Motivation, conceptual understanding, and critical thinking as correlates and predictors of metacognition in introductory physics

Abstract

The purpose of this study was to explore the relationship and prediction of motivation, conceptual understanding, and critical thinking on metacognition in introductory physics. A correlational research design with multiple regression analysis was used to analyze the data from 84 first-year pre-engineering students from two public universities in Ethiopia. The instruments used were the Physics Motivation Questionnaire II, the Electricity and Magnetism conceptual assessment, the critical thinking of electricity and magnetism, and the metacognitive awareness and regulation of electricity and magnetism. The results showed that metacognition was significantly and positively associated with all three predictor variables, with motivation being the most strongly related, followed by conceptual understanding and critical thinking. However, only motivation and conceptual understanding predicted metacognition in the regression model. These results highlight the specific and combined roles of motivation, conceptual understanding, and critical thinking on metacognition and emphasize the need to consider these factors in physics education and research.

Keywords:

• metacognition
• motivation
• conceptual understanding
• Critical thinking and physics education

1. Introduction

Metacognition is the ability to think about and regulate one’s own thinking in learning (Avargil et al., 2018; Schraw & Dennison, 1994; Zohar & Barzilai, 2013). In physics learning, metacognition involves being aware of and applying various cognitive processes and strategies, such as problem-solving, reasoning and conceptualizing (Veenman, 2012). Metacognition involves two main components: metacognitive knowledge, which refers to what learners know about their own cognitive processes and strategies, and metacognitive regulation, which refers to how learners plan, monitor, and evaluate their own learning processes (Schraw & Moshman, 1995). Metacognition is a key factor for effective learning and academic achievement in physics (Avargil et al., 2018; Zohar & Barzilai, 2013). According to Thomas (2013) and Veenman (2012),students with higher metacognitive skills can optimize their learning environment and overcome common difficulties or challenges in physics learning, such as misconceptions, lack of motivation, or low self-efficacy.

Physics demands mastering abstract concepts, applying mathematical skills, solving problems, and conducting experiments (Chabay & Sherwood, 2006).To achieve proficiency in physics, learners need to acquire domain-specific knowledge and skills and metacognitive skills that allow them to regulate their own learning processes and overcome challenges (Avargil et al., 2018). However, many students have difficulties with metacognition in physics and often lack appropriate strategies or self-monitoring of their comprehension (Morphew, 2021; Sundstrom, 2018; Taasoobshirazi et al., 2015; Thomas, 2013). Therefore, it is essential to investigate how metacognition can be supported and improved in physics education by examining the interplay of motivation, conceptual understanding, and critical thinking in introductory physics.

Metacognition is a skill that can be enhanced through deliberate practice (Stanton et al., 2022) and a process that is affected by various factors that determine your cognitive and emotional states. Previous research has suggested that motivation, conceptual understanding, and critical thinking are key factors impacting metacognition in physics education (Halpern, 1997; Mills, 2016; Pintrich & Schunk, 2002). Students’ inner drive or desire to do an activity (motivation) is linked to metacognitive activities like self-monitoring and self-regulation in physics (Glynn et al., 2011). Motivated and interested physics students tend to use metacognitive activities more (McDowell, 2019; Ryan, 2017).

According to Mcdermott and Mcdermott (1984), conceptual understanding is the comprehension of fundamental concepts and principles in physics. Students with strong conceptual understanding can use metacognitive strategies to monitor their understanding, seek clarification, and self-evaluate (Mills, 2016). In addition, critical thinking skills are also essential for metacognition in physics education. Ennis (1993) and Halpern (1997) argued that critical thinking involves applying logic and reasoning to identify strengths and weaknesses in arguments and make sound judgments. Students with strong critical thinking abilities are better equipped to evaluate their own understanding and recognize areas where they need improvement (Halpern, 1997). To think critically, students should reflect on their thinking process, evaluate their progress toward a suitable goal, verify their accuracy, and decide how to use their time and mental effort effectively (Ford & Yore, 2012).

