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DOI: 10.1039/D0RP00345J (Paper) Chem. Educ. Res. Pract., 2021, 22, 772-785

Chemistry self-efficacy in lower-division chemistry courses: changes after a semester of instruction and gaps still remain between student groups

Candido Moreno , Duyen Pham and Li Ye *
Department of Chemistry and Biochemistry, California State University, Northridge, 18111 Nordhoff Street, Northridge, California 91330, USA. E-mail: li.ye@csun.edu

Received 15th November 2020 , Accepted 2nd May 2021

First published on 3rd May 2021

Abstract

Chemistry self-efficacy (CSE) was identified as a critical affective construct to predict student success in chemistry classrooms. We surveyed students at the beginning and toward the end of a semester to measure students’ CSE beliefs in introductory and general chemistry courses at a Hispanic-serving institution in the United States. First, the relationships between CSE (initial and toward the end) and student achievement measured by course GPA were examined. Second, trends of changes in student CSE beliefs over a semester in relation to several aspects of student characteristics including course level, gender, underrepresented minority (URM) status were investigated. Lastly, the gaps in specific areas of CSE still remain between student groups after a semester of instruction were revealed. The results showed that CSE toward the end of the semester significantly predicted students’ course GPA in lower-division chemistry courses. Even though the CSE of different student groups all increased to some extent after a semester of instruction, the levels of changes were influenced significantly by certain factors such as course level and URM status but not gender. While URM students' CSE beliefs increased more than non-URM students after a semester of instruction, there were still gaps in certain areas between the two student groups. The remaining gaps in CSE beliefs between URM and non-URM students were found to be in the areas of interpreting chemical equations and choosing appropriate formulas to solve chemistry problems. Meanwhile, students who completed introductory chemistry still lagged behind in interpreting chemical equations as compared to students who completed general chemistry. Research literature related to these two specific areas in CSE with gaps between student groups was reviewed, instructional strategies and research directions along with theoretical perspectives for closing those equity gaps in college lower-division chemistry classrooms are discussed.

Introduction

The United States has become increasingly more diverse over the past few decades. However, graduation rates within Science, Technology, Engineering, and Mathematics (STEM) fields, our interest being chemistry, have not necessarily reflected the increase of the population of underrepresented minorities (URMs) in STEM fields. URMs include Black, Hispanic, and Native American/Native Alaskan origin (NSF, 2017). According to the data from National Science Foundation (NSF, 2020), the total number of bachelor chemistry degrees given out to US citizens were 143[thin space (1/6-em)]511 between 2008–2018. Among those, URMs only accounted for approximately 17% despite making up about 30% of the American population.

There has been an increasing interest in understanding and improving URM students’ retention and success in STEM fields in order to close the achievement gaps between student groups. General chemistry course series are the foundational courses that are required by many STEM majors in early years before students advance through other course requirements in their chosen majors. These courses are often considered as gateway courses because the success of those courses could be turning points for students and predict whether the students are able to complete the degree or not in STEM fields (Barr et al., 2010). A recent article published in Science Advances by Harris and colleagues analyzed demographics and grades of 25[thin space (1/6-em)]768 students who enrolled in general chemistry and organic chemistry at the University of Washington from 2000 to 2016 (Harris et al., 2020). They found URM students underperformed than non-URM students in the first course of general chemistry series after controlling for academic preparation. However, they discovered a “hyperpersistent zone” phenomenon, when URM students performed a C or better in the course, they are more likely to persist in chemistry as compared to their non-URM peers. This is not the case for the URM students who performed a C- and below in the general chemistry course. The hyperpersistent zone phenomenon reveals the need and significance for reducing the achievement gaps in lower-division chemistry courses and implies the disproportionate impact of such efforts on URM students in STEM fields.

Defining chemistry self-efficacy

Self-efficacy originated from Bandura's social cognitive theory in 1986, and it is defined as an individual's belief in their ability to complete a specific task in a field (Bandura, 1986). When an individual does not believe that he/she is capable of succeeding within a field, academic performance may suffer and can lead to avoidance and change of major. Numerous research articles have revealed the positive relationships between self-efficacy and academic performance or retention in a variety of subjects (Lent et al., 1984; Richardson et al., 2012). Bandura suggested that self-efficacy is domain specific (Bandura, 1997), which means that having high self-efficacy in one field will not translate to another. For example, an individual with a degree in physics might have high self-efficacy in physics but he/she might have low self-efficacy in other science subjects like chemistry or biology. In this study, we are interested in understanding students’ Chemistry Self-Efficacy (CSE) in the context of college introductory and general chemistry courses, defined herein as an individual's belief in his/her ability to complete chemistry-related tasks in the topics taught in introductory and general chemistry courses. Our aim of this study is to understand the trends in students’ CSE by investigating the changes of students’ CSE before and after a semester of instruction in lower-division chemistry courses and gaps between student groups according to course level, gender, and URM status. Lower-division chemistry courses in this study refer to an introductory chemistry and two courses of general chemistry series for mostly students with STEM related majors in a college setting. Deeper understanding in the affective domain by student groups in lower-division chemistry courses would provide insights into the needs of particular groups of students and tailor instructional strategies to meet their needs. The ultimate goal for the study is to improve students’ success and achieve equity in these gateway chemistry courses so as to increase retention and graduation rates in STEM fields.

