematical calculations involved (BouJaoude & Barakat, 2000; Mulford & Robinson, 2002; Niaz & Montes, 2012; Sanger, 2005).

One of the most persistent challenges in stoichiometry is the concept of limiting reagents. Limiting reagents are the reactants that are completely consumed in a chemical reaction, thereby determining the maximum amount of product that can be formed (Obour, 2012; Omari & Mandumpal, 2023). Accurately identifying the limiting reagent is crucial for ensuring efficient use of reactants and avoiding waste. Despite its importance, students often struggle with this concept, as they tend to rely heavily on algorithmic procedures without fully understanding the underlying principles (Cracolice et al., 2008; Fach et al., 2007).

Research has shown that students frequently resort to memorizing steps for solving stoichiometric problems, which leads to a lack of conceptual understanding (Nyachwaya et al., 2014; Sostarecz & Sostarecz, 2012). For example, Hanson (2016) found that Ghanaian pre-service teachers often used inexplicable procedures to solve stoichiometric problems, highlighting the need for alternative instructional approaches. Similarly, Marais and Combrinck (2009) reported that many undergraduate students in South Africa could not balance chemical equations or determine limiting reagents, attributing these difficulties to ineffective teaching methods, and their assertion is supported by Bridges (2015) and Shadreck and Enunuwe (2018).

To address these challenges, several studies have recommended the use of the first principle approach (FPA) in teaching limiting reagents (Antwi, 2013; Obour, 2012). FPA emphasizes conceptual understanding through visualizations, inquiry-based activities, problem-solving exercises, and real-world applications. For instance, if 1 part of sugar combined with 2 part of cocoa powder to form a perfect tea mix, thenx part of sugar would require 2xpart of cocoa powder. If 2xpart of cocoa powder was not available during the tea preparation, then the limiting reagent was cocoa powder and the excess reagent was sugar. However, if for instance, 3x part of cocoa powder was initially available, it means it was morethan adequate; and, so, the limiting reagent would be sugar. This approach to determining limiting reagents is an inquiry-based activity involving a real-world application and problem-solving exercise.

Also, Cheng et al. (2017) demonstrated that students taught using problem-solving (PS) approaches outperformed those taught with traditional methods, showing significant improvements in critical thinking and problem-solving skills. Similarly, Obour (2012) found that students’ performance improved significantly when FPA was used to teach limiting reagents, compared to traditional lecture methods.

Again, She et al. (2012) sampled 183 undergraduate students taking freshman chemistry course to solve three chemistry tasks across a semester. The regression model they developed revealed that existing or previous knowledge of students was the main factor that determined their problem-solving performance. Their findings support the idea that learners’ existing knowledge is crucial for a success in understanding new knowledge, and this is what FPA bedrocks on.

In this study, college of education students (pre-service teachers) were targeted in a quasi-experimental design study and it was to assess whether FPA could help deepen their conceptual understanding of limiting reagents. The findings will, therefore, contribute to literature and either reaffirm or belie the significance of FPA as a teaching strategy.

Conceptual Framework

Cognitive constructivism: The theoretical basis for FPA lies in cognitive constructivism, which emphasizes the active construction of knowledge by the learner through the integration of prior knowledge with new information (Merrill, 2012/2020). For instance, students already understand the concept of pairing items. In this study, to explore the concept of limiting reagents, seven red beads and twelve blue beads were mixed to react, with the assumption that one red bead reacts with one blue bead. The activity is illustrated below:

Figure 1. Limiting Reagent Before and After Reaction

From the illustration shown above, students observed that the limiting reagent was the red bead and it was the reason the reaction could not continue since there was nothing left to react with the excess five blue beads. This means, by engaging students in the exploration and understanding of the underlying principles of limiting reagents, the approach encourages them to construct a conceptual framework that promotes deeper learning.

Conceptual understanding: FPA emphasizes the development of conceptual understanding rather than relying solely on procedural knowledge (Gardner, 2011; Hall, 2018). In this study, several illustrative examples were used to arouse students’ conceptual understanding of limiting reagents. For example, students were guided to deduce the limiting reagent in the reaction: 0.5 mol LiOH + 0.8 mole CO2 = Li2CO3 + H2O. The tutor wrote a balanced equation and made assumption to students that one reactant would be used up. The tutor explained that since the reactants are not in stoichiometric proportions, one would be completely consumed and the other be in excess. Based on this assumption, students determined the moles of each reactant and compared them vis-à-vis their stoichiometric ratios. Consequently, they successfully determined the limiting reagent. Thus, the assumption helped facilitate students’ conceptual understanding.