Metacognition is related to factors such as critical thinking, motivation and conceptual understanding (Dori et al., 2018). However, these relationships are not well understood in the context of introductory physics. This gap limits our understanding of metacognition’s complex and dynamic nature and its role in physics learning (Avargil et al., 2018). Most of the existing research (Arslan, 2018; Carpendale & Cooper, 2021; Efklides & Efklides, 2011; Gurcay & Ferah, 2018; Mills, 2016; Tang et al., 2021) has focused on these factors individually in different domains, rather than how they affect and interact with metacognition in physics. This study explores both the correlations and the predictive effects of these three factors on metacognition in introductory physics i.e. how these factors separately and jointly predict metacognition.

This study aims to advance physics education by identifying the key factors that predict metacognition among introductory physics students. Physics educators can use this information to design and implement interventions that improve students’ metacognition by enhancing their motivation, critical thinking, and conceptual understanding in physics instruction. This could lead to better learning outcomes and deeper learning in physics, as well as skills that can be applied to other domains and contexts.

The research questions of the study are as follows:

1. How do motivation, conceptual understanding, and critical thinking relate to metacognition in introductory physics?

2. To what extent do motivation, conceptual understanding, and critical thinking predict metacognition in introductory physics?

2. Method

2.1. Research design

This study explored how motivation, conceptual understanding, and critical thinking were related to and predicted metacognition in students taking an introductory physics course. We used a correlational design to test hypotheses and examine variable relationships systematically and objectively (Creswell & Creswell, 2017). The correlational design enabled us to measure the strength and direction of the relationship of metacognition with motivation, conceptual understanding, and critical thinking, as well as the predictive power of these variables on metacognition, without implying causation or intervention (Tabachnick et al., 2013).

2.2. Participants and sampling

The population of this study consisted of first-year pre-engineering students from two public science and technology universities in Ethiopia in the 2021/2022 academic year. The universities were founded with the aim of producing highly skilled science and technology professionals who can contribute to the development of the country. Out of a population of 175 first-year pre-engineering students, this study involved 84 students (64 males and 20 females). The participants were selected using a convenience sampling method based on their availability and willingness to participate in the study. The inclusion criteria were that the participants had to be enrolled in the introductory physics course and had not taken any courses before. The participants took an introductory physics course that covered mechanics, thermodynamics, and electricity and magnetism (E&M). We focused on E&M because it is a difficult and complex topic that requires students to think at different levels and dimensions (Chabay & Sherwood, 2006). E&M is also challenging for teachers, who may lack time to develop students’ cross-curricular skills (van den Bos, 2021). Therefore, we found E&M an interesting domain to study in introductory physics. We chose the convenience sampling method because it is a quick and easy way to select participants for the study without requiring a lot of resources or time. Moreover, the convenience sampling method allows for a diverse range of participants, as it does not impose any restrictions on who can participate as long as they meet the inclusion criteria.

For ethical considerations, students were informed about the nature of the study and ensured that the study would not harm them; their data would be used for research purposes only, and their names would not be used elsewhere. For the confidentiality threat, all participant data were accessible to the researchers only.

2.3. Measuring tools

The Physics Motivation Questionnaire II (PMQ II) was used to measure motivation in introductory physics. We chose this questionnaire because it is a discipline-specific tool that has been validated and widely used in previous studies on physics education (Glynn et al., 2009, 2011; Salta & Koulougliotis, 2020; Tuan et al., 2005). The PMQ II has 10 questions that ask students how much they agree or disagree with statements like “I enjoy learning physics.” The questions are divided into intrinsic motivation (learning physics for its own sake) and extrinsic motivation (learning physics for external rewards or benefits). Students answer on a scale from 1 (strongly disagree) to 5 (strongly agree). For this study, the PMQ II has good reliability and validity, as shown by a Cronbach’s alpha of 0.74 for the whole scale and 0.71 for each motivation type, which agrees with the results of Glynn et al. (2011).