Relationships between chemistry self-efficacy and academic performance

Students’ chemistry self-efficacy has been found to be linked to students’ academic performance in different levels of chemistry courses. For instance, two studies have found CSE was a significant predictor for Turkish high school chemistry students’ chemistry achievement test scores (Kan and Akbas, 2006; Uzuntiryaki and Senay, 2015). The correlation between CSE and chemistry achievement was found to be 0.24 and 8.4% of total variance of chemistry achievement scores could be predicted by the CSE of students in a multiple regression model. In the context of college introductory and general chemistry courses, the majority of the studies used either the College Chemistry Self-Efficacy Scale (CCSE) or Chemistry Attitudes and Experiences Questionnaire (CAEQ) to measure students’ chemistry self-efficacy beliefs (Zusho et al., 2003; Dalgety and Coll, 2006; Lalich et al., 2006; Ramnarain and Ramaila, 2018). High levels of CSE have been found to lead to high final course percent scores; CSE towards the end of the course was found to be the best predictor (standardized beta coefficient of 0.40) of final course performance after controlling for prior knowledge and a series of motivational beliefs and cognitive strategies such as task-value and rehearsal strategies. In a multiple regression model, 32% of variance of student performance could be explained by student CSE in cognitive skills, psychomotor skills and everyday applications. CSE in cognitive skills, which is described as students’ beliefs on how well they are able to deal with intellectual tasks in chemistry, was found to be the best predictor of students’ academic performance. In terms of the connection between student performance and chemistry self-efficacy, Villafane and colleagues indicated there is a direct and reciprocal influence between the two (Villafañe et al., 2016). They developed an organic chemistry self-efficacy (OCSE) questionnaire to measure organic chemistry students’ self-efficacy. The questionnaire was administered five times before exams in a large organic chemistry course at a southeastern public university. Correlations between the scores of OCSE and student exam scores were positive and significant (ranging from 0.32 to 0.39) except for the first OCSE and first exam was 0.09. The authors used a reciprocal causation model to reveal the interrelated relationships between OCSE and exam performance as well as the positive and significant influence of the prior OCSE on the subsequent OCSE measure. Additionally, Zusho and colleagues measured chemistry self-efficacy multiple times across a semester in introductory chemistry and found the levels of chemistry self-efficacy of high-achievers in the course increased over time while low-achievers decreased over time, indicating chemistry tasks and feedback might change students’ chemistry self-efficacy levels (Zusho et al., 2003). In summary, research studies have revealed that chemistry self-efficacy is a critical affective construct that has an important impact on student success and retention in chemistry courses and STEM majors and there is an interplayed relationship between chemistry self-efficacy and performance in chemistry courses. However, the above research studies were all focused on studying chemistry self-efficacy in a single chemistry course, to extend the existing body of literature on chemistry self-efficacy, in this study we examined the relationships between chemistry self-efficacy and student achievement in multiple lower-division chemistry courses and compared the differences between those chemistry courses.

Differences in chemistry self-efficacy between student groups

Chemistry self-efficacy between different groups of students has been of interest to the chemistry education community because gaps in CSE between student groups have been revealed previously and this might explain the source of inequity and achievement gaps needed to be addressed in STEM fields. Researchers have reported students with chemistry majors rated higher CSE than non-science majors in a first-semester college general chemistry course (Ferrell and Barbera, 2015). Another study found no statistical differences between females and males in self-efficacy in a college analytical chemistry course even though females performed significantly lower in the achievement test (Tenaw, 2013). In the context of introductory chemistry, Villafane and colleagues examined the CSE trajectories over a semester and differences between students with different genders and ethnicities in a large college chemistry preparatory course at a public research-oriented university in the United States (Villafañe et al., 2014). The results showed increased trends in CSE scores after a semester of instruction for all combinations of gender and ethnic groups except for Hispanic and Black males. They indicated that Hispanic and Black males might be overconfident on their ability to complete chemistry tasks at the beginning of the semester and then their CSE dropped throughout the semester, indicating additional attention might need to be given to those student groups. The above studies suggested that students’ chemistry self-efficacy and trajectories in college chemistry courses might be influenced by certain student characteristics such as major, gender, and ethnicity. However, patterns of CSE between student groups revealed by research studies in the literature up to now are still limited. The above three studies are the only studies the authors found to identify the differences in college chemistry self-efficacy between student groups. In addition, all of the aforementioned studies were conducted in one chemistry course at a particular type of institution, more collective evidence is still needed to better understand which characteristics influence students’ chemistry self-efficacy and how those characteristics explain and contribute to students' success in chemistry courses at different educational settings.

Study purposes and research questions

Understanding student affective domain is critical for improving student learning in the context of college chemistry courses, especially for lower-division chemistry courses since they play very important roles in determining whether students would be able to complete their degrees in the STEM fields or not. To fill in the gaps in the chemistry self-efficacy, the research purposes for this study were: First, we intended to investigate the relationships between students’ chemistry self-efficacy and academic performance in multiple lower-division chemistry courses after controlling for student backgrounds and prior knowledge. Second, chemistry self-efficacy trends before and after a semester of instruction were explored and the differences between student groups (divided by gender, ethnicity, and course level) and interactions between those factors were examined. These results could be used to compare with the existing findings in the chemistry education literature and we wondered whether the same trends would be found with students in multiple chemistry courses in an unique context (primary undergraduate, Hispanic-serving institution) that has not been reported in the literature yet. Third, to extend the existing body of literature on chemistry self-efficacy in college chemistry courses, this study also aimed to focus on post-test item analysis for the chemistry self-efficacy scale and with the goal to reveal which areas of chemistry self-efficacy (not just chemistry self-efficacy as a whole) were still lacking after a semester of instruction by certain student groups. That is, investigating the gap areas between students who completed introductory chemistry courses and general chemistry courses. Also, the gap areas between those students with ethnicity that are considered as an underrepresented minority in STEM fields and their counterparts. These efforts would provide insights to future instruction and experimental design for improving students’ affective domain (i.e., chemistry self-efficacy) for certain disadvantaged student groups in lower-division chemistry courses. The following three research questions were used to guide this study:

1. How well does chemistry self-efficacy predict students’ course GPAs after controlling for demographics, prior knowledge, and course level in lower-division chemistry courses at a Hispanic-serving institution? Which is the best predictor of students’ course GPAs?

2. Is there a significant change in students’ chemistry self-efficacy after a semester of instruction? How is the change different between student groups (Males vs. Females; non-URM students vs. URM students; introductory chemistry vs. General chemistry)?

3. What gaps still remain in areas of chemistry self-efficacy between certain student groups after a semester of instruction?

Methods

Study context and data collection

The data was collected in the 2018 Spring semester from three lower-division chemistry courses including introductory chemistry, general chemistry I, and general chemistry II courses in a primarily undergraduate, Hispanic-serving university in southwestern United States. Hispanic-serving university is defined as having at least 25% of the undergraduate full-time student enrollment is made of Hispanic students (U.S. Department of Education, 2019). Chem 100 is a prerequisite introductory chemistry course before enrolling in Chem 101 (general chemistry I). Passing Chem 101 is a requirement for taking Chem 102 (general chemistry II). The majority of the students who take Chem 100, 101, and 102 are STEM related majors. Completing these courses are required for students to obtain degrees and pursue future careers in STEM fields. Chem 100 have 2.5 hours lecture per week, students meet with instructors twice a week, 75 minutes each. The instructors who teach Chem 100 and 101 employ active learning strategies in the lectures, such as polling questions, in-class small group activities focusing on problem solving skills on chemistry problems. Chem 101 and 102 follow the same lecture schedule as Chem 100. In addition, there is a 50 minute discussion session per week for these two courses taught by the same instructors who taught the lectures. The discussion session is focused on reviewing the lecture materials and problem-solving of chemistry problems. Student grades in the lecture courses are mostly evaluated based on their performance on quizzes and exams (70–80%) and participation in homework assignments and class activities (20–30%). All of the three courses have independent laboratory classes that are taught and evaluated by graduate teaching assistants and students enrolled in the laboratory classes are given a separated letter grade that is independent of the lecture grade.

