Adding Self-Efficacy Features to an Online Statistics Lesson

Abstract

This study investigated the effectiveness of adding four self-efficacy features to an online statistics lesson, based on Bandura’s four sources of self-efficacy information. In a randomized between-subjects experiment, participants learned statistical rules in an example-based online environment with four self-efficacy features added (treatment group) or not (control group). Results of analyses of variance showed that the treatment group performed better on practice (d = 0.36), retention (d = 0.39), and transfer (d = 0.42) tests as well as reporting higher self-efficacy (d = 0.44) and lower task anxiety (d = −0.45). Further, mediation analyses revealed that the effect of treatment group on performance was fully mediated by task anxiety and self-efficacy. The results support the inclusion of self-efficacy features in online mathematics lessons, when the goal is to improve learning outcomes by reducing anxiety and increasing self-efficacy. The results show the utility of applying Bandura’s model of self-efficacy to technology-based learning environments.

Keywords

self-efficacy task anxiety statistics learning multimedia learning blended learning online intervention worked example

Introduction

Objective

Consider an online learning scenario in which a student is confronted with a multimedia lesson on statistics that is likely to prime increased task anxiety and reduced self-efficacy. Statistics courses are often required for college students to complete their degree programs but tend to prime high levels of anxiety and low levels of self-efficacy for many students (Bartsch, Case, & Meerman, 2012). With the increasing popularity of distance education and blended courses, statistics instruction is increasingly being offered in online environments. Online learning of mathematical content is particularly prone to elicit learner anxiety that tend to consume limited cognitive resources and interfere with learning (Maloney & Beilock, 2012), which may account for high drop-out rates in online courses (Bonk, Lee, Reeves, & Reynolds, 2015). Instructional manipulations intended to increase self-efficacy and reduce anxiety during online statistics instruction can free up cognitive capacity in learning and foster more task-appropriate cognitive processing, allowing students to use their effort for learning the instructional material (Bandura, 1977). Although research on instructional design of computer-based multimedia lessons generally focuses on cognitive factors such as techniques for reducing extraneous cognitive processing or fostering generative cognitive processing (Mayer, 2009, 2014; Sweller, Ayres, & Kalyuga, 2011), the present study focuses on motivational factors such as techniques for enhancing self-efficacy and reducing task anxiety, which in turn, can improve learning outcomes.

The central goal of the study is to investigate the effectiveness of supplementing an online statistics lesson with four features that are all intended as a package for improving self-efficacy and reducing task anxiety inspired by Bandura’s model of the four sources of self-efficacy (Bandura, 1997; Schunk & DiBenedetto, 2016). It is not the intent of this study to dissect the set of four features and investigate the effect of individual features. In short, the focus of the present study is to examine the impact of an intervention on self-efficacy and task anxiety, and subsequently and more importantly, learning outcomes, in which motivational features are maximized along multiple dimensions in an online statistics lesson. Specifically, the intervention consists of an integrated set of four research-based strategies related to Bandura’s four sources of self-efficacy in an online, example-based statistical learning environment. We are interested in investigating if the set of strategies will have an impact on learner self-efficacy, task anxiety, and learning performance. A secondary goal of the study is to better understand the role that self-efficacy and task anxiety play in the learning process by testing their mediating effects in predicting performance.

Rationale

Self-efficacy is a crucial motivational variable that has been shown to exert considerable influence on a number of academic outcomes, such as individuals’ interest, their task performance, and the amount of effort and persistence that they are willing to devote when dealing with difficulties (Bandura, 1997). Abundant research has shown that a low level of self-efficacy tends to result in various undesirable consequences, such as poor performance and avoidance of more advanced courses or career choices requiring skills in the specific academic area (Bandura, 1997; Chemers, Hu, & Garcia, 2001; Pajares, 1996; Schunk & DiBendetto, 2016). Self-efficacy involving mathematical tasks is of special concern as low self-efficacy in mathematics contributes to the problem of insufficient participation in science, technology, engineering, and mathematics fields in the United States (Betz & Hackett, 1983; Lent, Brown, & Larkin, 1986; Zeldin, Britner, & Pajares, 2008).