To evaluate students’ critical thinking abilities in Electricity and Magnetism (E&M), the Critical Thinking Test Electricity and Magnetism (CTEM) was utilized. The CTEM test was developed by Tiruneh et al. (2017) and modified by adopting 12 out of the original 20 questions to match the course content. The modified test consisted of forced-choice and open-ended questions, which were reviewed by experts and instructors prior to use. The test had a time limit of 50 minutes, and a pilot test showed acceptable internal consistency of Cronbach’s alpha = 0.74 (Nunnally, 1978).

The study used the Critical Thinking Test Electricity and Magnetism (CTEM) to assess students’ critical thinking skills in E&M. The CTEM test was adapted from Tiruneh et al. (2017) and modified by selecting 12 out of the original 20 questions that matched the course content. The modified test had forced-choice and open-ended questions, which were checked by experts and instructors before use. The test had a time limit of 50 minutes, and a pilot test showed a good internal consistency of Cronbach’s alpha = 0.74 (Nunnally, 1978).

The study also used the Electricity and Magnetism Conceptual Assessment (EMCA) test by McColgan et al. (2017) to measure students’ conceptual understanding of E&M. This is a multiple-choice test with correct answers and misconceptions as distractors, which was designed to cover the wide content of E&M. The original test had 30 questions, but this study used only 21 expert-validated questions covering electrostatics, direct current circuits, and magnetism. According to Tabachnick et al. (2013), after pilot testing, the EMCA showed a satisfactory reliability level with an alpha value of 0.76 and took 30 to 40 minutes to complete.

The Metacognitive Awareness and Regulation in Electricity and Magnetism (MARS-EM) is a tool that assesses how university students use metacognition in E&M. It was created based on Schraw and Dennison (1994) model and a literature review of other metacognition tools in science education. The MARS-EM has 15 items, but three items were removed after experts checked the content validity. The MARS-EM was given to 200 pre-engineering students at Addis Ababa Science and Technology University, and the data were analyzed using EFA after making sure the assumptions for factor analysis were met. The analysis results showed that the MARS-EM had two factors with eight items. The two factors were metacognitive awareness and metacognitive regulation, which had a moderate positive relationship. The model fit measures also indicate that the MARS-EM fits the data well. The RMSEA with a 90% CI of 0.00 to 0.0538 is an acceptable fit, and the TLI of 1.08 also supports this conclusion (Hu & Bentler, 1999). The BIC value of −59.2 shows a good fit for the data, and the non-significant p-value of 0.706 from the χ² test with 9.85 and 13 degrees of freedom confirms this result (Haeruddin et al., 2020). The reliability of the MARS-EM was measured by calculating the Cronbach’s Alpha reliability coefficient, which was 0.71 for the first factor (metacognitive awareness), 0.69 for the second factor (metacognitive regulation), and 0.74 for the whole scale. These results suggest that the MARS-EM is reliable (Tabachnick et al., 2013).

2.4. Data collection procedures

The first author was in charge of collecting the data for the study using various instruments. These included the Physics Motivation Questionnaire II (PMQ II), Critical Thinking Electricity and Magnetism (CTEM), Electricity and Magnetism Conceptual Assessment (EMCA), and Metacognitive Awareness and Regulation in Electricity and Magnetism (MARS-EM). The data collection took two days. On the first day, he met with the university student, participants, explained the purpose of the study and obtained their consent. Then, the participants filled out the questionnaires, including the MARS-EM, which had eight items in two factors. He gave clear instructions to ensure accurate responses. On the second day, the participants took the tests. They had 50 minutes to complete the CTEM test, assessing their electricity and magnetism critical thinking abilities. After that, they took the EMCA test, which measured their conceptual understanding using multiple-choice questions. He provided the necessary instructions and support throughout the test-taking process. By collecting the data personally, he ensured consistency and adherence to the established procedures. The direct involvement also enabled effective communication, clarity of instruction, and a systematic approach to collecting data related to metacognition, critical thinking ability, and conceptual understanding of electricity and magnetism.