The chemistry self-efficacy scale used to measure students’ chemistry self-efficacy beliefs is listed in Table 1. The items in the scale were selected and adapted from the College Chemistry Self-Efficacy Scale (CCSS). The CCSS was originally designed by Aydin and Uzuntiryaki to assess college students’ chemistry self-efficacy beliefs in Turkey (Aydin and Uzuntiryaki, 2009). It contains three subscales: self-efficacy for cognitive skills, self-efficacy for psychomotor skills, and self-efficacy for everyday applications. The CCSS was then renamed as the Chemistry Self-Efficacy Scale (CSES) by Uzuntiryaki and Senay (Uzuntiryaki and Senay, 2015). Ferrell and Barbera selected and adapted eight items from the self-efficacy for cognitive skills subscale and used them in a college introductory chemistry setting in the U.S (Ferrell and Barbera, 2015). Given the reasons that our research setting is most similar to Ferrell and Barbera's study and we are interested in measuring students’ cognitive skills for specific tasks that are required in the introductory and general chemistry courses such as choosing a formula to solve a chemistry problem and describing the structure of an atom, we used those eight items in the study.

Table 1 Chemistry self-efficacy scale (Ferrell and Barbera, 2015)
Very poorly Poorly Average Well Very well
1 2 3 4 5
1. To what extent can you explain chemical laws and theories? 1 2 3 4 5
2. How well can you choose an appropriate formula to solve a chemistry problem? 1 2 3 4 5
3. How well can you describe the structure of an atom? 1 2 3 4 5
4. How well can you describe the properties of elements by using the periodic table? 1 2 3 4 5
5. How well can you read the formulas of elements and compounds? 1 2 3 4 5
6. How well can you interpret chemical equations? 1 2 3 4 5
7. How well can you interpret graphs/charts related to chemistry? 1 2 3 4 5
8. How well can you solve chemistry problems? 1 2 3 4 5

The survey data along with student demographics and prior knowledge metrics were collected through google form online. The course instructors sent the survey links to students at the beginning of the semester (pre-test) and in the end of the semester (post-test). Pre-test data was collected in the first two weeks of the semester, and no assessments were administered in those chemistry courses yet. Post-test data was collected in the last two weeks of semester. The class sizes are ranged from 50 to 80 students. Students were given a few points of extra credit to complete the surveys. The survey response rate was 75%. Student final grades were obtained from the instructors. The Institutional Research Board at the University reviewed and approved the study before the study was implemented.

Data analysis

First, reliability and validity of the scale were examined by Cronbach's alpha coefficient, Confirmatory Factor Analysis (CFA), and relations to other variables. Cronbach's alpha coefficient is most commonly used in the chemistry education research articles to tell the internal consistency reliability of a scale. It concerns the homogeneity of the items and the precision of a measurement (Arjoon et al., 2013; Komperda et al., 2018). A scale with high value of Cronbach's alpha indicates that the items are highly intercorrelated and they are all measuring the same construct in a unidimensional scale or a subscale of a multidimensional scale. A value above 0.7 is considered as acceptable (DeVelli, 2012). Additionally, CFA was used to confirm the one factor internal structure of the scale reported by other studies in the literature (Aydin and Uzuntiryaki, 2009; Ferrell and Barbera, 2015). We specified a one-factor CFA with all the eight items each time. The robust maximum-likelihood estimation (MLR) was used given the ordinal and non-normal nature of the data (Knekta et al., 2019). Multiple fit indices include chi-square test (χ2 values), comparative fit index (CFI), the root-mean-square error of approximation (RMSEA), and the standardized root-mean-square-residual (SRMR) were considered to evaluate the models. A non-significant chi-square test is favorable for model fit but it is sensitive to sample size and are likely to have significant results even with small deviations. Thus, the adequacy of the models is mainly guided by other indices with the following criteria suggested in the literature: CFI ≥ 0.95, RMSEA < 0.08, and SRMR < 0.10 (Hu and Bentler, 1999). CFA was run using the R package lavaan and the syntax suggested by Knekta and colleges (Knekta et al., 2019). The validity of the scale also examined by correlation analysis between students’ CSE scores and their course Grade Point Average (GPA). Course GPA is calculated using the weighted average of all the quizzes and exams and other tasks associated with points in the chemistry courses. The association between chemistry self-efficacy and student achievement in chemistry courses has been indicated by other studies (Kan and Akbas, 2006; Uzuntiryaki and Senay, 2015).

To answer the research questions, hierarchical multiple regression models were performed to make predictions about student course GPAs of the lower-division chemistry courses using demographics (gender, URM status), prior knowledge (high school GPA, SAT math), course level, and chemistry self-efficacy. The SAT is a standardized test measuring a high school student's readiness for college, it is administered by the College Board and widely used for college admissions in the United States. In order to differentiate the influence of initial CSE and CSE toward the end of the semester, the variables were entered into the models in steps in predetermined orders. In the first block, we entered the demographics, prior knowledge, and course level into the analysis for the purpose of controlling those variables (Model 0). Then, the CSE pre-test was entered into the model (Model 1) to see how much variance was added to the previous model. Similar process was performed for CSE post-test to generate Model 2. The listwise deletion was used in the regression models. To address the missing data issue, students with and without SATM scores were compared and no evidence was found that the two groups of students to be substantially different (see Table 11 in the Appendix). Furthermore, to explore the changes of CSE after a semester of instruction and whether these changes were impacted by different student groups, a factorial analysis of variance (ANOVA) was performed. This statistical approach was selected because we are also interested in whether the changes in CSE across time depend on certain factors (gender, URM status, course level) and the interactions between those factors. The factorial ANOVA allows us to investigate the main effects of the time and groups, as well as the interaction effects between time and the nature of the groups. Lastly, multivariate analyses of variance (MANOVAs) were performed to investigate the group differences in individual scale items on the CSE post-test. Instead of conducting a series of paired t-tests to compare post-test items between the student groups, the advantage of using MANOVA is that it reduces the risk of type I error (Pallant, 2010). This type of error is associated with the number of analyses are run; the significant result is more likely to be found with the higher number of tests run even if there are no differences between groups. We consider each item as an essential skill (e.g., explaining chemical laws and theories, describing the structure of an atom) that is required in the college introductory and general chemistry courses in the MANOVAs. In the model, MANOVA creates a new linear combination of the dependent variables and tells whether there is a significant difference between student groups on the composite dependent variable and it also provides the univariate results for each skill separately. Even though the chemistry self-efficacy scale is a unidimensional construct representing a student's belief in his/her ability to complete chemistry tasks, just like students might perform differently on certain topics on chemistry exams, it is possible that students might be more or less confident in particular skills. IBM SPSS Statistics Version 26 were used for the above statistical analyses and constructing diagrams.

