Investigating the Effects of Practice Time on Student Achievement Considering Variations in Demographics across Various Chemistry Topics

Abstract

This study examined the relationship between the time students spend on practice problems and their performance on exams in various chemistry topics, considering their demographics. The researchers divided 91 general chemistry students into three groups based on the time allotted for solving intervention questions: Minimum, Average, and Maximum. The results showed that the Minimum and Average time groups benefited almost equally, but the performance of the Maximum time group declined. This suggests that, while additional practice is beneficial, there could be an optimal amount of time that students should spend on each question. Spending too much time on a single question can lead to mental and emotional fatigue, resulting in a decline in performance. Additionally, the researchers noted variations in performance across different chemistry topics and student groups, and they examined the relationship between student demographics and their problem-solving performances. The study provides recommendations for educators, testing services, and online homework systems to improve the effectiveness of chemistry instruction, highlighting the importance of finding the right balance between practice time and student engagement, and suggesting that a uniform approach to practice problems may not be ideal for every student.

1. Introduction

The development of problem-solving skills, which includes critical thinking and analytical abilities, is widely recognized as essential for academic success in general chemistry [1]. Research consistently shows a strong correlation between higher academic achievement and proficient problem-solving skills. However, many students struggle with developing these skills, often resorting to passive study strategies that lack active engagement or critical thinking [2]. For example, students may believe that repeated rereading of text passages is more effective for learning than being quizzed on the material, despite the latter promoting cognitive processes that are essential for problem-solving abilities [3].

Active learning strategies, such as completing problem sets, self-quizzing, and synthesizing notes, have consistently been linked to better learning outcomes and improved exam performance [2]. Conversely, passive studying methods like watching lectures or simply reviewing content may yield nonsignificant correlations or even negatively impact academic achievement [2]. Therefore, encouraging students to adopt active learning strategies is crucial as they lead to deeper cognitive engagement and long-term benefits.

In addition to study strategies, internal factors such as self-efficacy and motivation can significantly impact academic problem-solving performance [4]. According to Albert Bandura’s social cognitive theory [5], self-efficacy influences individuals’ cognitive processes, emotions, and behaviors. Students with high self-efficacy demonstrate greater flexibility in problem-solving approaches and achieve higher intellectual performance [6,7]. Academic self-efficacy has also been identified as a predictor of overall academic performance, including grade point average and expected course grades [8,9]. In a study assessing problem-solving performance in an economics classroom, students with higher GPAs were more likely to report greater perceived problem-solving ability and employ adaptive study strategies [8]. Conversely, students with lower GPAs tended to report lower levels of perceived problem-solving ability [9].

Another effective method to enhance problem-solving abilities of students within the context of general chemistry and foster their academic achievement is to provide dedicated practice sessions during discussion sections or lectures. These focused practice opportunities allow students to concentrate on refining their skills and knowledge in chemistry. Research has shown a positive association between the allocation of time for subject review and academic achievement. This concept gained prominence in the 1960s with the introduction of the Time-on-Task Hypothesis, made by Carroll [10], which prompted extensive investigations to explore the idea that learning is contingent upon the amount of time spent engaging with a given task. In relation to this hypothesis, Gondra et al. [11] conducted a study to evaluate how varying amounts of practice time impact problem-solving performance of general chemistry students. They found that providing students with dedicated practice time did improve performance, but only to a certain extent. In their study, students were divided into three groups: Minimum (2–3 min), Average (4–6 min), and Maximum amount of time (6–9 min) to solve nine free-response chemistry questions. Results indicated that students in the Minimum and Average groups saw improvements in problem-solving performance, with the greatest improvements and question completion rates observed among the students placed in the Average group. Conversely, students in the Maximum group observed minimal improvements or even declines in problem-solving performance. This suggested that there could be an optimal time-allocation threshold per study problem. However, it is important to recognize that the mere duration of time spent on practice sessions may not exclusively determine students’ learning outcomes and exam performance. Demographic factors such as socioeconomic status, previous academic achievement, and ethnicity could also influence problem-solving success and outcomes.

For instance, research has found the influence of socioeconomic status (SES) on students’ problem-solving abilities to be multifaceted. Students from higher socioeconomic backgrounds often demonstrate greater confidence in their problem-solving skills, likely due to increased access to learning resources such as books, tutoring, and academic opportunities [12,13]. Moreover, high SES students may benefit from enhanced parental involvement, which fosters self-regulation and problem-solving skills [13]. However, the impact of SES on problem-solving motivation presents contradictory findings. In a study involving 235 undergraduate students, Cassidy and Giles [14] found that variations in family support and SES accounted for 44% of the differences in grade point averages. Importantly, the influence of these factors is mediated through intrinsic motivation and problem-solving styles, indicating that family support and economic background affect students’ motivation and their approach to academic challenges, ultimately shaping their academic achievement. Conversely, McGeown et al. [15] discovered that SES did not significantly affect either extrinsic or intrinsic motivation among high school students. In contrast, a subsequent study by Manganelli et al. [16] revealed that adolescents from lower SES backgrounds exhibited lower levels of intrinsic motivation and identified regulation, along with higher levels of motivation and external regulation, compared to their higher SES counterparts.