2.5. Data analysis techniques

The data analysis consisted of Pearson correlation coefficients and multiple regression analysis using SPSS software version 25. The Pearson correlation was used to examine the relationship between the variables and metacognition. At the same time, the standard multiple regression analysis methods were applied to assess how much critical thinking, conceptual understanding, and motivation explained the variations in metacognition. In multiple regression, all independent variables were included in the model, and the predictive power of each independent variable was evaluated after controlling for the combined effect of all other independent variables (Tabachnick et al., 2013). The study verified the assumptions of multivariate normality, linearity, and multicollinearity before performing the analysis.

3. Result

3.1. Assumption checking

Before conducting multiple linear regression analysis, several assumptions were checked. These included normality of residuals, independence of residuals, absence of multicollinearity among predictor variables, homoscedasticity of residuals, and absence of influential cases. The normality of the residuals was examined using a P-P plot (see Figure 1), which showed that the dots were close to the line, indicating that the normality assumption was met. The independence of residuals was tested using the Durbin-Watson statistic (see Table 4), which was found to be 1.745, falling within the acceptable range of 1.5 to 2.5, indicating no autocorrelation. Multicollinearity among predictor variables was assessed by examining correlation coefficients (see Table 1), tolerance values, and variance inflation factor (VIF) values. The correlation coefficients between predictor variables were relatively low, indicating no evidence of multicollinearity (Tabachnick et al., 2013). The tolerance values were greater than 0.1, and the VIF values were less than 10 (see Table 2), indicating no multicollinearity. Homoscedasticity of the residuals was evaluated by examining the scatter plot of the residuals (see Figure 2), which showed no discernible pattern, indicating that the homoscedasticity assumption was met. The absence of influential cases that could bias the model was checked by examining Cook’s distance values. The maximum Cook’s distance value for this model was 0.249, which is less than 1, indicating that no influential cases could bias the model. Overall, the assumptions for multiple linear regression analysis were found to be satisfactory.

Figure 1. Normal P-P plot of regression standardize the residuals.

Figure 2. Scatter plot.

Table 1. Correlation among metacognition, critical thinking, and conceptual understanding, and motivation

	1	2	3	4
Metacognition	1.000
Critical Thinking	.163*	1.000
Conceptual Understanding	.311**	.348**	1.000
Motivation	.439**	.071	.027	1.000

Note: ** p < .01, * p < .05.Correlation coefficients are based on Pearson’s product-moment correlation. N = sample size.

Table 2. Regression coefficients and correlations between predictor variables and metacognition

Model	Unstandardized Coefficients		Standardized Coefficients	t	Sig.	Correlations			Collinearity Statistics
	B	Std. Error	Beta			Zero-order	Partial	Part	Tolerance	VIF
(Constant)	.543	.573		.948	.346
Critical Thinking	.007	.022	.032	.321	.749	.163	.036	.030	.875	1.143
Conceptual Understanding	.066	.023	.288	2.851	.006	.311	.304	.270	.879	1.138
Motivation	.532	.118	.429	4.517	.000	.439	.451	.428	.995	1.005

Note: Dependent Variable: Metacognition

3.1.1. Correlation analysis of the relationships between motivation, conceptual understanding, critical thinking, and metacognition

One of the objectives of this study was to explore the association between motivation, critical thinking, and conceptual understanding with metacognition in introductory physics. The research question that guided this objective was: What is the association between motivation, critical thinking, and conceptual understanding with metacognition in introductory physics? To answer this research question, the following data analysis techniques were applied.

A Pearson correlation analysis was conducted to investigate the relationship between predictor variables (critical thinking, conceptual understanding, and motivation) and metacognition in introductory university-level physics courses. According to the correlation statistics presented in Table 1, there were zero-order correlation coefficients between the predictor variables (critical thinking, conceptual understanding, and motivation) and the outcome variable (metacognition). The correlation coefficient between critical thinking and metacognition was r = 0.163, indicating a weak positive correlation between the two variables. The correlation coefficient between conceptual understanding and metacognition was r = 0.311, indicating a moderate positive correlation between the two variables. The correlation coefficient between motivation and metacognition was r = 0.439, indicating a moderate positive correlation between the two variables. In general, the correlation statistics suggested that all three predictor variables positively correlated with metacognition, with motivation having the strongest correlation, followed by conceptual understanding and critical thinking.