Results

Reliability and validity

Cronbach's alpha coefficient was 0.92 for CSE pre-test and 0.88 for CSE post-test, suggesting the internal consistency of the scale is very good with the sample in the study and the items correlated well to measure chemistry self-efficacy as a construct (DeVellis, 2012). In Ferrell and Barbera's article, they reported Cronbach's alpha coefficient of 0.89 for a sample of college general chemistry students using the same items, which is very similar to our study (Ferrell and Barbera, 2015).

Furthermore, confirmatory factor analysis (CFA) was conducted for CSE pre-test and post-test, respectively. Values of the CFA fit indices of the CSE pre-test and post-rest are listed in Table 2. Results from the CFA showed that all the fit indices were acceptable except for only one of the values (RMSEA for the CSE post-test). Ferrell and Barbera reported similar CFA fit indices (CFI = 0.98, RMSEA = 0.10, and SRMR = 0.06) with a sample of college introductory chemistry students (Ferrell and Barbera, 2015). It is worth noting that they also found the RMSEA value was the only index that did not meet the criteria. The index was not improved in another run of CFA using a modified scale with two items removed from the scale. In our models, standardized factor loadings for items were all considered as high, ranging from 0.68 to 0.86 for pre-test and from 0.60 to 0.81 for post-test. Given the evidence from the models and literature, we consider the proposed one-factor model had a reasonable fit for the data collected from the sample in the study. Thus, it is appropriate to interpret the scores of CSE scale as a whole for measuring student chemistry self-efficacy beliefs.

Table 2 CFA fit indices of the CSE pre-test and post-rest
Scale χ 2 values df p-Value CFI RMSEA SRMR
CSE pre-test 53.88 20 <0.001 0.96 0.08 0.03
CSE post-test 102.35 20 <0.001 0.96 0.13 0.06

Lastly, correlations between CSE (pre-test and post-test) and course GPA were examined. Positive and significant correlation was found between CSE pre-test and course GPA (r = 0.25). Stronger relationship between CSE post-test and course GPA (r = 0.33) was found with the sample. Those correlations indicated small to moderate yet significant relationship between students’ chemistry self-efficacy and course performance. Uzuntiryaki and Senay reported similar correlation (r = 0.24) between chemistry self-efficacy and chemistry achievement for a sample of high school Turkish students (Uzuntiryaki and Senay, 2015).

 

Research Question 1: How well do chemistry self-efficacy predict students’ final course GPAs after controlling for demographics, prior knowledge, and course level in lower-division chemistry courses at a Hispanic-serving institution? Which is the best predictor of students’ final course GPAs?

Students’ chemistry self-efficacy was measured at the beginning and toward the end of the semester in the study. In order to better understand whether the initial chemistry self-efficacy students have when they enter the courses or the resulting chemistry self-efficacy after a semester of instruction predicts more of student course GPA, two multiple regression models were performed. Model 1 used demographics (gender, URM status), prior knowledge (SAT math scores, high school GPA), course level, and CSE pre-test to predict student course GPA in the chemistry courses. Model 2 used CSE post-test to replace pre-test while keeping the rest of the predictors as the same.

Descriptive statistics and correlations between variables

Descriptive statistics of all the variables in the two models are listed in Table 3. In this sample, there were 56% females and 58% URM students. These percentages were similar to the relative proportions of the student groups in the university of the semester (55% females and 51% URM students). The average high school GPA was 3.59 and average SAT math score was 529 for the sample. The average CSE score for the pre-test was 2.86, which was slightly below “3: Average” in the rating scales in the CSE scale. Average CSE post-test score was increased to 3.78, which is closed to “4: Well”. The dependent variable course GPA was 2.44, which between the letter grade of C+ (2.3) and B− (2.7). Table 3 also lists the descriptive statistics divided by course level (Introductory Chemistry, IC vs. General Chemistry, GC), introductory chemistry had more female and URM students and students had lower values on the majority of other measures than general chemistry students.
Table 3 Descriptive statistics of variables in the multiple regression models
Variable All sample (N = 239) IC (N = 160) GC (N = 79)
Avg. SD Avg. SD Avg. SD
a Gender: female coded as 1, male coded as 0; URM status: URM coded as 1, non-URM coded as 0; Course level: GC coded as 1, IC coded as 0; HSGPA means High school GPA, SATM means SAT math score.
Course GPA 2.44 1.18 2.33 1.27 2.68 0.97
CSE pre-test 2.86 0.90 2.57 0.80 3.45 0.80
CSE post-test 3.78 0.68 3.74 0.70 3.86 0.64
Gendera 0.56 0.50 0.57 0.50 0.53 0.50
URM statusa 0.58 0.49 0.65 0.48 0.44 0.50
HSGPAa 3.59 0.41 3.60 0.39 3.57 0.46
SATMa 529 138 510 130 575 149
Course levela 0.33 0.47 — — — —

Pearson product-moment correlation coefficients between variables are listed in Table 4. The absolute values of the correlations ranged from 0.01 to 0.46. Among the correlations, the largest positive correlation was between CSE pre-test and course level, indicating that students in the lower-level course (introductory chemistry) tended to report lower chemistry self-efficacy, and vice versa. Additionally, correlation between CSE pre-test and URM status was also relatively large but negative, indicating that URM students rated themselves lower in CSE than non-URM students when they enter the chemistry courses.

Table 4 Correlations between variables in the multiple regression models
1 2 3 4 5 6 7 8
1. Course GPA 0.32 0.38 −0.06 −0.26 0.13 0.11 0.23
2. CSE pre-test 0.35 0.07 −0.42 0.27 0.37 0.46
3. CSE post-test 0.05 −0.21 0.28 0.23 0.14
4. Gender −0.16 0.14 −0.04 0.09
5. URM status −0.18 −0.27 −0.19
6. HSGPA 0.10 −0.01
7. SATM 0.28
8. Course level