Variation in academic achievement, particularly in problem-solving tasks, is also evident across students of different ethnicities. Studies have consistently shown that in STEM courses, Asian and white students tend to outperform their Black and Hispanic peers [12]. This performance gap may partly stem from disparities in access to resources between ethnic groups [17]. Additionally, cultural differences may play a role, with some cultured valuing cooperative learning over independent problem-solving [17]. However, studies have also found that ineffective test-taking strategies significantly contribute to the observed test performance differences across ethnic groups. In a 2003 study by Ellis and Ryan [18], it was reported that the variance in cognitive-ability test performance explained by ethnic background dropped by 48% when controlling for the mediator, ineffective test-taking strategies. A more recent study found that ineffective test-taking strategies accounted for 19% to 25% of the variance originally explained by ethnic background, suggesting that differences in test scores among ethnic groups may partly result from use of these strategies [19].

Despite these findings, the precise relationship between time invested in learning, demographic variables, and learning outcomes remains unclear due to inconsistent results observed in numerous studies evaluating performance and time on task. For instance, a study by Godwin et al. [20], aimed at assessing the impact of time on elementary students’ success, found that the on-task behavior of elementary students reliably predicted their learning scores. In contrast, Roberge et al. [21] highlighted that the duration of off-task behavior did not significantly predict learning success among middle school students when examining the influence of time-on-task using the educational software Cognitive Tutors. Similarly, Kovanovic et al. [22] noted that only a small portion (15%) of the variation in problem-solving strategies’ effectiveness in online classes could be attributed to specific time-on-task strategies. It is important to note that these studies also do not consider how demographic factors overall engagement with problem-solving tasks.

Furthermore, student performance in problem-solving tasks can vary significantly depending on the specific subtopic being assessed. Certain concepts consistently pose challenges for learners, even at advanced levels. For example, Kautz et al. [23] found that even advanced students struggle with gas laws, particularly Dalton’s Law of partial pressures. This suggests a deeper issue with grasping fundamental submicroscopic models and processes that govern gas behavior. Similarly, Sanger [24] reported a common confusion among general chemistry students regarding subscripts and coefficients when balancing chemical equations. This indicates a potential misunderstanding of the role and significance of these elements in representing reaction stoichiometry. Finally, Raviolo et al. [25] highlight the inherent challenge associated with molarity. Understanding molarity requires a strong foundation in concepts like solutions, concentration, and the relationship between solutes and solvents. Students who lack this foundation might struggle with calculations involving molarity, as they would not grasp the relationship between moles, solution volume, and concentration. These examples illustrate how specific subtopics within chemistry can present unique hurdles for students, especially when compounded by time constraints. Gondra et al. [11] determined that, among undergraduate general chemistry students, having too much time to solve a problem led to the development of mental and emotional fatigue, whereas bigger time constraints would impact performance for more complicated problems, such as those involving multiple calculations and synthesis across course topics. By identifying these challenges and the underlying reasons (e.g., weak grasp of fundamentals, confusion with terminology), instructors can develop targeted strategies to improve student comprehension and performance.

1.1. The Goal of the Study

Previous studies [20,22,26] have not investigated the connection between variations in problem-solving performances across various chemistry topics and demographic variables such as socioeconomic status and ethnicity, considering the time spent on practice questions. Further investigation is necessary to attain a complete understanding of the intricate connection that exists between external demographic variables, the amount of time dedicated to a particular task, and the problem-solving performance of general chemistry students. By addressing these research gaps, this study seeks to inform pedagogical practices and enhance instructors’ understanding of variables that may affect student problem-solving performance, thereby contributing to the broader discourse on academic success and achievement.

1.2. Research Questions

This study aimed to answer the following research questions:

• Is there a differential impact of the time-on-question intervention on students’ performances across different chemistry topics?
• To what extent do various characteristics, including socioeconomic status and ethnic origin, influence the problem-solving performances of the students across time groups?

2. Methods

2.1. Participants and Design

Following approval from the Institutional Review Board (IRB) and provision of an overview of the study’s purpose, 972 first-year general chemistry students at a research institution in Northern California were invited to take part in the research project. Of those invited, 146 students participated in the research session. Participants were randomly assigned to three groups—Minimum, Average, and Maximum—with nearly equal numbers. However, after fifty-five students dropped out or did not complete the post-test during the intervention phase, the distribution across these groups became uneven.

Table 1. The attributes of participants organized by time groups.

		Minimum (2–3 min Task Time) (N = 35)	Average (3–5 min Task Time) (N = 32)	Maximum (4–9 min Task Time) (N = 24)
High School GPA Level	High GPA	22 (62.8%)	14 (43.8%)	14 (58.3%)
	Medium GPA	8 (22.9%)	9 (28.1%)	3 (12.5%)
	Low GPA	3 (8.6%)	4 (12.5%)	4 (16.7%)
	Unknown	2 (5.7%)	5 (15.6%)	3 (12.5%)
Socioeconomic Status	High Income	8 (22.9%)	6 (18.8%)	8 (33.3%)
	Medium Income	16 (45.7%)	9 (28.1%)	6 (25.0%)
	Low Income	9 (25.7%)	11 (34.3%)	7 (29.2%)
	Unknown	2 (5.7%)	6 (18.8%)	3 (12.5%)
Ethnic Background	African American (3.7%) *	2 (5.7%)	1 (3.1%)	0 (0%)
	Asian/Pacific Islander (36.6%) *	9 (25.7%)	12 (37.5%)	12 (50.0%)
	Hispanic/Latino (23.4%) *	15 (42.9%)	8 (25.0%)	3 (12.5%)
	White (20.7%) *	3 (8.6%)	4 (12.5%)	2 (8.3%)
	Other (15.6%) *	6 (17.1%)	7 (21.9%)	7 (29.2%)