3.1.2. Regression analysis of the predictors of metacognition development

Another objective of this study was to examine how motivation, critical thinking, and conceptual understanding predict metacognition in introductory physics. The research question addressed this aim: To what extent do motivation, critical thinking, and conceptual understanding predict metacognition in introductory physics? To answer this research question, the following data analysis techniques were used.

A multiple linear regression analysis was conducted to investigate the predictive power of the independent variables (motivation, conceptual understanding, and critical thinking) on the dependent variable, metacognition. The results of the coefficients table (see Table 2) showed that motivation was a significant predictor of metacognition (B = .532, SE = .118, β = .429, t (80) = 4.517, p < .001). conceptual understanding was also a significant predictor of metacognition (B = .066, SE = .023, β = .288, t (80) = 2.851, p = .006). However, critical thinking was not a significant predictor of (B = .007, SE = .022, β = .032, t (80) = .321, p = .749). Overall, the results suggest that motivation and conceptual understanding are significant predictors of metacognition in this study, while critical thinking does not play a significant role.

A one-way analysis of variance (ANOVA) was conducted to examine the relationship between the predictors (motivation, conceptual understanding, critical thinking) and the dependent variable, metacognition (see Table 3). The results showed a significant main effect for the model, F (3, 80) = 10.524, p < .001, indicating that the predictors significantly predicted metacognition

Table 3. A one way ANOVA results for the relationship between predictors and metacognition

Model		Sum of Squares	Df	Mean Square	F	Sig.
	Regression	8.668	3	2.889	10.524	.000^b
	Residual	21.964	80	.275
	Total	30.632	83

Note: ^a: Dependent Variable: Metacognition

^b: Predictors: (Constant) Critical thinking, Conceptual understanding, Motivation

The regression model (see Table 4) accounted for 28.3% of the variance in metacognition, with a regression sum of squares of 8.668 and a residual sum of squares of 21.964. The mean square for the regression was 2.889, and the mean square for the residual was 0.275.

Table 4. Model summary for the relationship between predictors and metacognition

Model	R	R Square	Adjusted R Square	Std. Error of the Estimate	Durbin-Watson
1	.532^a	.283	.256	.52398	1.745

Note: ^a: Predictors: (constant), critical thinking, conceptual understanding, motivation

^b: Dependent Variable: Metacognition

4. Discussion

The main purpose of this study was to explore the roles of motivation, conceptual understanding, and critical thinking on metacognition in university-level introductory physics courses. In this section, we will discuss the interpretations and implications of our findings and the limitations and directions for future research.

One of the key findings of this study was that metacognition was positively correlated with motivation, conceptual understanding, and critical thinking. This finding confirmed our hypothesis and was consistent with previous research that showed positive associations between metacognition and these factors in physics and other domains (Arslan, 2018; Carpendale & Cooper, 2021; Efklides & Efklides, 2011; Gurcay & Ferah, 2018; Mills, 2016; Tang et al., 2021).This finding indicates that metacognition is not a static or isolated skill, but a complex and interactive process that involves various cognitive and affective factors. Therefore, enhancing students’ metacognition requires addressing their motivation, conceptual understanding, and critical thinking skills as well. This implies that physics instructors should employ strategies to stimulate students’ interest and curiosity in physics, offer feedback and guidance to assist students in correcting their misconceptions and deepening their understanding of physics concepts, and urge students to apply critical thinking skills to solve physics problems and reflect on their thinking processes (Dori et al., 2018).