Contextualization and application: FPA incorporates real-world contexts and applications to enhance students’ engagement and facilitate the transfer of knowledge (Gardner, 2011; Lee, 2013; Merrill, 2002). By providing students with authentic scenarios and chemical reactions, they are challenged to identify the limiting reagent by considering the reactant stoichiometry in the context of the reaction’s requirements (Obour, 2012). For instance, the following were some of the real-life scenarios used in this study to contextualise limiting reagents: (1) If hot-dogs combine with buns to give ‘complete hot-dogs’, and you were given five hot-dogs and four buns, how many ‘complete hot-dogs’ could be made? – Assumption: hot-dog and buns combine in a 1:1 ratio – Reaction gives four ‘complete hot-dogs’ and one leftover hot-dog. This means the number of buns determined how many ‘complete hot-dogs’ that could be made and, so, the limiting reagent was the bun; (2) If you had twelve party-invitations (I) and twenty stamps (S), and each party-invitation required two stamps to be complete for posting, how many ‘complete party-invitations’ could be dispatched? – Equation: I + 2S → IS2 – Reaction gives ten ‘complete party-invitations’ and two party-invitations with no stamps. This means stamp is the limiting reagent.

Metacognition: Metacognitive strategies play a crucial role in FPA as students are encouraged to reflect on their own thinking processes and monitor their understanding. By engaging in metacognitive activities such as self-questioning, self-monitoring, and self-explanation, students can identify any misconceptions or gaps in their understanding of limiting reagents (da Silva, 2017). This metacognitive awareness enables them to actively regulate their learning, resulting in a deeper comprehension of the concept. For instance, students were asked to critique, check and recheck each step they reach whenever they were determining limiting reagents by self-questioning, think-aloud pairing and collaborating with their colleagues.

Teacher facilitation: Effective implementation of FPA requires the teacher to act as a facilitator, guiding students through the learning process. The teacher’s role involves promoting active engagement, posing thought-provoking questions, encouraging critical thinking, and providing timely feedback (Lee & Koszalka, 2016; Odo et al., 2021). For example, in order to spark learners’ critical thinking, students were guided to follow an instructional procedure and identify the limiting reagent in a simple kitchenette experiment. By fostering a supportive and inquiry-based learning environment, teachers help students construct their knowledge and develop a robust understanding of concepts (Omari & Mandumpal, 2023).

Conceptual framework summary: The conceptual framework presented above provides a theoretical foundation for examining the impact of FPA on students’ ability to determine limiting reactants. By emphasizing cognitive constructivism, conceptual understanding, contextualization and application, metacognition, and teacher facilitation, the approach aims to enhance students’ ability to comprehend and apply the concept of limiting reagents. This framework provides a guide for empirical research investigating the impact of the FPA and serves as a basis for evaluating the effectiveness of instructional strategies.

Problem Statement

Traditionally, students are taught to determine limiting reagents using basic stoichiometric calculations or empirical approaches based on ratios of coefficients in balanced chemical equations (Cano, 2022; Gauchon & Méheut, 2007; Omari & Mandumpal, 2023). This has been observed in the researchers’ college. These traditional teaching methods often focus on rote memorization of steps without emphasizing the underlying principles, leading to limited comprehension and poor application of concepts (Chandrasegaran et al., 2009). There is, therefore, a need to explore alternative instructional approaches that enhance students’ understanding of limiting reagents.Despite the growing body of research supporting FPA, there is limited evidence of its effectiveness in Ghana and other parts of West Africa. This study, therefore, aims to fill this gap by investigating the impact of FPA on students’ ability to determine limiting reagents in chemical stoichiometry.

Research Questions

The following research questions were raised to guide the study:

What effect would FPA have on students’ performance on algorithmic problems?

What effect would FPA have on students’ performance on conceptual problems?

Significance of the Study

This study seeks to contribute to the literature on effective teaching strategies for stoichiometry and provide practical recommendations for chemistry educators. The findings are expected to highlight the benefits of FPA in fostering deeper conceptual understanding and improving students’ problem-solving skills in chemistry.

Methodology

Research Design and Sampling

A quasi-experimental design was employed to investigate the effect of the first principle approach (FPA) on students’ performance in determining limiting reagents. The study involved 120 second-year science students from two colleges of education in the Western North Region of Ghana. The students were randomly assigned to either the experimental group (EG) or the control group (CG), with 60 students in each group. Random sampling was used to select participants from each college to ensure unbiased representation (Arnab, 2017). The EG was taught using FPA, while the CG followed the traditional teaching approach (TTA).

Potential Confounding Variables and Control Measures

Several potential confounding variables were considered in this study, including institutional differences, teacher effects, students’ prior knowledge, and instructional time. Both colleges follow the same curriculum, offer the same programmes, and have similar facilities and teaching staff with comparable educational backgrounds (MPhil and PhD). This similarity between the colleges helped minimize potential confounding variables related to institutional differences.