* The overall student ethnic diversity data at the research institution [27].

provides a summary of the high school GPA categories, socioeconomic status (SES) levels, and demographic characteristics of the students who took part in the study. GPA classifications were divided into three groups: “Low GPA” for GPAs below 2.5, “Medium GPA” for GPAs between 2.5 and 3.5, and “High GPA” for GPAs above 3.5. Socioeconomic status was categorized based on reported income: students with family incomes under USD 50,000 were considered “Low Income”; students with family incomes between USD 50,000 and USD 150,000 were considered as “Medium Income”; students with family incomes exceeding USD 150,000 were considered as “High Income”. The table also summarizes the ethnic distribution of students in each study cohort, comparing it with the university’s overall ethnic composition, indicated in parentheses. This provides a clear view of how each cohort’s demographics align with or differ from the university’s general demographic profile.

A quasi-experimental design was used to investigate the impact of the time spent on questions upon students’ performance with chemistry questions. Data from all the participants were collected on the same day in three stages: pre-test, intervention, and post-test. A 5 min break was given between each stage. Students were placed in three different rooms based on time allocation. For the pre- and post-tests, students were given 30 min to solve five questions covering chemistry concepts related to solution chemistry, stoichiometry, and gas law concepts. Testing material was based on current topics in the course in which students were enrolled. Questions asked in the post-test had identical concepts to those in the pre-test but contained minor modifications such as alternative chemicals or numerical values. These adjustments had no impact on the methodology for solving the problems.

The intervention portion of the study was designed to assess students’ understanding of the same concepts assessed in the pre- and post-tests. During this stage, students were assigned nine free-response chemistry questions to complete on Qualtrics, a survey platform that allows instructors to control the amount of time students could spend on each question. When the allotted time was up, students were automatically directed to the next question. To ensure uniformity, all participants were provided with a periodic table, response sheet templates, and formula sheets. The set time for each question varied depending on the time-group: Minimum, Average, and Maximum. Time also varied based on the level of difficulty, which was assessed by a chemistry professor, a graduate student, and three undergraduates who recently successfully completed the same general chemistry course. After analyzing data from a pilot study where undergraduate chemistry students completed a Qualtrics survey with 9 chemistry problems related to the intervention topics, it was determined that students in the Minimum group would be given 2–3 min per question, the Average group would be given 3–6 min, and the Maximum group would be given 4–9 min. The same 9 questions were assigned to all participants; however, the time allocated to solve each question depended on their respective time group. Despite being given different amounts of time to solve the questions, all students had the same time (45 to 90 s, depending on the complexity of the answer) to reflect on the solution provided for each question. Since the study aimed to inspect the effect of time on independent problem-solving performances, students were discouraged from discussing answers with fellow students or referring to online resources. However, they were permitted to utilize personal notes and listen to music during the intervention but not during the pre- and post-tests.

2.2. Data Analysis

The participants’ written solutions were scanned and uploaded to the Gradescope platform (see Figure 1). Although Gradescope was initially designed as a grading system, it was used for coding in this study due to its ability to break down problems into distinct subproblems. Each subproblem was then assigned a unique code, enabling a more detailed and systematic analysis. This method enhanced collaboration among coders and allowed for a more efficient examination of the data. By focusing on specific components of each problem, coders were able to streamline the coding process and ensure a thorough, structured analysis of the solutions. In addition to determining the impact of time-on-task on students’ general problem-solving performance with the tested topics, the pre- and post-test questions were broken down into subproblems to pinpoint students’ learning challenges. While the study focused mainly on determining the impact of time on tasks on students’ general problem-solving performance on the tested topics, we were able to pinpoint students by breaking down the pre- and post-test questions into subproblems.

Instead of only being able to comment generally on whether students were able to do a particular question, this approach allowed researchers to identify the exact step where students got stuck. For example, in a percent yield question, researchers could determine what students found the most difficult, whether that be writing a chemical equation, balancing it, performing mole calculations, determining the correct mole ratios, or carrying out stochiometric conversions.

The Coding System for Investigating Subproblems and Networks (COSINE) [28] was utilized to analyze students’ solutions per subproblem and allowed the researchers to measure and compare students’ performances more easily. This coding system consisted of the following 8 codes: Successful (S); Not Required (NR); Did not know to Do (DD); Did Something Else (DSE); Could not Do (CD); Unsuccessful—Guessed (UG); Unsuccessful—Received Hint (URH); Unsuccessful—Did Incorrectly (UDI). Each of the eight codes were grouped under one of three categories: successful (S), neutral (DSE, DD, and NR), and unsuccessful (UDI, CD, URH, and UG).

Table 2. Acronyms for stoichiometric concepts and COSINE codes.

Acronym	COSINE Codes and Formulas	Acronym	Stoichiometry Topics
S	Successful	WEQ	Writing Chemical Equation
NR	Not Required	BEQ	Balancing Chemical Equation
DD	Did Not Know to Do	EF	Empirical Formula
DSE	Did Something Else	LR	Limiting Reagent
CD	Could Not Do	MC	Mole Concept
UG	Unsuccessful—Guessed	MF	Molecular Formula
		PY	Percent Yield
CSR	Complete Success Rate	SR	Stoichiometric Ratio
ASR	Attempt Success Rate	DC	Density Calculation
		MLC	Molarity Calculation
		IGL	Ideal Gas Law
		UC	Unit Conversion
		DL	Dalton’s Law
		CM	Conservation of Mass
		IEM	Identifying Element based on Molar Mass
		RIGE	Recalling Ideal Gas Equation

provides a comprehensive list of acronyms related to the codes and chemistry topics utilized in the study. It serves as a reference for identifying the abbreviations associated with various subject areas and coding schemes mentioned throughout the paper.