Multiple regression models

Assumptions of multiple regression were checked before proceeding with the analysis. Tabachnick and Fidell recommend a formula for calculating sufficient sample size, N > 50 + 8 m where m = number of independent variables in the model (Tabachnick and Fidell, 2013). There were 6 independent variables in each model, so a sample size of 98 would be considered as sufficient for the model. Other assumptions include correlations between independent variables are not highly correlated (r < 0.9); outliers, and normality were also checked, and no serious violations were found (Stevens, 2009). Results of the three multiple regression models are listed in Table 5 (demographics and prior knowledge), Table 6 (adding CSE pre-test), and Table 7 (adding CSE pos-test). The unstandardized coefficient (B) and standard error (SE), standardized coefficient (β), and significance (p) of each predictor are shown in the tables. The equations generated from the multiple regression to predict students course GPA using the predictors are listed below:
Table 5 Results from the multiple regression (Model 0): predictors of students’ course GPA
Variable B SE β p
a Significant at the 0.05 level; significant predictors are bolded.
Constant 1.90 1.06 0.076
Gender −0.30 0.21 −0.13 0.160
URM status −0.53 0.23 −0.23 0.022
HSGPA 0.31 0.26 0.11 0.237
SATM −0.0003 0.001 −0.03 0.755
Course level 0.52 0.24 0.21 0.031
R 2 = 0.13 0.013

Table 6 Results from the multiple regression (Model 1): predictors of students’ course GPA
Variable B SE β p
a Significant at the 0.05 level.
Constant 1.80 1.06 0.092
Gender −0.29 0.21 −0.13 0.176
URM status −0.41 0.24 −0.18 0.085
HSGPA 0.20 0.27 0.07 0.462
SATM −0.001 0.001 −0.06 0.528
Course level 0.35 0.26 0.14 0.178
CSE pre-test 0.22 0.14 0.19 0.110
R 2 = 0.15 0.009

Table 7 Results from the multiple regression (Model 2): predictors of students’ course GPA
Variable B SE β p
a Significant at the 0.05 level; significant predictors are bolded.
Constant 0.74 1.06 0.490
Gender −0.29 0.20 −0.13 0.147
URM status −0.44 0.22 −0.19 0.045
HSGPA 0.08 0.26 0.03 0.749
SATM −0.001 0.001 −0.08 0.385
Course level 0.46 0.23 0.18 0.048
CSE post-test 0.58 0.16 0.33 0.000
R 2 = 0.22 <0.001

Model 0: demographics and prior knowledge

Course GPA = 1.90–0.30 × Gender – 0.53 × URM status + 0.31 × HSGPA – 0.0003 × SATM + 0.52 Course level

Model 1: adding CSE pre-test

Course GPA = 1.80–0.29 × Gender – 0.41 × URM status + 0.20 × HSGPA – 0.001 × SATM + 0.35 Course level + 0.22 × CSE pre-test

Model 2: adding CSE post-test

Course GPA = 0.74–0.29 × Gender – 0.44 × URM status + 0.08 × HSGPA – 0.001 × SATM + 0.46 Course level + 0.58 × CSE post-test

Model 1 had a significance of p = 0.009 and a R2 value of 0.15, which means the independent variables significantly predicted students’ course GPAs and accounted for 15% of the variances. There was no significant predictor in this model, although chemistry self-efficacy pre-test had the highest standardized beta coefficient (β = 0.19) among all the predictors. In Model 2 with CSE post-test, R2 value increased to 0.22, indicating the 22% of the total variances explained by this model. Additionally, there were three significant predictors in this model: CSE post-test, URM status, and course level. The standardized beta coefficient of CSE post-test (β = 0.33) was also the highest among all the predictors and it was about twice compared to the β of CSE pre-test in Model 1. In order to better understand how much the CSE contributed to the total variance compared to other predictors, Model 0 only contained the demographics and prior knowledge variables without CSE pre-test or post-test. R2 value in this model was found to be 13%. Comparing to the R2 value in Model 1, CSE pre-test explained an additional 2% of the variance in students’ course GPAs, after controlling for student demographics and prior knowledge measures, R2 change = 0.02. Model 2 with CSE post-test explained an additional 9% of the variance, R2 change = 0.09, which is 7% higher than Model 1, indicating CSE post-test explained more variance than the pre-test. URM status and course level were also significant predictors in Model 0. Interesting, beta coefficients for these two variables were smaller after CSE pre-test was added in Model 1 and they become insignificant predictors in the model. Both variables were significant predictors along with CSE post-test in Model 3. Potential explanations for the changes could be related to the interaction effects between the two variables (see next research question Table 9) and how different groups of students changed in their self-efficacy over time.

According to the equation in Model 1, every 1 unit change in CSE pre-test would lead to an increase of 0.22 (0.3 is half a letter grade) in the course GPA after holding all the other variables in the model constant. However, every 1 unit change in CSE post-test would lead to an increase of 0.58 (0.6 is a letter grade) in the course GPA after controlling for other variables in Model 2. For instance, when students with same demographic and academic backgrounds in the same chemistry course increase their CSE pre-test changes from “3: Average” to “4: Well”, this would increase the students’ final grades about half a letter grade. But when the same condition applies to CSE post-test, the students’ final grades could be increased to a whole letter grade. The above results suggested that students’ chemistry self-efficacy toward the end of the courses was the best predictor of students' final grades in the setting.

Additionally, as indicated in Model 2, being an URM student decreased student course GPA by 0.44 when controlling for other variables. Students in higher-level of chemistry course (general chemistry) tended to gain higher course GPA. It is worth noting that SAT math was found to be not a significant predictor for student course GPA in the regression model. This is surprising because many studies had shown that SAT math could be a significant predictor of chemistry performance in college settings (Pickering, 1975; Spencer, 1996; Lewis and Lewis, 2007). Possible explanations for this might be due to the unique context in the study setting. At the institution, there are about 13% transfer students who might not take SAT. For first-time freshman students, alternative tests like ACT can also be used for admission; a high school GPA of 3.00 or above for resident students and 3.61 or above for non-resident students are not required to submit those standardized test scores. The university uses its own math and chemistry placement tests for placing students into appropriate levels of science courses such as introductory and general chemistry. The above reasons might explain why SATM math was nonsignificant for predicting chemistry performance since students have a variety of other options to demonstrate their readiness for college and be placed into the courses.

 

Research Question 2: Is there a significant change in students’ chemistry self-efficacy after a semester of instruction? How is the change different between student groups (Males vs. Females; non-URM students vs. URM students; Introductory chemistry vs. General chemistry)?

To further explore whether the impact of instruction on students’ chemistry self-efficacy was statistically significant across time (use CSE pre-test and post-test) and whether the change in CSE was the same for different student groups, a factorial ANOVA was performed.