To control for teacher effects, the same tutors were trained to deliver both FPA and TTA lessons, ensuring consistency in teaching quality and delivery. Additionally, the tutors were provided with detailed lesson plans and instructional materials to standardize the teaching process across both groups.

Students’ prior knowledge of stoichiometry was assessed through a pre-test, which confirmed that both groups had comparable entry knowledge (EK) levels. This pre-test ensured that any differences in post-test performance could be attributed to the teaching methods rather than prior knowledge disparities. Furthermore, the instructional time for both groups was kept constant, with each group receiving the same number of lessons over the same period.

Instructional Procedure

The instructional intervention spanned two weeks, with both groups covering topics related to limiting reagents as outlined in the JBI 232 (particulate nature of chemistry) course syllabus. The EG was taught using FPA, which emphasized conceptual understanding through inquiry-based activities, real-world applications, and problem-solving exercises (see Table 1). In contrast, the CG was taught using TTA, which primarily focused on algorithmic procedures, step-by-step calculations, and rote memorization of steps. For instance, there are 5 steps outlined in several textbooks in Ghana that guide students to determine limiting reagents: (1) Balance the equation; (2) Deduce the moles from the given data; (3) Determine the mole ratio of the species; (4) Compare the deduced ratio to the actual ratio; and (5) Deduce which reactant is limiting (will run out first).

Research Instruments

Data were collected using pre- and post-tests. Both the EG and the CG were assessed using common tests. The questions were sampled, readjusted, validated and developed by the researchers, with input from two senior chemistry lecturers, and were trialed among 15 students in a comparable situation to ensure construct validity and internal consistency. The reliability of the test was confirmed using Cronbach’s alpha (α = 0.78).

The pre-test consisted of 5 multiple-choice questions (2 marks per correct answer) drafted from the West African Senior Secondary Certificate Examination (WASSCE) past questions and was designed to assess students’ entry knowledge (EK) of basic stoichiometry.Multiple-choice questions were used since only basic knowledge of stoichiometry was being solicited with less emphasis on students’ algorithmic skills and/or conceptual understanding.

The post-test consisted of 5 open-ended test items drafted from JBI 232 examination past questions, with two items focusing on algorithmic problems (AP) and three items assessing conceptual problems (CP), and was aimed at assessing the impact of the teaching methods used.

Data Collection

The pre-test was administered to both groups before the intervention (Week 1) to establish baseline knowledge. Following the pre-test, tutors were trained in the same week on the intervention methods. The instructional intervention was then conducted over two weeks (Weeks 2 and 3), with the EG receiving FPA-based instruction and the CG receiving TTA-based instruction. After the intervention (Week 4), the post-test was administered to both groups to evaluate the impact of the teaching methods. The entire study was completed in four weeks.

Table 1. Weekly Plan for First Principle Approach Intervention

Lesson Plan	Week 2 – 120 minutes	Week 3 – 120 minutes
Objective(s)At the end of the week, students will be able to:	1. Explain the concept of limiting and excess reactants2. Deduce and balance equations from real-life scenarios	Calculate the moles of limiting and excess reactants
Resources	Loaves of bread, butter, coloured beads, sandwich, hot dog buns, hot dogs, invitation cards and stamps	Lab worksheet, various laboratory equipment, baking soda, vinegar
Teaching methods
1. Lesson introduction	1. Review previous lesson on mole ratios2. Give an example to introduce the concept of limiting and excess reactants	Guide students in groups to balance a chemical equation to revise limiting and excess reactants
2. Lesson progression	1. Use the example to engage students in discussing the concept of limiting and excess reactants2. Use 3 real-world scenarios to engage learners in inquiry-based learning to deduce reactants, products, limiting reactants and excess reactants3. Engage students in peer collaborations to deduce balanced equations from the real-world scenarios	1. Guide students in groups to carry-out a simple kitchenette experiment using baking soda and vinegar in the laboratory2. Use 3 illustrative examples of chemical reactions to engage students in group work to determine the moles of limiting reactants and excess reactants
3. Guided practice	Real-world application, discussion, inquiry-based learning, collaboration	Laboratory activity, illustrative examples, discussion
4. Student practice	Self-questioning, peer critique	Laboratory worksheet
5. Learner accommodations	More guidelines for students in groups to formulate concepts in writing	1. Direct Instruction2. Hands-on activity 3. More guidelines on laboratory procedure during activity
6. Assessment	Questions and answers	1. Students’ understanding will be assessed as teacher circulates through the class2. Completion of laboratory worksheet
7. Lesson closure	Summarize lesson through question and answer	Collect worksheet
Measuring student Progress	Students will be given homework on the concept of limiting and excess reactants	Students will be given homework on the concept of limiting reactants, excess reactants and percent yields

Data Analysis

The test results were analyzed using descriptive and inferential statistics.