The coding team consisted of five undergraduate students who were recruited and trained in using the COSINE coding system. Each coder was assigned to code all student responses for a specific question and its respective subproblems. To ensure that codes were assigned correctly and consistently among all coders, the coders and the principal investigator, who developed the COSINE codes and published several papers [29,30] about them, met weekly to clarify any confusion that arose during the coding process. Furthermore, coders worked in pairs to discuss each subproblem and resolve any discrepancies between the assigned codes. By using this collaborative approach, we maintained consistency and accuracy in the grading process. The coding process involved comparing student responses with the steps outlined in the solution key and assigning the designated COSINE code to each subproblem. Regardless of the final answer, so long as the student’s solution demonstrated a correct understanding or approach to the key concept, the corresponding subproblem was coded as successful. If a mistake was made or understanding was not evident, alternative codes were assigned. Each subproblem was coded independent of students’ performance on the previous or subsequent subproblems.

Table 3. Examples of code assignments to different subproblems taken from some pre-test questions.

Codes	Subtopic	Evidence from Student Written Responses
S	BEQ	The student successfully balanced the chemical equation of the given reaction.	$W{O}_3+3H_2\to W + 3H_{2}O$
DD	IGL	The student failed to convert pressure of H2 from torr to atm in this subproblem. As a result, an incorrect number of moles of gas was calculated using the ideal gas law formula.	$PV=nRT$ $n={\displaystyle \frac{PV}{RT}}$ $n={\displaystyle \frac{\left(680.8 torr\right)\left(0.15 \mathrm{L}\right)}{\left(0.08206\right)\left(298 \mathrm{K}\right)}}=4.17 mol$
DSE	MC	Instead of correctly determining the number of moles of unknown gas by using PV = nRT, the student attempted to calculate the moles of CH4 gas. CH4 was given as the empirical formula for the unknown gas.	$0.495 \mathrm{L}\cdot {\displaystyle \frac{1000 \mathrm{g}}{1 \mathrm{L}}}$ $495 \mathrm{g}\cdot {\displaystyle \frac{1 mol C{H}_4}{16.042 \mathrm{g} C{H}_4}}=30.86 mol C{H}_4$
CD	PY	The student was unable to determine the percent yield for the product of the given reaction. This is evidenced by the break in their work. Their written equation for percent yield is also incorrect.	$Percent Yield = {\displaystyle \frac{theoretical}{actual}}$ $34.8 \mathrm{g} W{O}_3\cdot {\displaystyle \frac{theoretical}{231.94 g}}\cdot {\displaystyle \frac{1 mol}{1 mol}}\cdot {\displaystyle \frac{18.02 \mathrm{g}}{1 mol}}=$ $2.13 mol H_{2}O\cdot {\displaystyle \frac{1 \mathrm{L}}{1000\mathrm{m}\mathrm{L}}}$
UG	MF	The student provides no additional work after calculating the number of moles of gas. The student instead circles the empirical formula as a guess for the final answer and writes next to it “what is the molecular formula?”	$n=0.0133 mol$ $C{H}_4$ What is the molecular formula?
UDI	MC	Instead of correctly determining the number of moles of HCl by multiplying the molarity of HCl by amount in liters used, the student mistook the units of molarity to be grams/liters. They then divided this value by the molar mass of HCl to obtain the incorrect moles of HCl.	$0.673M={\displaystyle \frac{x}{0.180 \mathrm{L}}}$ $x=0.12114 \mathrm{g}\mathrm{ }HCl \cdot {\displaystyle \frac{1 mol HCl}{36.46 \mathrm{g}}}$ $=0.0033225 mol HCl$

illustrates how the codes were applied.

There was a major issue when students missed a subproblem or were unable to identify a subproblem. These cases were identified with the DD (Did not know to Do) code. Since the Complete Success Rate (CSR) calculation looks at overall performance, it requires the inclusion of all codes including the DD code. The DD code was left out of the Attempt Success Rate (ASR) calculation because it does not provide direct evidence regarding students’ ability to solve the given subtopic. For both the CSR and ASR formulas, the NR (Not Required) code was excluded since the inclusion of this code would make the total applied codes different for each student as not every student used a correct alternative method to get the same answer. If included, it would invalidate the comparisons.

$$\mathrm{ASR}={\displaystyle \frac{S}{S+CD+UG+UDI+URH}}$$

(1)

$$\mathrm{CSR}={\displaystyle \frac{S}{S+DD+DSE+CD+UG+UDO+URH}}$$

(2)

Comparing the differences between the ASR and CSR scores allowed us to determine how successful the intervention was for each group. The ASR scores generally tend to be larger than CSR; however, a more successful intervention would minimize the difference between these two values. A greater difference between the ASR and CSR scores is usually accompanied by more DD or DSE codes, which indicates a decreased understanding of connecting individual subproblems to the overall problem.

3. Results and Discussions

This study aims to further explore the effect of time-on-question on success rate in introductory general chemistry topics under simulated exam conditions. Student performance was observed through the comparison of pre- and post-test results generated by different time groups. Rather than merely marking answers as correct or incorrect, data resolution was enhanced via the division of test questions into subtopics and assignment of COSINE codes, which offers a more detailed, quantitative analysis of student answers. Further performance patterns were also examined from self-reported demographics (i.e., ethnic background, socioeconomic status, and educational background) taken during the onboarding phase of the study.