Descriptive statistics and factorial ANOVA

Descriptive Statistics of students’ average scores of CSE pre-test and post-test breakdown by groups are listed in Table 8. The changes in CSE across time for all students and breakdowns by different groups were visualized by line charts and box plots in Fig. 1. In the factorial ANOVA, the independent variables included three grouping variable (Gender, URM status, Course Level) and time (pre-test vs. post-test), and the dependent variable was the chemistry self-efficacy scores of students. The violation of assumptions including homogeneity of variance and equality of covariance matrices were examined and no serious violations of assumptions were found. An alpha value of 0.05 was used as for considering statistically significance for the analysis. Results of the factorial ANOVA are listed in Table 9.
Table 8 Descriptive statistics of CSE pre-test and post-test breakdown by groups
Variable IC N = 160 GC N = 79 Males N = 106 Females N = 133 Non-URMs N = 100 URMs N = 139
CSE pre-test 2.57 3.45 2.91 2.83 3.18 2.63
CSE post-test 3.74 3.86 3.80 3.76 3.93 3.67
Difference 1.17 0.41 0.89 0.93 0.75 1.04


image file: d0rp00345j-f1.tif
Fig. 1 Profile plots of CSE pre-test and post-test breakdowns by groups (A1–A3: averages, B1–B3: boxplots).
Table 9 Results of the factorial ANOVA
Independent variable/interaction F p-Value η 2
a Significant at the 0.05 level; significant variables or interactions are bolded. Guidelines used for effect size of η2 (Cohen, 1988): 0.01 = small effect; 0.06 = moderate effect; 0.14 = large effect.
Model 20.49 <0.001 0.40
Time 110.30 <0.001 0.19
Gender 0.32 0.573
URM status 13.35 <0.001 0.03
Course level 31.84 <0.001 0.06
Time x Gender 0.001 0.980
Time x URM status 0.78 0.377
Time x Course level 26.21 <0.001 0.05
Gender x URM status 0.005 0.945
Gender x Course level 1.46 0.228
URM status x Course level 8.72 0.003 0.02

First, there was a statistically significant interaction in the CSE scores between course level and time, p < 0.001, effect size of partial eta squared η2 = 0.05. Guidelines used for size of η2 (Cohen, 1988): 0.01 = small effect; 0.06 = moderate effect; 0.14 = large effect. A moderate effect size was evident. This suggests that the effect of instruction on student chemistry self-efficacy change from pre-test to post-test was different for students who enrolled in introductory and general chemistry courses. As indicated in Table 8 and Fig. 1, the students in introductory chemistry course (IC) rated their initial CSE much lower than students in general chemistry (GC). However, after a semester of instruction, their CSE increased greatly and the gaps between students in different levels of course decreased from 0.88 on pre-test to 0.12 on post-test. Second, the interaction effect between time and gender was not statistically significant, p = 0.980, indicating the differences in CSE change between male and female students were unnoticeable. Both male and female students had an increased about 0.90 from pre-test to post-test. Additionally, URM students started 0.55 lower than non-URM students on CSE pre-test but the gaps narrowed to 0.26 on post-test. Although the URM-students increased more in CSE across time, but their average CSE post-test score was still lower than the non-URM students. The CSE change across time was also not statistically significant different between URM and non-URM students. It is worth noting that the gaps between the three student groups from CSE pre-test to post-test were all decreased after a semester's instruction, especially the gaps between students enrolled in different levels of chemistry course.

In additions to the interactions between grouping variables and time, there was one more significant interaction effect in the model, which was between URM status and course level, p = 0.003, η2 = 0.02, with small to moderate effect. This suggests that the influence of the course level on students’ chemistry self-efficacy beliefs were different between URM students and non-URM students. From Fig. 2, we can see URM students increased more in CSE from pre-test to post-test in introductory chemistry course, but they still lagged behind than URM in general chemistry. However, non-URM students in introductory chemistry surpassed their counterparts in general chemistry after a semester of instruction even though they rated themselves lower initially. All the rest of the interaction effects involving three or more factors that did not shown in the table were not statistically significant, so we do not discuss them herein.

 


image file: d0rp00345j-f2.tif
Fig. 2 CSE trends by URM status and course level.

Research Question 3: What gaps still remain in areas of chemistry self-efficacy between certain student groups after a semester of instruction?

To answer this research question, MANOVAs were performed to explore and understand the differences in individual items of the CSE post-test between student groups. The eight post-test items were used as dependent variables. The independent variables were course level, gender, and URM status in each MANOVA.

MANOVA analysis

Assumption tests were conducted to check, and no serious violations were found. These tests included sufficient sample size (N > 30) for each cell, univariate and multivariate normality (no extreme scores), homogeneity of variance–covariance matrices (significant value of Box's M test is larger than 0.001), multicollinearity (correlations between variables are ranging between 0.3–0.7), and equality of variances for the variables (significant value of Levene's test is larger than 0.05). Results from the MANOVAs are listed in Table 10. Fig. 3 shows the item level comparison between student groups. As shown in Table 10, the MANOVA using gender as the independent variable showed that there was no difference between males and females for the combination of scale items on CSE post-test, p = 0. 216. The differences in items of CSE post-test between students in introductory and general chemistry was significantly different, p = 0.0011, η2 = 0.08, suggesting a large difference due to course level. When the results for dependent variables (the eight CSE post-test items) were considered separated, the only difference to reach statistically significance, using a Bonferroni adjusted alpha level of 0.017 was item 6 (p = 0.016, η2 = 0.02), “How well can you interpret chemical equations?” between students who completed introductory chemistry and general chemistry. Students who completed introductory chemistry rated themselves with significantly lower self-efficacy on interpreting chemical equations as compared to those students who completed general chemistry (see Fig. 3). For non-URM and URM students, significant difference was also found based on the combinations of all eight post-test items (p < 0.001) with a large effect size of 0.12. When the results for dependent variables were considered separated, two items (item 6 as listed above, p = 0.001, η2 = 0.06 and item 2 “How well can you choose an appropriate formula to solve a chemistry problem?”, p < 0.001, η2 = 0.05) were found to be significantly different between non-URM and URM students with URM students being lower for both items (see Fig. 3).
Table 10 Results from the MANOVAs
Dependent variables: post-test CSE items
Independent variables Wilk's lambda F p η 2
a Bonferroni adjusted alpha level of 0.017 was used for considering statistically significance; significant variables are bolded. Guidelines used for size of η2 (Cohen, 1988): 0.01 = small effect; 0.06 = moderate effect; 0.14 = large effect.
Course level 0.92 2.55 0.011 0.08
Gender 0.96 1.36 0.216 —
URM status 0.89 3.72 <0.001 0.12


image file: d0rp00345j-f3.tif
Fig. 3 CSE post-test item comparison between student groups.