A number of studies have tested interventions or strategies to increase learner self-efficacy in learning mathematical content. Nevertheless, little research has taken an integrated approach by systematically addressing the four sources of self-efficacy information described in Bandura’s (1997) theory, that is, vicarious experience, mastery experience, social persuasion, and affective and physiological states. Most previous interventions in mathematics targeted only one source of self-efficacy information, such as mastery experience (Cordero, Porter, Israel, & Brown, 2010), vicarious experience (Bartsch et al., 2012; Huang, 2017; Schunk & Hanson, 1985, 1989), affective states (Huang & Mayer, 2016), or a combination of mastery experience and vicarious experience (Luzzo, Hasper, Albert, Bibby, & Martinelli, 1999). In addition, few of these interventions succeeded in increasing not only self-efficacy but also performance in mathematical learning. For example, some of these studies did not examine the impact of the interventions on student performance despite the evidence of their success in developing self-efficacy in mathematical learning (Bartsch et al., 2012; Cordero et al., 2010; Luzzo et al., 1999). In studies where both self-efficacy and learning performance were measured, the interventions might have resulted in improved performance (Huang & Mayer, 2016; Im, 2012; Ramdass & Zimmerman, 2008) or enhanced self-efficacy (Im, 2012) but rarely both, except in the early work in 1980s by Schunk and his coworkers targeting the social persuasion source in the form of ability feedback versus effort feedback (e.g., Schunk, 1983). However, their results are considered inconclusive, and today’s online education does not tend to highlight self-efficacy features.

Accordingly, developing an intervention targeting all four of these primary sources of self-efficacy with an aim to enhance self-efficacy and reduce anxiety, and subsequently, improve learning performance is an understudied aspect of designing online science, technology, engineering, and mathematics instruction. In addition, technology-based interventions focusing specifically on self-efficacy development and anxiety reduction are scarce, despite the advantages that technology can provide in terms of availability, customizability, and scalability. Thus, the unique contribution of the present study is (a) to examine an integrated set of four motivational strategies, (b) using computer-based technology, and (c) within the context of an online statistics lesson, and more specifically, in an example-based learning environment.

Example-Based Learning Environment

Studying examples plays an essential role in learning. Unlike conventional instruction that emphasizes problem solving after initial presentation of a few examples in instruction, example-based learning underscores the importance of having learners study a much heavier number of examples to facilitate learning by reducing unnecessary cognitive load induced by problem solving. Abundant empirical research has documented the benefits of having novice learners study examples in initial skill acquisition (Renkl, 2011), including learning effectiveness (Sweller, 1988, 1994), learning efficiency (Salden, Koedinger, Renkl, Aleven, & McLaren, 2010; Zhu & Simon, 1987), and confidence building or positive attitudes development in learning (Carroll, 1995; Hoogerheide, Loyens, & van Gog, 2014; Miller, 2010, 2014).

Within example-based learning research, the strategy of pairing an example with a similar practice problem for students to solve has been proposed based on the argument that it is more effective for learning than having students study examples only. For example, Trafton and Reiser (1993) claimed that “the most efficient way to present material to acquire a skill is to present an example, then a similar problem to solve immediately following” (p. 1022). This claim has been supported by empirical research (Leppink, Paas, Van Gog, Van der Vleuten, & Van Merriënboer, 2014; Renkl, 2011, 2014; Van Gog, 2011; Van Gog, Kester, & Paas, 2011).

Technology-based learning environments have great potential to further enhance the impact of example-based learning (Renkl, 2014), yet few studies have taken the affordance of technology to design a scalable intervention focusing on developing self-efficacy beliefs in learning mathematical content. In this study, within a multimedia learning environment incorporated with example-problem pairs, a set of strategies related to the four sources of self-efficacy has been tested on the intended learning and motivational outcomes.