3.1. Interpreting the Variations in Attempt Success Rate (ASR) Scores

Attempt Success Rate (ASR) scores for each subtopic were calculated, enabling a more in-depth analysis of the influence of time on students’ success. Figure 2 shows changes in the ASR scores for the Minimum, Average, and Maximum groups, categorized by the chemistry topics as parts of the pre- and post-test questions.

Analysis of the trends observed in Figure 2 offers valuable insights into the students’ understanding of each subtopic in each time group. All three groups had a positive ΔASR with varying success levels for three subtopics, Molecular Formula (MF), Stoichiometric Ratio (SR), and Conservation of Mass (CM), which demand relatively less effort and time to complete. Therefore, the scores were likely not significantly influenced by student’s mental and emotional fatigue, which was built up due to the extra problem-solving time.

Interestingly, among all the time groups, the Minimum group had the highest number of positive ΔASR, for 12 subtopics out of 13, indicating that the intervention under a considerable time constraint was successful in helping the students in this group learn and perform better with the post-test questions. Although the Minimum group performed better in the shortest time allotted, this was not quite the case for students in the Maximum group, as they experienced a decrease in ASR scores across the nine subtopics. It was speculated that the Maximum group may not have allocated their full effort to tackling more time-consuming and mentally demanding subtopics like Dalton’s Law (DL). The Average group also had a negative ΔASR for this subtopic suggesting that both groups may have lacked a strong conceptual understanding of the processes and variables related to Dalton’s Law. As a result, they performed poorly on related questions, 4 and 5, as their solutions required executing a subproblem involving Dalton’s Law of partial pressures. In line with these findings, Kautz et al. [23] documented that undergraduate students could not properly interpret the gas variables of pressure, temperature, and volume even after introductory and advanced instruction in physics and chemistry. This was attributed to a significant misunderstanding of the fundamental submicroscopic models and processes.

Balancing Chemical Equations (BEQ), which primarily requires setting the proper ratios by determining the correct coefficients, is another topic in which the Maximum group showed relatively poor performance. This could be attributed mainly to two factors. Some students might have a limited understanding of coefficients and what they represent, as explained by Sanger [24]. They reported that the general chemistry students who were asked to write a balanced chemical equation and perform stoichiometric calculations had difficulty distinguishing between equation subscripts and coefficients. Another possibility is that the Maximum group and to some extent the Average group may not have been fully engaged in balancing chemical equations due to emotional fatigue, as it could be a time-consuming and complex process at times. Because students were randomly split into time groups, the second possibility gains more importance because it is less likely that all the students with a poorer understanding of scripts and coefficients were in the Maximum group. Even though Raviolo et al. [25] documented that many students found the concept of molar concentration challenging to understand because it required knowledge of concepts such as mixtures and dissolution, as well as an understanding of how to determine the ratio between solutes and solvents, the same factor can be used to explain the Maximum group’s poor performance with subproblems involving the calculation of molarity (MLC).

Another topic that both Maximum and Average groups performed poorly with was Unit Conversion (UC). Given that uniter conversions are typically completed toward the end of the solution, mental fatigue may have been more greatly felt at this step. Of course, it is also possible that students did not attempt the step due to emotional fatigue or because they felt impatient and wanted to finish the study session. Some studies [31] revealed middle and high school students’ poor performance with respect to this subtopic and how it was connected to teachers’ insufficient emphasis on that topic.

To thoroughly explore other perspectives within the data, demographic influences (i.e., high school grade point average, socioeconomic status, and ethnic origin) on student problem-solving performance during the pre- and post-tests were analyzed. An investigation of the correlations between these demographic variables and CSR scores may provide insight and help explain the variances in the performances observed across the Minimum, Average, and Maximum groups.

Figure 3 categorized changes in CSR (ΔCSR) scores based on students’ self-reported ethnic background. Among the ethnic groups examined, the greatest positive ΔCSR was observed among students of Asian and Pacific Islander origin. This trend was observed in both the Minimum and Average groups. However, ΔCSR did noticeably decrease as the time allotted for problem-solving increased, suggesting the existence of a time-on-question threshold that leads to negative problem-solving performance.

Numerous empirical studies [32,33,34] have explored the influence of ethnicity on academic performance. These studies have found that students of Asian and Pacific Islander heritage tend to demonstrate higher academic performance than peers from other ethnic backgrounds. This academic success is commonly linked to factors such as increased time spent on homework, higher performance expectations from parents, and a greater emphasis on academic learning outside of school [33]. These findings are consistent with the results in Figure 3, as Asian and Pacific Islander students performed significantly better on the post-test relative to their peers. The decline in ΔCSR with increased time may also indicate that Asian and Pacific Islander students perform better in high-pressure, time-constrained environments. This group has historically demonstrated higher performance on timed standardized exams than their peers [35]. Asian and Pacific Islander households were observed to prioritize “home learning programs”, characterized by extensive learning opportunities, support, and higher academic pressure [33]. These “home learning programs” instill traditional cultural values that propel children to excel and build academic resilience. These findings align with the observations in the present study and provide additional support for the idea that moderate time pressure can enhance academic performance [36].