Classification of students’ pre-test responses:The full score for the multiple-choice questions of the pre-test was 10 but the final mark was given in percentages. The students’ achievement level was used to categorize the scores into high, moderate and low performances (Sangguro et al.,2019). Table 2 submits the score categories applied.

Table 2. Score Level

Score (%)	Achievement level
70-100	High
40-69	Moderate
0-39	Low

*Adapted from Sangguro et al. (2019)

Classificationof students’ post-test responses:To classify the open-ended questions used in the post-test in this study, we were guided by a rubric developed by Niaz and Montes (2012). Students’ response to the AP (Items 1 and 2) in the post-test were categorized as: i) Correct, if all the necessary steps needed to solve the problem are presented; ii) Incorrect, if the various steps are presented incoherently and the necessary calculations are not performed; and iii) No response, if the question is not answered at all. Also, students’ responses to the CP (Items 3-5) were categorized as: i) Conceptual, if calculations and reasoning are presented in a clear and systematic manner; ii) Partially Conceptual, if some reasoning are presented but lacks a clear and systematic scheme; iii) Rhetorical, if some aspects of the problem situation are reproduced and no clear and systematic presentation of deductions are shown; and iv) No Response, if the question is not answered at all. Additionally, two conceptual test items involved multiple small parts or steps; Test Item 4 – If two out of the three parts are correct, it is classified as a partially conceptual response and if one out of the three parts is correct, it is classified as a rhetorical response; Test Item 5 – if one out of the two parts is correct, it is classified as a partially conceptual response.

Validation of students’ post-test responses:The classification of students’ responses to items 3-5 was validated through inter-rater agreement – both researchers classified all responses of the EG individually, using the scheme developed. These were the results obtained: Item 3: 85% agreement; Item 4: 90% agreement; Item 5: 78% agreement. Discussions were, then, held to resolve all disagreements. Using the approved scheme, the second author categorized the responses of the CG.

Statistical analysis:A chi-square analysis was conducted to determine significant differences between the EG and CG in the post-test at a significance level of 0.05. This analysis helped identify the effectiveness of FPA in improving students’ performance on both AP and CP.

Results

Assessing Entry Knowledge of Students in Basic Stoichiometry

This part focused on finding students’ achievement levels in basic stoichiometric problems by analyzing responses from multiple-choice questions in the pre-test. Marks were assigned based on students’ correct responses. Table 3 presents the performance of students. Detailed data is submitted in Appendix-02.

Table 3. Achievement of Students in the Pre-Test

Group	Mean	Overall mean	Achievement level
	Score	%	Score	%	Group	Overall
Experimental	6.60	66.00	6.72	67.15	Moderate	Moderate
Control	6.83	68.30			Moderate

From Table 3, the pre-test results revealed that both the experimental group (EG) and control group (CG) had moderate levels of entry knowledge (EK) in basic stoichiometry. The mean scores for the EG and CG were 66.00% and 68.30%, respectively, with an overall mean score of 67.15%. These results indicate that both groups had comparable baseline knowledge, justifying the comparison of the effects of the first principle approach (FPA) and traditional teaching approach (TTA) on their performance.

Algorithmic versus Conceptual Problems

In this study, algorithmic problems (AP) refer to such problems where balanced equations are already provided and require students to apply procedural steps and formulae ((Martin, 2009; Rittle-Johnson & Schneider, 2015), while conceptual problems (CP) refer to those problems where real-world scenarios are presented and require students to demonstrate deeper understanding by interpreting the scenarios, deducing balanced equations and performing calculations (Hurrell, 2021; Jonsson et al., 2014).

Research question 1: What effect would FPA have on students’ performance on algorithmic problems?

Item 1

Given the reaction: 8Fe + S8→8FeS. If given 293 g Fe and 17.2 g S8, determine the limiting reagent. [Molar masses: Fe = 55.845 gmol-1; S = 32.065 gmol-1]

Item 1 is a typical AP. Students were required to deduce the moles of the reactants from their given masses and molar masses, and use the moles and mole ratio to determine the limiting reactant (see Appendix-03a). Table 4 presents the analysis of students’ responses to Item 1.