Conclusions and discussions

In this study, students’ chemistry self-efficacy beliefs at the beginning and toward the end in multiple lower-division chemistry courses were measured and used to predict students course GPAs at a primary undergraduate, Hispanic-serving institution. Results showed that students' initial chemistry self-efficacy predicted student course GPA (standardized beta coefficient = 0.19) positively but nonsignificant in a multiple regression model after controlling for demographics (gender, URM status), academic preparation measured by high school GPA and SAT math score, and course level. However, after a semester of instruction, student chemistry self-efficacy beliefs played a positive and significant role in predicting students’ course GPA (standardized beta coefficient = 0.33) with those variables. Second, the factorial ANOVA revealed that students’ chemistry self-efficacy beliefs improved significantly after a semester of instruction and the level of improvement was much more for introductory chemistry students than general chemistry students. This could be due to the less exposure to chemistry for introductory chemistry students. Students’ initial CSE levels might be related to individuals’ prior experiences in chemistry before they took the specific courses in this study. For example, students who enrolled in introductory chemistry might rate themselves with lower self-efficacy because they did not take chemistry or took chemistry a long time ago in high school and the experiences of understanding chemistry and completing chemistry tasks improved students’ chemistry self-efficacy greatly. Similarly, students who enrolled in general chemistry with higher self-efficacy might be due to the reason that they performed well on assessments or tasks in the introductory chemistry as a prerequisite or performed well on the chemistry placement test for being eligible to enroll in general chemistry.

URM students rated their chemistry self-efficacy much lower at the beginning of the semester as compared to non-URM students, the gap still remained after a semester's instruction even though URM students’ chemistry self-efficacy increased more than non-URM students by time. The level of chemistry self-efficacy improvement was similar for male and female students. Finally, the differences in survey items for these two student groups with gaps in chemistry students’ self-efficacy post-test were investigated. The major significant difference between introductory chemistry and general chemistry students was found to be the area related to interpretation of chemical equations. The areas that URM students still lagged behind in chemistry self-efficacy compared to non-URM students were interpreting chemical equations and choosing appropriate formulas to solve chemistry problems.

Connecting findings in this study to the existing literature about chemistry self-efficacy

A recent review article about affective chemistry education research reported fourteen existing chemistry education research studies about chemistry self-efficacy in lower-division college chemistry courses after the year of 2000 (Flaherty, 2020). In a study reported by Zusho and colleagues, they found students’ chemistry self-efficacy decreased over time and chemistry self-efficacy toward the end of the semester was the best predictor (standardized beta coefficient = 0.40) for students’ final grades in introductory chemistry classes after controlling SAT math and other motivation and cognitive strategies (Zusho et al., 2003). It is worth noting that the sample in the aforementioned study had very few (4%) URM students and the study was conducted at a research-oriented university, which is very different from the sample and context in our study (58% URM students). We found students’ chemistry self-efficacy increased over time regardless of gender and ethnicity, this is consistent with Ferrell and Barbera's study. The study did not report the proportions of URM students in their samples, but they found that all students reported higher chemistry self-efficacy at the end of the semester than at the beginning regardless of majors in general chemistry at a four-year university (Ferrell and Barbera, 2015). Additionally, we also found that students ‘chemistry self-efficacy toward the end was the best predictor of students' performance in lower-division chemistry courses, the standardized beta coefficient in our study was slightly lower (standardized beta coefficient = 0.33). Among those studies in the review article, only one study reported by Villafane and colleagues examined the trends of students’ chemistry self-efficacy throughout a semester and how these trends were influenced by student demographics such as gender and ethnicity in a preparatory chemistry course at a large research-oriented university (Villafañe et al., 2014). They found females’ chemistry self-efficacy increased by time. Same trend was observed for White and Asian males; however, Hispanic and Black males’ chemistry self-efficacy was decreased over time in the course. To explore whether the same trends occur in our data, the authors in this study also investigated the interaction between gender and ethnicity, the interaction effect between gender and ethnicity was found to be not statistically significant (see Table 9) in our setting. In fact, we did not observe the downward trends in chemistry self-efficacy for Hispanic and Black males in our data. Chemistry self-efficacy of all ethnic groups increased over time to some extent with variations. Black females tend to have the smallest growth over the semester among all gender/ethnic groups (see Fig. 4). At a Hispanic-serving institution, the interactions between gender and ethnicity might be different because the majority of the population in the chemistry courses are actually URM students. In both Villafane and colleagues’ study and our study, the relatively small sample sizes for certain ethnic groups like Black male and Black female students in the study might limit the generalizability of the findings. This interaction trends between gender and ethnicity in chemistry self-efficacy are worth further investigation.
image file: d0rp00345j-f4.tif
Fig. 4 Trends for CSE scores by gender and ethnicity. WF: White Females, WM: White Males, AM: Asian Males, AF: Asian Females, BF: Black Females, HM: Hispanic Males, HF: Hispanic Females and BM: Black Males.

Limitations

The authors in this study are aware of the limitations of this study. First, we only study a sample of participants in one Hispanic-serving university, which might not be representative to the whole population of such institutions. Future studies replicating the research study with more samples in lower-division chemistry courses from multiple Hispanic-serving institutions would help validate the interactions between gender and ethnicity for chemistry self-efficacy and increase the generalizability of the findings in similar institutions. Second, this study did explore the interplays between student performance in chemistry assessments and chemistry self-efficacy beliefs. Implementing multiple measures before and after important assessments in chemistry courses could help researchers understand the direction of causality between chemistry self-efficacy and performance. Another limitation of the study is that the authors did not investigate how different student groups function with the chemistry self-efficacy scale used in the study due to the relatively small sample size of the study, future researchers could consider statistical techniques such as measurement invariance or differential item functioning to determine whether different subgroups respond differently to the scale items.

Implication for teaching in lower-division chemistry

Where are we going with the findings in this study?

In addition to studying the chemistry self-efficacy trends in lower-division courses between student groups across time, we also focus on investigating the specific areas of chemistry self-efficacy that gaps still remain between student groups after a semester of instruction. Our study uncovers that students who completed introductory chemistry course still need to improve their chemistry self-efficacy in interpreting chemical equations as compared to those who completed general chemistry courses. In particular, for URM students in lower-division chemistry courses, improving areas of chemistry self-efficacy in how to interpret chemical equations and choose an appropriate formula to solve a chemistry problem are still needed. We review literature in these areas that need to be addressed and leverage different theoretical perspectives to discuss potential instructional strategies for closing these gaps between these student groups in chemistry courses.