Hispanic/Latino students also demonstrated a positive ΔCSR, albeit to a lesser extent. The positive trend in ΔCSR for Hispanic students persisted across all three-time conditions, with gradual improvements in ΔCSR observed as more problem-solving time was given. This contrasted with the observed trend among Asian/Pacific Islander students who performed better when given less time. Like Hispanic students, students exhibited a slight but positive change in problem-solving performance (ΔCSR) in the Minimum group (0.0382). However, the ΔCSR decreased in the Average group, indicating a notable negative shift in problem-solving performance. In the Maximum group, the ΔCSR was positive, demonstrating improvement in problem-solving performance. It should be noted, however, that, due to the small sample size, statistical significance about this group could not be drawn.

The relationship between time and ΔCSR indicated that, unlike their Asian/Pacific Islander counterparts, students of Hispanic origin performed significantly better when given additional time to solve problems. An early study conducted by Llabre and Forman [37] explored test-taking time differences between Latino and Caucasian students enrolled in a community college algebra course. Participants were given unlimited time to respond to a sixteen-question multiple-choice reasoning test but were also instructed to work swiftly. The results revealed no significant differences in score performance across ethnic groups. However, a significant variation in testing time emerged: Latino examinees took longer to complete the exam in comparison to white students. A parallel pattern was observed on more challenging questions, with Latino students requiring additional time to attain scores that were similar to their white counterparts.

While data from African American students were collected, the small number of students who identified as this ethnicity prevented meaningful conclusions from being drawn. This imbalance may stem from the host university’s demographic composition, which primarily consists of White, Asian, and Hispanic students [27]. Furthermore, the departure of some students from the study could contribute to this disparity. Future studies should be conducted at universities of a different demographic composition to reveal any possible differences between African American students and Asian and Pacific Islanders, White, or Hispanic and Latino students.

The socioeconomic background of a student’s family was also observed to have an influence on the study data. Numerous studies have shown a clear link between a student’s socioeconomic status and their academic performance [38,39,40]. As a result, educational institutions and policymakers have been implementing various initiatives to address and bridge the achievement gap that exists between underserved minority groups and Asian and Pacific Islander or white counterparts in higher education. Advantages or disadvantages associated with socioeconomic standing impact various aspects of student academics, including access to quality early childhood education, availability of resources at home, and exposure to enriching experiences [38,41]. Such students may also have limited access to educational resources, including books, technology, and tutoring. Additionally, financial constraints may hinder participation in extracurricular activities or specialized programs that could provide enhanced learning opportunities [38,41]. Figure 4 displays the changes in CSR scores of students in each time group separated by socioeconomic status.

Students from low-income backgrounds demonstrated a positive ΔCSR in the Minimum (0.0839) and Average (0.0858) groups, but a negative ΔCSR (−0.0207) in the Maximum group. A similar trend was observed among students from high-income socioeconomic backgrounds, with a positive ΔCSR in the Minimum (0.3533) and Average (0.0172) groups, followed by a negative ΔCSR (−0.1324) in the Maximum group. This suggested that problem-solving performance decreased for both groups as time on question increased, which may be attributed to emotional fatigue [42]. Average-income students exhibited a positive ΔCSR across all time conditions, although the ΔCSR decreased with time. Despite being positive, the magnitude approached zero, suggesting minimal improvement in problem-solving performance in the Maximum group—a similar trend to those seen in the other two groups.

The ΔCSR for all students appeared to decrease as more time was allocated, irrespective of socioeconomic status. Large variations in performance were observed only when examining groups within a specific time condition. Notably, in the Minimum group, the students from high-income socioeconomic backgrounds exhibited the most substantial improvement in problem-solving performance, with a ΔCSR 0.1353 compared to ΔCSR of 0.0451 and 0.0839 in the low- and medium-income groups, respectively. Furthermore, problem-solving performance among average socioeconomic students appeared to improve between the Minimum and Average groups. However, when considered collectively, the similarity in trends across all groups suggests that socioeconomic status itself did not appear to be a significant determinant of problem-solving performance. Regardless of economic background, all students likely experienced emotional fatigue after a certain point.

Notably, students from high-income socioeconomic backgrounds seemed to exhibit fatigue earlier compared to the other groups. The intervention was presented as a study session where students could gain additional practice to supplement their schoolwork. Studies have indicated that students from high-income socioeconomic status typically have greater access to external learning opportunities such as additional tutoring and academic support [38,39,40]. Consequently, they may not be as inclined to approach the intervention with the same level of seriousness, given their access to other resources. In contrast, students from low- and average-income economic backgrounds may not have access to as many resources, making them more motivated to engage fully, attempt each problem, and utilize any available study opportunity.

In line with our findings, several studies identified a positive, albeit slightly weak, association between socioeconomic status and academic performance [38,39]. For example, Richardson et al. [39] observed a small correlation between socioeconomic status and academic performance, while Westrick et al. [40] reported a weak link between socioeconomic status and first-year GPA. Conversely, negative associations between socioeconomic status and academic performance have also been documented. Pedrosa et al. [43] reported that students from public schools exhibited better academic performance than their counterparts from private schools. Interestingly, students with less favorable socioeconomic conditions demonstrated a form of “educational resilience”, a concept described by Pedrosa et al. [43] as the process of transforming early-life disadvantages into improved academic performance in higher education [38]. This “educational resilience” may explain why students in the low- and medium-income groups performed better than high-income students as problem-solving time increased.