Four Sources of Self-Efficacy and Relevant Strategies

The overall theoretical framework of the study involves adding features inspired by Bandura’s (1997) four sources of self-efficacy to an online, example-based statistics lesson. Building on both cognitive and social cognitive perspectives, we examine the impact of a collection of intervention strategies related to the four sources of self-efficacy. Specifically, the present study seeks to develop instructional strategies to be inserted in an online statistics lesson, based on our interpretations of Bandura’s (1997) model of four primary sources of self-efficacy information, namely, vicarious experience, mastery experience or previous performance, social persuasion, and affective states (e.g., anxiety). Each of the four sources of self-efficacy and the related features implemented in the study are discussed next.

Vicarious experience: Modeling examples

The first feature to be added to our online statistics lesson is vicarious experience in the form of modeling. Vicarious experience refers to experience gained by observation of others or modeled performance, which serves as an important source of self-efficacy (Bandura, 1997). Different than the focus of worked example research on reducing unnecessary cognitive processing while facilitating essential cognitive processing, modeling example research emphasizes the role of modeling in enhancing self-efficacy (Bandura, 1986, 1994; Schunk, Hanson, & Cox, 1987). Bandura (1997) discussed how the congruence between model characteristics and observer characteristics can influence self-efficacy development, such as similarity in age or gender. In addition, self-efficacy development can be influenced by the perceived competence of a model, for example, a mastery model who demonstrates an expert-like problem-solving process or a coping model who shows the process of gradually reaching the mastery level by overcoming initial mistakes and difficulties. Model competence carries a heavier weight than attribute similarity and can override dissimilarity in model attributes in promoting self-efficacy, and it is especially influential for novice learners (Bandura, 1997).

Furthermore, with regard to model competence, it has been argued, on one hand, that coping models should be more effective in promoting self-efficacy and consequently learning and performance due to the perceived learner-model similarity in competence level. On the other hand, highly competent models, despite coming from a dissimilar source for novice learners as compared with coping models, possess competencies that novice learners seek as well as high instructive value, and thus could be equally effective in self-efficacy development (Bandura, 1997). Empirical studies have produced mixed results comparing the two types of modeling (Braaksma, Rijlaarsdam, & Van den Bergh, 2002; Cumming & Ramsey, 2011; Hoogerheide, van Wermeskerken, Loyens, & van Gog, 2016; Schunk & Hanson, 1985, 1989), and the inconsistent findings may be attributed to the number of strategies demonstrated by these models along the dimension of coping-mastery competence (Bandura, 1997).

In a technology-based learning environment, modeling is sometimes done by a pedagogical agent, that is, virtual models designed for teaching and learning purposes (Veletsianos, 2010). For example, a recent study in college statistics (Huang, 2017) showed that both peer modeling and expert modeling implemented through pedagogical agents are beneficial as compared with typical worked out examples. The present study intended to incorporate expert modeling in the form of a pedagogical agent demonstrating and verbalizing the problem-solving process as an expert.

Mastery experience: Imagination or mental practice

The second feature to be added to our online statistics lesson is mastery experience in the form of mental practice. Mastery experience or successful previous performance serves as another important source of self-efficacy and has been identified as key to self-efficacy development (Bandura, 1997; Usher, 2009; Usher & Pajares, 2009). Strategies focusing on increasing students’ performance should effectively increase self-efficacy as successful performance provides “the most authentic evidence” that students have what it takes to achieve mastery (Bandura, 1997, p. 80). One promising strategy related to mastery experience is mentally rehearsing the process of executing activities successfully (Bandura, 1997), which has been termed mental practice (Feltz & Landers, 1983), imagination (Leahy & Sweller, 2004, 2008; Leopold & Mayer, 2015), and visualization (Bandura, 1997). Regardless of how it is named, mentally rehearsing problem-solving procedure can serve as a form of mastery experience.

It might be argued that mental practice is different than actual mastery experiences. However, this strategy can be used effectively as an adjunct to (although not a substitute for) actual performance and thus considered a mastery-oriented strategy, similar to the case of facilitating mastery experiences through simulated virtual reality environments instead of actual performance as discussed in Bandura (1997). In addition, according to Bandura (1997), it is not the performance per se, but how the learners interpret the performance in relation to their capability, that influences self-efficacy beliefs: “[t]he same level of performance success may raise, leave unaffected, or lower perceived self-efficacy depending on how various personal and situational contributors are interpreted and weighted” (p. 81). Therefore, students’ sense of their success in performance, whether in the form of actual, virtual, or mental performance, seems more important than the performance per se. This requires creating enabling conditions with performance mastery aids to provide appropriate scaffolds that are important for performance-based or performance-oriented treatments (Bandura, 1997). In an example-based learning environment, asking learners to mentally practice the procedures in an example can be considered a performance-oriented strategy because the examples serve as a mastery aid that scaffolds student learning and helps create a sense of success.