Table 4. Performance of Students on Post-Test Item 1 (Algorithmic)

Response	Experimental(n = 60)	Control(n = 60)	Chi-square
			χ2 (P-value)	Decision
Correct	53 (88.33%)	50 (83.33%)	0.69 (p < 0.71)	Not significant
Incorrect	6 (10.00%)	9 (15.00%)
No response	1 (1.67%)	1 (1.67%)

*p < 0.05

Majority of students in both groups performed well, with 88.33% of the EG and 83.33% of the CG providing correct responses (Table 4). Though 5.00% (88.33% - 83.33%) more students from the EG responded correctly than those from CG, the chi-square analysis indicated no significant difference between the groups (χ2 = 0.69, p = 0.71). Some of the students whose responses were incorrect (EG: 10.00%; CG: 15.00%) presented wrong formulae for calculation while others could not follow the needed algorithmic procedures. Also, 1.67% of students from each group did not respond to Item 1.

Item 2

15 g aluminum sulphide and 10 g water react until the limiting reagent is used up. The balanced equation is:

Al2S3 + 6H2O →2Al(OH)3 + 3H2S. Deduce the limiting reagent?

[Molar masses: Al= 27 gmol-1; H = 1 gmol-1; O = 16 gmol-1; S = 32 gmol-1]

This is an AP. Like Item 1, it required students to compute the initial moles of each reactant and use mole ratio to deduce the limiting reagent (see Appendix-03b). Table 5 summarizes the analysis of students’ responses.

Table 5. Performance of Students on Post-Test Item 2 (Algorithmic)

Response	Experimental(n = 60)	Control(n = 60)	Chi-square
			χ2 (P-value)	Decision
Correct	57 (95.00%)	55 (91.67%)	0.57 (p < 0.75)	Not significant
Incorrect	2 (3.33%)	3 (5.00%)
No response	1 (1.67%)	2 (3.33%)

*p < 0.05

Again, both groups performed well, with 95.00% of the EG and 91.67% of the CG providing correct answers (Table 5). The chi-square analysis confirmed no significant difference between the groups (χ2 = 0.57, p = 0.75). Few students (EG: 3.33%; CG: 5.00%) presented incorrect responses to Item 2 while 1.67% and 3.33% from the EG and CG, respectively, did not attempt responding. The incorrect responses were basically as a result of students’ wrong use of formulae and wrong unit conversions.

Research question 2: What effect would FPA have on students’ performance on conceptual problems?

Item 3

When ethyl acetate, CH3CO2C2H5, a solvent in many fingernail polish removers, is prepared by reacting ethanol, C2H5OH, with acetic acid, CH3CO2H, water is released. Given 10 ml each of the ingredients, find the limiting reagent. [Densities: acetic acid = 1.0492 gml-1; ethanol = 0.7893 gml-1; Molar masses: C = 12 gmol-1; H = 1 gmol-1; O = 16 gmol-1]

This is a typical CP. Students were expected to understand the question and translate it into equation. They were required to balance the equation, use the respective densities and volumes to deduce the masses, and to compute the moles from the calculated masses and the molar masses. They were then to use mole ratios to determine the limiting reagent (see Appendix-03c). Analysis of students’ responses to Item 3 is summarized in Table 6.

Table 6. Performance of Students on Post-Test Item 3 (Conceptual)

Response	Experimental(n = 60)	Control(n = 60)	Chi-square
			χ2 (P-value)	Decision
Conceptual	32 (53.33%)	10 (16.67%)	30.89 (p < 0.00)	Significant
Partially conceptual	16 (26.67%)	9 (15.00%)
Rhetorical	11 (18.33%)	29 (48.33%)
No response	1 (1.67%)	12 (20.00%)

*p < 0.05

From Table 6, the EG outperformed the CG, with 53.33% of the EG providing conceptually correct responses compared to 16.67% of the CG. The chi-square analysis revealed a significant difference between the groups (χ2 = 30.89, p < 0.00).

Students from the EG (26.67%) and CG (15.00%) whose responses were categorized partially conceptual were able to deduce a correct balanced equation and the masses of the reactants from their densities. However, they used the masses to determine the limiting reagent. Figure 2 presents a sample ‘partially conceptual’ response from student 1 in the EG.

Figure 2. ‘Partially Conceptual’ Response to Item 3 From Student 1 in the Experimental Group

Also, some students (EG: 18.33%; CG: 48.33%) had their responses to Item 3 categorized rhetorical. Although they realized they needed to write a balanced reaction equation, in their attempt, did not include water as a product. This made it difficult for them to get a correct balanced equation and, hence, some obtained wrong mole ratios. Also, though they introduced the concept and formula of density, they could not correctly deduce the masses of the reactants from their volumes. Some of these challenges are revealed in a sample ‘rhetorical’ response from student 56 (CG) in Figure 3. Some students (EG: 1.67%; CG: 20.00%), however, did not attempt Item 3.