Neither students’ ethnic origins nor their families’ socioeconomic status showed a clear and consistent pattern in the graphs representing the changes in their problem-solving performances across time groups. To gain a deeper understanding of the factors influencing students’ problem-solving abilities in chemistry, their high school GPAs were also considered. This additional variable explored the connection between a student’s overall academic achievement and their ability to tackle complex problem-solving tasks in chemistry. Figure 5 illustrates the changes in the CSR scores for the students with a low, medium, or high GPA in each time group. Among students with a low reported GPA, the ΔCSR was the lowest in both the Minimum (0.0022) and Maximum (−0.2845) groups. However, the ΔCSR for low-GPA students was positive in the Average group. These results would suggest that students with low GPA perform poorly when not given enough time to solve questions, but an excess of time may also negatively impact their problem-solving performance. Between the two conditions, having more time to solve a question appeared to have yielded the greatest decline in problem-solving performance.

A positive ΔCSR was observed among medium-GPA students in all time groups. There was a slight decrease in ΔCSR between the Minimum (0.1024) and Average (0.0608) groups, but the difference was not considered significant. Notably, ΔCSR for medium-GPA students substantially increased in the Maximum group. The positive performance seen across all time groups and the significant increase in ΔCSR suggested greater sustained motivation and educational resilience among students with average performance. The study intervention required students to actively engage with the material for long intervals. Successful performance, denoted by the positive ΔCSR, is therefore suggestive of a stronger ability to engage actively with the material over sustained periods of time. Interestingly, the ΔCSR scores were only positive for students with high reported GPAs in the Minimum and Average groups. In the Maximum group, the ΔCSR was negative, indicating a decline in problem-solving performance when more time is provided. These findings provide additional support for the hypothesis that problem-solving performance declines as time on task increases, most likely due to emotional and, to some extent, mental fatigue.

Empirical evidence underscores the impact of cognitive ability, self-conceptualization, and academic motivation on academic performance. Variations in these factors may elucidate the differences in ΔCSR observed among students with low, medium, and high GPAs. In a study involving 148 high school students, Haynes et al. [44] identified significant distinctions between low-achieving students and their average- and high-achieving peers in cognitive skills, study habits, and motivation. Motivation emerged as the most prominent factor distinguishing low achievers from their peers. Self-regulation also played an important role in shaping academic outcomes. Students considered self-regulated learners comprehended the motives and strategies necessary for learning and implemented these strategies in their learning process. In contrast, students with poor self-regulation may be more inclined to give up when faced with difficulties. High-achieving students also tended to exhibit greater intrinsic motivation and a sense of competence, characteristic of self-regulated learners [44]. Consequently, they were more likely to employ active study strategies that fostered the development of independent problem-solving skills and may help explain the stronger problem-solving performance observed in medium- and high-GPA students.

Low self-regulation and self-efficacy may explain the poorer overall performance demonstrated by students with low GPA in this study. In general, low-GPA students were thought to more likely engage in self-handicapping behaviors and to refrain from attempting a problem if they anticipate failure, thus resulting in a decreased ΔCSR [44]. Between medium- and high-GPA students, however, there was little difference in ΔCSR for students in the Minimum and Average groups. However, in the Maximum time conditions, there was a greater positive ΔCSR for medium-GPA students, suggesting that medium-GPA students were better equipped to engage with material for longer periods of time. In a study investigating differences between low-, medium-, and high-achieving students, no significant difference was found in the cognitive skills, study habits, and motivation between medium- and high-achieving students [45]. Results from this study, however, suggest a difference in performance between the two groups when tested for extended periods of time. When considering study time, students with high academic GPAs may possess greater prior knowledge or effectively utilize study strategies. This may allow them to spend less time mastering a specific subject than an average-performing student [46]. Medium-GPA students may need to spend more time actively engaging with the material, which could explain the stronger performance observed in the Maximum time condition.

The decline in performance observed among high-GPA students may also be attributed to boredom, a prevalent factor within the learning environment associated with poorer learning and problem-solving performance [47]. For instance, during extended testing periods, a student who is bored may still be motivated to engage but not necessarily with their current environment. If a student does not perceive a valued purpose in their task or feels their activities demand too little effort and ability, they are less likely to engage with the material [48].

3.2. Limitations

Several key limitations prevent the findings of the present work from being universally applicable. Due to the voluntary student selection method, there is some self-selection bias. Furthermore, the sample size per group was smaller than ideal for conducting statistical tests with sufficient power. Despite the initial interest from the entire student body, complete attendance at the study sessions was significantly reduced. Participation was then further complicated by attrition that occurred throughout the study with a severity related to time and question difficulty. These factors were not expected to affect participation to this extent before the study began. The considerable number of participants who withdrew over time also compelled the team to conduct only one intervention as opposed to three. To fully assess the impact of time-on-question overall, analysis over several iterations and topics of active instruction would have been preferred. However, despite such setbacks, the data thus analyzed provide a valuable and detailed snapshot into problem-solving performance as affected by practice time.

Of importance was the method by which students were incentivized to participate in the study. Painstaking care was taken to present the events as comprehensive review sessions so that students may exhibit a more genuine work ethic during observation. There was a potential for certain students to have been uninterested in the intervention due to the substantial time investment necessary to finish the questions and take the pre- and post-tests. To alleviate this, alternative incentive schemes such as bonus credit or gift card raffles may be considered for future iterations. Alternatively, or in conjunction, think-aloud protocols may be employed to gather comprehensive qualitative data from participants; inclusion of such feedback would also expand the usable portions of the COSINE code system. To further investigate students’ mental and emotional states during tasks, it would be advantageous to employ protocols and conduct semi-structured interviews with participants regarding the cognitive and affective processes undergone when faced with varying time limitations.