Another important finding of this study was that motivation and conceptual understanding were significant predictors of metacognition in the multiple regression analysis, while critical thinking was not a significant predictor. This finding contrasts with some studies that found critical thinking to be a significant predictor of metacognition (Arslan, 2018; Gurcay & Ferah, 2018; Magno, 2010), which suggests that the relationship between critical thinking and metacognition may vary depending on the context and the domain of learning. Critical thinking may interact with other factors that were not measured in this study, such as prior knowledge, instruction, or individual differences. For instance, prior knowledge may influence critical thinking and metacognition by providing a basis for evaluating and monitoring one’s reasoning (Kuhn & Dean, 2004; Schraw & Moshman, 1995). Instruction may also affect critical thinking and metacognition by providing explicit strategies and feedback for improving one’s thinking (Abrami et al., 2008; Zohar & Dori, 2003). Individual differences may also play a role in critical thinking and metacognition by influencing one’s cognitive style, personality traits, or self-efficacy (Schraw & Dennison, 1994). Therefore, future research should explore these potential factors and their interactions with critical thinking and metacognition in physics learning.

This study contributes to the literature on metacognition and physics education by showing that students’ metacognition in physics is influenced by their motivation, conceptual understanding, and critical thinking skills. These findings have practical implications for physics instructors who want to foster metacognition and improve student learning outcomes. For example, instructors can use engaging and relevant examples to spark students’ interest and curiosity in physics, provide feedback and guidance to help students correct their misconceptions and deepen their understanding of physics concepts, and encourage students to apply critical thinking skills to solve physics problems and reflect on their thinking processes (Džinović et al., 2019; Fleur et al., 2021; Stanton et al., 2022). Moreover, this study highlights the need for more research on the relationship between critical thinking and metacognition in physics. Future studies could investigate whether critical thinking skills vary across different physics topics or domains and whether they can be enhanced by explicit instruction or practice in metacognitive strategies.

This study had some limitations that should be acknowledged. First, the sample size was relatively small and limited to two universities in Ethiopia. Therefore, the generalizability of the findings may be restricted to similar contexts and populations. Second, the study used convenience sampling, a non-probability sampling method that may introduce bias and reduce the sample’s representativeness. Third, the study used self-report measures to assess motivation and metacognition, which may be influenced by social desirability and response tendencies. Fourth, the study used a correlational design, which does not allow for causal inference between the variables. A fifth limitation of this study is that we did not consider other variables that may be related to metacognition, such as IQ. IQ is a measure of general cognitive ability that may influence how students think and learn in physics. Previous studies have found some correlations between IQ and metacognition in different domains (Ackerman & Heggestad, 1997; Schraw & Moshman, 1995). However, the relationship between IQ and metacognition in physics is unknown and may depend on other factors such as motivation, conceptual understanding, and critical thinking.

For the above limitations, this study suggests directions for future research. Future studies should use larger and more diverse samples that include students from different universities, regions, and countries to increase the generalizability and validity of the findings. To reduce bias and increase the representativeness of the sample, future studies should use probability sampling methods that ensure a fair and equal chance of participation. To overcome the limitations of self-report measures, future studies should use objective measures or multiple data sources that capture students’ motivation, critical thinking, and metacognition more accurately. To establish causal relationships between variables, future studies should use experimental or quasi-experimental designs that manipulate or track motivation, critical thinking, or metacognition and measure their effects on physics learning outcomes. As a further avenue for future research, the role of IQ and other variables in physics metacognition should also be investigated.

5. Conclusions

This study examined the roles of motivation, critical thinking, and conceptual understanding on metacognition in introductory physics learning among university students in Ethiopia. The study found that metacognition was positively related to all three predictor variables, but only motivation and conceptual understanding were significant predictors of metacognition. These findings suggest that metacognition is an important factor for physics learning and performance that is influenced by students’ motivation and conceptual understanding. The findings also imply that physics educators should foster metacognition in their students by using strategies to enhance their motivation and conceptual understanding. Furthermore, the findings indicate that more research is needed to explore the role of critical thinking in metacognition in physics across different contexts and domains

Disclosure statement

No potential conflict of interest was reported by the authors.