Figure 3. ‘Rhetorical’ Response to Item 3 From Student 56 in the Control Group

Item 4

When 50 g of nitrogen gas reacted with 10 g of hydrogen gas at STP, two gases, including a new gas, were observed. Deduce the limiting reactant showing all reasoning. What two gases were observed and why? [Molar masses: N = 14.01 gmol-1; H = 1.00 gmol-1]

Item 4 is a CP. It required students to determine the moles of the gases from the given masses and their calculated molar masses. Also, they were to write a balanced chemical equation for the reacting gases and to systematically deduce the limiting reactant with supported explanations and reasoning behind each step.To further assess their understanding of limiting reagents, students were required to identify and give reasons for the two gases that would be observed (see Appendix-03d). Table 7 submits the analysis of students’ responses to Item 4.

Table 7. Performance of Students on Post-Test Item 4 (Conceptual)

Response	Experimental(n = 60)	Control(n = 60)	Chi-square
			χ2 (P-value)	Decision
Conceptual	44 (73.33%)	8 (13.33%)	52.42 (p < 0.00)	Significant
Partially conceptual	11 (18.33%)	12 (20.00%)
Rhetorical	4 (6.67%)	25 (41.67%)
No response	1 (1.67%)	15 (25.00%)

*p < 0.05

From Table 7, the EG again performed significantly better, with 73.33% of students providing conceptually correct responses compared to 13.33% of the CG. The chi-square analysis confirmed a significant difference (χ2 = 52.42, p < 0.00).

Also, some students (EG: 18.33%; CG: 20.00%) had their responses to Item 4 categorized partially conceptual. They deduced the correct molar masses and moles of the reacting gases as well as the mole ratio. However, they wrongly deduced that the limiting reagent was nitrogen, probably, due to its lower moles (1.784 mol) than that of hydrogen (5 mol). They did not factor in the contribution of the stoichiometric coefficients on the determination of limiting reagents.

Again, some students’ responses to Item 4 were categorized as rhetorical (EG: 6.67%; CG: 41.67%). It was observed that, though they went through the entire deductions well, they encountered several conceptual difficulties: Some assumed that the molar masses of nitrogen and hydrogen gases were 14.01 and 1.00, respectively, mistakenly assigning their atomic masses as molar masses of their respective molecules or gases; some ended up with the wrong limiting reactant; and some could not provide tangible reasons for their choice of the two gases observed. Figure 4 is a response to Item 4 from student 39 in the EG which was categorized “rhetorical”. Meanwhile, some students (EG: 1.67%; CG: 25.00%) did not attempt Item 4.

Figure 4. ‘Rhetorical’ Response to Item 4 From Student 39 in the Experimental Group

Item 5

Khadija found out that she could neutralize an acid with an impure limestone sample (which is basically calcium carbonate) from her kitchen. If it is known that the impure limestone from her kitchen contains 95% pure CaCO3, what mass of limestone sample will she require to neutralize 50 ml of 0.5 M HCl solution completely? Explain why HCl is the limiting reagent.

This is a CP. The first part required students to deduce a balanced chemical equation for the reaction between the pure form of CaCO3 and HCl. Students were to determine the moles of HCl from the given data and use mole ratio to deduce the moles and, hence, the mass of pure CaCO3. They were then required to exhibit their understanding of percentage composition by correctly deducing the mass of the limestone sample required from the mass of the pure CaCO3 obtained. The second part presented students the opportunity to apply their reasoning to the concept of limiting reagent (see Appendix-03e). Analysis of students’ responses to Item 5 is presented in Table 8.

Table 8. Performance of Students on Post-Test Item 5 (Conceptual)

Response	Experimental(n = 60)	Control(n = 60)	Chi-square
			χ2 (P-value)	Decision
Conceptual	47 (78.33%)	8 (13.33%)	62.49 (p < 0.00)	Significant
Partially conceptual	10 (16.67%)	9 (15.00%)
Rhetorical	2 (3.33%)	30 (50.00%)
No response	1 (1.67%)	13 (21.67%)

*p < 0.05

The EG outperformed the CG, with 78.33% of the EG providing correct responses compared to 13.33% of the CG (Table 8). The chi-square analysis showed a significant difference (χ2 = 62.49, p <0.00).

Some students’ responses (EG: 16.67%; CG: 15.00%) were deemed partially conceptual. Like for Item 3, some presented correct balanced equations and systematically deduced the mass of pure CaCO3. However, they could not apply the concept of percentage composition: Some deduced the mass of the limestone sample wrongly as 95% of the mass of the pure CaCO3 instead of as 100/95. Also, some of their responses to the second part were wrong and/or from rote memorization, such as: (1) It is because HCl has the smallest moles [CG students: #4, #8, #31, #58]; (2) HCl is the limiting reagent because it is the one that is being neutralized [EG students: #6, #41, #60; CG students: #21, #46]; and (3) There is no limiting reagent [EG students: #5, #40; CG students: #23, #35].