Lastly, it is important to highlight a limitation which pertains to student demographics. Specifically, the representation of African American students and white students within the available sample was quite sparse. This paucity of participants from these ethnic backgrounds was mainly influenced by the institution’s demographic composition rather than any aspect that could be addressed through experimental design. This limitation underscores the need for future research to expand the study’s participant pool to include people from a more diverse range of ethnicities so that the research can provide a more comprehensive understanding of the effects and outcomes of the variables under investigation.

4. Conclusions

This study investigated the effects of time-on-question on general chemistry students’ problem-solving performances under controlled conditions in relation to question topics and demographic information. The analysis of the data gathered from each time group helped uncover some intrinsic relationships between time, performance, and the impact of mental and emotional fatigue on the problem-solving success of students with different academic success levels and socioeconomic status, which were not readily available in prior studies [2,22,42,49,50]. The results of this study provide insights on topics that would help shape socioeconomically informed teaching methodologies that could be used by educators, standardized testing services, and any digital platform that utilizes artificial intelligence to help students develop better problem-solving skills.

Investigations into the overall effects of time-on-question on student performance were acquired from a previous study. In the previous work [11], it was suggested that two factors, time-pressure training and emotional fatigue, contributed significantly to observed success and failure ratios between time groups. Results from the current study regarding subtopics reinforced the importance of fatigue management in study strategies. The Minimum group showed the best overall Attempt Success Rate (ASR) and had a positive score for all but one subtopic. This observation suggested that this group improved their comprehension of topics during the intervention and applied more effective strategies during the post-test [51]. The Average group was the next-best group but saw a decrease in the ASR scores of four topics. The Maximum group saw negative scores in nine subtopics. This difference in the ASR scores was attributed to a deterioration in performance due to the mental and emotional fatigue experienced by these groups. This reinforced the argument that educators should be mindful of the effects of fatigue when creating practice assignments. Question length should be reasonable, vary in difficulty level, and should encourage students to think about the general structure of the questions within the chapters of interest. These principles should be mirrored during testing; consideration of time should be given in the exam design to ensure that students are not tested on their mental endurance but on their knowledge.

In the latter part of the analysis, Complete Success Rate (CSR) scores were grouped based on students’ ethnic backgrounds, socioeconomic statuses, and high school GPAs. The evaluation of problem-solving performance, measured by ΔCSR, unveiled distinct performance patterns influenced by ethnic backgrounds under different time conditions. Notably, students of Asian/Pacific Islander heritage demonstrated the most significant improvement in problem-solving performance under time pressure but experienced a noticeable decline with extended time. In contrast, students of Hispanic origin exhibited an inverse trend, improving their problem-solving performance as more time was allocated. Caucasian students fell in between these two extreme groups, suggesting the existence of an optimal time threshold for problem-solving that does not induce emotional fatigue. These observed differences in problem-solving performance across ethnic groups are thought to be intricately tied to the diverse cultural learning environments in which students are immersed.

In consideration of socioeconomic status (SES), this study concludes that distinctions in problem-solving performance between low-, medium-, and high-income SES students were predominant only in the minimum time condition, where students were pressed for time. Notably, students from higher-income socioeconomic backgrounds tended to outperform their peers when given less time to solve each problem, likely due to a greater access to external resources such as tutoring. However, this difference became negligible when more time was provided, indicating that SES primarily mediated problem-solving performance on tasks significantly constrained by time; consequently, this supports the notion that effective and equitable education occurs under conditions like those used for the Average group. This nuanced understanding offers valuable insights for educators and researchers seeking to customize effective teaching methods for diverse student populations.

The evaluation of problem-solving performance based on students’ self-reported GPAs also revealed noteworthy insights. Across all time conditions, students reporting lower GPAs demonstrated more significant declines in problem-solving performance relative to their peers, potentially attributable to low self-regulation and self-efficacy. Interestingly, students with medium GPAs were the only group with a consistently positive ΔCSR across all time conditions, suggesting greater sustained motivation and educational resilience over time. Students with high GPAs also exhibited positive ΔCSR in the minimum and average conditions; however, scores noticeably declined in the maximum condition, possibly indicative of decreased motivation or boredom.

The overall analysis of the combined data suggests that demographic differences impacting performance are minimized when students are given 4–5 min to solve each general chemistry problem. Allocating excessive time for problem-solving tasks leads to a significant decline in performance and should be minimized in assignments. Both the Minimum and Average time conditions yielded positive outcomes, but the Average time group benefits a larger and more equitable student population. It is recommended that instructors promote eustress through learning strategies that allow reasonable time for each question, aiming for an optimal range that maximizes benefits for all students while avoiding emotional fatigue. These findings are particularly useful for developing practice exams and helping instructors allocate appropriate time to foster maximal engagement with problem-solving tasks.

Future iterations of this study are planned. In addition to the ideas previously suggested in the limitations section, the next study will involve two groups of students: one large group that will solve an extensive number of questions over several weeks and a second group will participate in think-aloud protocols in order to help the research team to gather in-depth information on emotional and mental fatigue. To better identify the changes in the amounts of fatigue, the students will be surveyed and prompted to share their perspectives after each intervention question. In this way, researchers will be able to determine the conceptual shortcomings and algorithmic mistakes in the solutions generated by the students.