Interpreting chemical equations via the lens of Johnstone's triangles of representations

Why is learning chemical equations so hard? Interpreting chemical equations appropriately requires many aspects from learners, which could be a daunting task for new learners. Those aspects might involve the structures and states of reactants and products, the rearrangements and dynamic interactions between particles, the differences between subscripts and coefficients, the large numbers of particles, and the quantitative relationships between particles (Nakhleh, 1992). In 1993, Johnstone proposed the triangle of three representations (macroscopic, submicro/particulate, and symbolic) to understand chemistry knowledge (Johnstone, 1993). Since then, these three types of representations are used by chemistry educators to help students visualize chemistry molecules and chemical equations in textbooks and instruction. Unlike experts in chemistry, researchers have found novice students struggle in comprehending submicro representations and linking the submicro and symbolic levels of representation of molecules in chemical equations (Chittleborough and Treagust, 2008). To help learners overcome these challenges, research studies have reported instructional strategies to improve novice students’ understanding and interpretation of chemical equations. For instance, Davidowitz and colleagues found that the increased exposure to student-generated submicroscopic diagrams and extensive feedback could improve students’ ability to correctly draw and complete conceptual questions on chemical equations and stoichiometry (Davidowitz et al., 2010). A recent study incorporated three levels of Johnstone's representations into flipped-classroom instructional videos with chemical equations (Petillion and McNeil, 2020). The study showed significant improvement on general chemistry students’ understanding of bonding and resonance measured by pre-post quizzes, as well as student beliefs on their understanding on those topics. Additionally, supplemental molecular dynamics simulation activities that allow students to assess their mental models and connect the submicroscopic level of chemical equations to the symbolic level diagrams have also been reported to be useful for first-year chemistry students to learn chemical equations (Schwedler and Kaldewey, 2020). The researchers in this study are also currently investigating the effects of using formative assessment and targeted feedback designed along with simulation activities on improving students understanding and connections-making between different types of chemical representations.

Another effective strategy to reduce the gaps between student groups could be incorporating multiple representations into chemistry assessments. Most recently, Ralph and Lewis studied the impact of representations in assessments on general chemistry students’ performance (Ralph and Lewis, 2020). The study found that when the assessment items were supplemented with symbolic and mathematical representations (tables showing the ratio of moles of molecules in the chemical equations), overall performance of students improved significantly. More importantly, the improvement was more pronounced in students with standardized math test scores at the bottom quartile. The same effects were not observed when substituting symbolic representation or supplementing symbolic representation with particulate representation, which indicated mathematical representations might play a very unique role for certain disadvantaged student groups and should also be considered along with the Johnstone's triangles of representations.

Choosing an appropriate formula to solve a chemistry problem via the lens of scaffolding and metacognition

A review of literature indicated students have difficulties with formulas in chemistry might be due to a mixture of chemical formulas and mathematical formulas that are required in chemistry courses (Gulacar et al., 2013). For example, when asking to solve a percent yield problem, students might not be able to differentiate molecular and empirical formulas of chemical substances, or they might have difficulty in remembering or applying the mathematical formula of percent yield. Not knowing the names of chemical formulas or being able to identify the implicit information from the chemical formulas such as mole ratios could also lead to unsuccessful problem solving for chemistry problems. These students would benefit from instructional strategies that are designed to scaffold the complex problem-solving process.

Scaffolding refers to the type of pedagogical assistance provided when a novice is working to complete a learning task that could not be accomplished unassisted. Those assistance should be lessened or removed when the learner is on the right track for task completion. Common guidance includes metacognitive and procedural prompting that direct students' attention to important phases they may have overlooked, make their thinking “visible”, organize their thoughts, and engage them in evaluation and reflection.

Several innovative instructional methods such as using flow charts for a specific chemistry topic like the mole ratio flow chart (Wagner, 2001), a general problem-solving workflow chart (Yuriev et al., 2017), and using ill-structured tasks (Ge and Land, 2003) have shown improved problem-solving abilities and performance in chemistry courses. In a study by Loo and Choy, mastery experience was found to be the main source of self-efficacy influencing academic performance in college STEM courses (Loo and Choy, 2013). Providing extensive opportunities for students in class and outside of class to interact with the formulas learned in the chemistry courses are essential to build problem solving skills. For example, implementing activities like giving students a mixture of cards of different kinds of formulas and problems and asking them to match the appropriate formulas for chemical problems would be helpful for practicing the use of proper formulas. Grouping students with diverse problem-solving abilities to complete the activities and providing prompting questions such as “why do you choose the formula to this chemical problem?” or ill-structure tasks with common misuses and ask students to identify and discuss the errors might promote deeper discussions among students and improve the area of chemistry self-efficacy of choosing formulas and applying to chemical problems.

Implications for future research in chemistry self-efficacy

Innovative instructional strategies or interventions that design specifically to improve chemistry self-efficacy in lower-division chemistry courses should be considered. The evaluation of such studies should not only rely on the metrics of academic performance and retention but also include the scale of the chemistry self-efficacy as an assessment tool. More importantly, as revealed by our study, strategies that are specifically designed for improving chemical equation interpretation and problem-solving via appropriate formulas would be more likely to bring equitable outcomes in chemistry self-efficacy between student groups in lower-division chemistry courses. It is worthwhile to design research studies on those particular areas and measure to what extent the strategies impact students’ chemistry self-efficacy and whether those strategies help close the equity gaps between student groups. As indicated by this study, the trends in chemistry self-efficacy might be influenced by the institution type and the student population. Qualitative research studying the reasons why underrepresented minorities rating low in certain areas of chemistry self-efficacy, how they change throughout the semester, and the factors related to those changes would be informative and help the chemistry education community understand the gaps between student groups more thoroughly. Mixed-method research designs to collect quantitative data on the effectiveness of novel instructional or assessment strategies for improving specific areas of chemistry self-efficacy to a larger sample, supplementing with interviews with a focus on underrepresented minorities would help the chemistry education community understand why or why not certain strategies work for improving chemistry self-efficacy and closing equity gaps between student groups.

Conflicts of interest

The authors claim no conflicts of interest.

Appendix

The mean scores of the variables included in the regression models for the students with SATM and without SATM scores were listed in Table 11. Independent t-tests were run to compare the means and effect sizes (Cohen's d) were calculated. No statistically significant difference was found between the two groups of students for those variables and the effect sizes were either negligible or small (d < 0.2), indicating the sample used for analysis in the regression analysis was not much different than the overall population.
Table 11 Comparison between students with and without SATM scores
Variable Students with SATM mean (SD) Students without SATM mean (SD) Cohen's d
Course GPA 2.47 (1.17) 2.40 (1.21) 0.06
CSE pre-test 2.92 (0.91) 2.77 (0.88) 0.17
CSE post-test 3.82 (0.68) 3.71 (0.69) 0.16
Gender 0.53 (0.50) 0.59 (0.49) 0.12
URM status 0.58 (0.50) 0.59 (0.49) 0.02
HSGPA 3.60 (0.40) 3.57 (0.44) 0.07
Course level 0.32 (0.45) 0.40 (0.49) 0.17

Acknowledgements

We would like to thank all the students who participated in this study and all the instructors who helped with the data collection in this study. Additionally, we appreciate the valuable feedback provided by the reviewers for this article.

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