The major challenges faced by some students (EG: 3.33%; CG: 50.00%) who gave rhetorical responses were their inability to: (1) correctly balance the reaction equation, and (2) conceptualize that the CaCO3 that reacted was pure and should be used to deduce the mass of the impure limestone sample – they simply equated even the wrongly calculated mass of CaCO3 to the mass of the limestone sample. Also, 1.67% and 21.67% of students from EG and CG, respectively, did not answer Item 5.

Discussion

In this study, the control group (CG) was taught using the traditional teaching approach (TTA) where formulae or algorithmic procedures were utilized. In contrast, the experimental group (EG) was taught using the first principle approach (FPA) and, so, participated in deductions, reasoning and construction of events, which encouraged the ability to develop deep understanding and analysis of problems.

The pre-test results indicated that the performance of both groups in basic stoichiometry was moderate. This means both groups had an appreciable knowledge in general stoichiometry despite belonging to different colleges of education. Also, since it was established that students from both groups had relatable baseline entry knowledge (EK) of stoichiometry, a comparison of the impacts of FPA and TTA on the teaching of limiting reagents was justified and appropriate.

The findings of this study demonstrate that the FPA significantly enhanced students’ performance on conceptual problems (CP) compared to the TTA. However, there was no significant difference between the groups in their performance on algorithmic problems (AP). The rest of this section discusses the implications of these results, provides literature evidence of these results, explores the role of individual learning differences, and considers possible reasons why FPA did not significantly impact algorithmic problem-solving.

Supporting Literature

This finding is supported by Frick et al. (2010). They reported in their study that when an Indiana University professor designed a student evaluation questionnaire to evaluate a course, the course instructors found that students made more progress in courses which involved first principles of instruction. Also, in a study by Lo and Hew (2017) where two groups, underperforming students and high ability students, participated in a flipped classroom mathematics remedial approach and a flipped classroom mathematics training approach, respectively, it was indicated that there were significant learning gains in both groups of students when first principles of instruction were utilized. The findings of this study are, therefore, consistent with well-established empirical evidence that supports the notion that FPA leads to higher levels of comprehension, enabling students to make informed decisions and, invariably, improve their performance (Badali et al., 2022; Frick et al., 2010; Jalilehvand, 2016; Moozeh et al., 2022; Zandi et al., 2023).

Impact of FPA on Conceptual Understanding

The superior performance of the EG on CP highlights the effectiveness of FPA in fostering deeper conceptual understanding. FPA emphasizes inquiry-based learning, real-world applications, and metacognitive strategies, which encourage students to actively construct knowledge and engage in critical thinking (Merrill, 2012/2020). These elements likely contributed to the EG’s ability to interpret complex scenarios, deduce balanced equations, and apply stoichiometric principles effectively.

The significant differences in performance on CP suggest that FPA helps students move beyond rote memorization and procedural fluency, enabling them to develop a more robust understanding of limiting reagents. This aligns with previous studies that have shown the benefits of FPA in improving conceptual understanding and problem-solving skills (Cheng et al., 2017; Obour, 2012).

Role of Individual Learning Differences

While the overall results favour FPA, it is important to consider the role of individual learning differences in shaping these outcomes. Students vary in their learning styles, prior knowledge, and cognitive abilities, which can influence how they respond to different teaching methods. For instance, some students may thrive in inquiry-based environments that encourage exploration and reasoning, while others may prefer structured, step-by-step approaches that provide clear guidelines.

In this study, the variability in individual learning styles may explain why some students in the EG excelled in CP, while others struggled. Future research could explore how FPA can be tailored to accommodate diverse learning preferences, ensuring that all students benefit from this approach.

Why FPA did not Significantly Impact Algorithmic Problem-Solving

The lack of significant difference in AP performance between the EG and CG suggests that FPA and TTA are equally effective in teaching algorithmic problem-solving. This may be because AP primarily require procedural knowledge and the application of formulae, which can be effectively taught through both approaches.

One possible reason for this outcome is that algorithmic problems are often more straightforward and less dependent on conceptual understanding. Students can solve these problems by following a set of predefined steps, regardless of whether they fully grasp the underlying principles. As a result, the additional emphasis on conceptual understanding in FPA may not have provided a significant advantage for AP.

Another factor could be the nature of the instructional intervention. While FPA focuses on conceptual understanding, it may not have provided sufficient practice in applying algorithmic procedures. In contrast, TTA, which emphasizes step-by-step calculations, may have better prepared students for AP. This highlights the need for a balanced approach that combines conceptual understanding with procedural fluency.

Implications for Teaching and Learning

The findings of this study have important implications for chemistry education. FPA is a valuable instructional strategy for fostering conceptual understanding and problem-solving skills, particularly in complex, real-world scenarios. However, educators should also recognize the importance of procedural knowledge and ensure that students receive adequate practice in applying algorithms.

A blended approach that integrates FPA with traditional methods may offer the best of both worlds, catering to diverse learning needs and ensuring that students develop both conceptual and procedural competencies. Additionally, teachers should be mindful of individual learning differences and adapt their instructional strategies to accommodate varying learning styles.

Conclusion

The first principle approach (FPA) has proven to be an effective instructional strategy for students’ performance on limiting reagents. The study results indicated that the experimental group taught with FPA significantly outperformed the control group taught with the traditional teaching approach (TTA), particularly, on conceptual problems. Evidently, the first principle approach has a positive impact on students’ conceptual understanding of limiting reagents. Like other researchers’ findings (Cheng et al., 2017; Obour, 2012; She et al., 2012), the study demonstrates that using demonstrations, deductions, logical reasoning, integration, and real-world examples, FPA enhances students’ understanding and enables them to make informed decisions regarding limiting reagents. By incorporating this approach into the teaching curriculum, educators can foster a deeper understanding of limiting reagents in stoichiometry and prepare students for advanced studies in chemistry and related disciplines.

Recommendations

The findings of this study highlight the effectiveness of the first principle approach (FPA) in enhancing students’ conceptual understanding of limiting reagents in chemical stoichiometry. To maximize the benefits of FPA and promote its broader adoption, the following recommendations are proposed:

Integration of FPA into Chemistry Curricula

Educational policymakers and curriculum developers should consider integrating FPA into chemistry curricula at both secondary and tertiary levels. This can be achieved by incorporating inquiry-based activities, real-world applications, and problem-solving exercises into lesson plans. Teachers should be encouraged to move beyond traditional lecture methods and adopt FPA to foster deeper conceptual understanding.

Professional Development for Teachers

Successful implementation of FPA requires teachers to be well-trained in its principles and methodologies. Professional development programs should be organized to equip teachers with the necessary skills and knowledge to effectively deliver FPA-based lessons. These programs should include hands-on workshops, demonstrations, and collaborative learning opportunities to help teachers gain confidence in using FPA.

Balanced Approach to Teaching

While FPA excels in promoting conceptual understanding, it is important to recognize the value of procedural knowledge in solving algorithmic problems. A balanced approach that combines FPA with traditional teaching methods can provide students with both conceptual and procedural competencies. Educators should design lessons that integrate FPA with opportunities for students to practice algorithmic problem-solving.

Scaling Up FPA in Educational Settings

Scaling up FPA in broader educational settings requires careful planning and resource allocation. Schools and colleges should invest in the necessary materials, such as molecular models, laboratory equipment, and real-world simulation tools, to support FPA-based instruction. Additionally, class sizes should be manageable to allow for individualized attention and active student participation.

Addressing Potential Challenges

Implementing FPA on a larger scale may face several challenges, including resistance to change, lack of resources, and time constraints. To address these challenges, stakeholders should engage in continuous dialogue to build consensus and support for FPA. Pilot programs can be initiated to demonstrate the effectiveness of FPA and address any concerns before full-scale implementation.

Research on Long-Term Effects

Further research should be conducted to explore the long-term effects of FPA on students' learning outcomes and retention of knowledge. Longitudinal studies can provide valuable insights into how FPA influences students’ performance in advanced chemistry courses and their ability to apply stoichiometric principles in real-world contexts.

Adaptation to Diverse Learning Needs

Educators should be mindful of individual learning differences and adapt FPA to accommodate diverse learning styles. Differentiated instruction strategies, such as group work, peer tutoring, and multimedia resources, can be used to ensure that all students benefit from FPA.

By implementing these recommendations, educators can create a more engaging and effective learning environment that prepares students for success in chemistry and related disciplines. The integration of FPA into teaching practices has the potential to transform chemistry education, fostering a generation of students who are not only proficient in solving problems but also deeply understand the underlying principles of chemical reactions.

Limitations

Though the intervention strategy produced positive results in improving students’ conceptual understanding of limiting reagents, the results do not generalize students (pre-service science teachers) in Ghana as only 120 students from only two colleges of education were involved.

Ethics Statements

This research involving human participants has been reviewed and approved by the colleges involved. The participants provided their written consent to participate in this study.

Acknowledgements

We wish to acknowledge the management and the second-year science students in the 2022/2023 year group of the two colleges for allowing this study to be carried out in their institutions.

Conflict of Interest

There are no conflicts to declare.

Funding

Funding was sourced from authors of this study.

Authorship Contribution Statement

Abban-Acquah: Concept and design, drafting of manuscript and revision of manuscript. Ackah: Editing, data collection, data analysis and critical revision of manuscript.