To date, research on the effect of mental practice has focused mostly on physical tasks or motor skills, with only limited studies on cognitive activities (Feltz & Landers, 1983; Leahy & Sweller, 2004; Leopold & Mayer, 2015). However, meta-analysis research indicated that the strategy has potential for use with cognitive tasks (Driskell, Copper, & Moran, 1994; Van Meer & Theunissen, 2009), especially for learning complex information (Leahy & Sweller, 2008).

Mental practice has also been studied in example-based learning environments. In a theoretical paper based on prior research, Renkl (2014) has pointed out that cognitively practicing the procedure in examples after studying an example is more effective on learning as compared with studying examples only. For example, in a series of experiments in a computer-based learning environment including example-problem pairs in coordinate geometry or spreadsheet application, Cooper, Tindall-Ford, Chandler, and Sweller (2001) showed that mental practice after studying the examples promoted learning for middle schoolers who had the prerequisite schemas for the tasks. In their mental practice instruction, students were given clear instruction and asked to go back to review the examples when they encountered difficulty. Bandura (1997) noted that mental practice was often used with little or no guidance, which could undermine the potential of this strategy. Having students mentally practice following an example with clear guidance as in Cooper et al. (2001) can help create enabling conditions for successful performance and should be effective in developing self-efficacy beliefs. Cooper and coworkers did not integrate self-efficacy in their theoretical model though, which was the focus of the present study.

Social persuasion: Attributional feedback

The third feature that we add to our online statistics lesson is social persuasion in the form of attributional feedback. Social persuasion received from others is another source of self-efficacy information. When significant others such as parents, teachers, and peers express belief in one’s capabilities, it strengthens one’s self-efficacy perceptions (Bandura, 1997). Attributional feedback given to students is a common form of social persuasion (Bandura, 1997), which includes effort feedback and ability feedback. Effort-based feedback associates achievement outcomes with effort (e.g, “You have been working hard.”), whereas the ability-based feedback ties achievement outcomes to ability (e.g., “You’re good at this.”; Schunk, 1983). Schunk and his coworkers have extensively examined the effects of attributional feedback on task-specific self-efficacy through a series of experiments involving mathematical tasks, comparing ability feedback, effort feedback, or a combination of the two (Schunk, 1981, 1982, 1983, 1984; Schunk & Cox, 1986). Ability feedback has been found more effective than effort feedback in the early stages of skill development (Bandura, 1997; Schunk, 1984), but it also has been argued that effort feedback has to be credible in order for it to be effective, and it is in the early stages of learning that effort feedback is credible when a student truly has to work hard to succeed (Schunk, 1983).

Despite inconclusive findings regarding which type of feedback is more effective for increasing self-efficacy, more recent literature on the implicit theories of intelligence (Dweck, 2007; Kamins & Dweck, 1999; Mueller & Dweck, 1998; Romero, Master, Paunesku, Dweck, & Gross, 2014) tends to favor effort feedback for increasing students’ confidence (i.e., self-efficacy) and persistence. According to Dweck (2008), ability (i.e., intelligence) feedback tends to promote a fixed mindset that views intelligence as an unchangeable trait, which could subsequently result in decreased confidence while increased likelihood of giving up in face of challenges; on the contrary, effort feedback tends to promote a growth mindset that views intelligence as malleable or improvable with effort, which can increase student confidence when facing challenges. Empirical research in K-12 settings has supported the benefits of effort feedback in increasing self-efficacy and performance (Herrington & Kervin, 2007; Mueller & Dweck, 1998; Schweinle, Meyer, & Turner, 2006).

Integrating effort feedback in a multimedia lesson has the potential to enhance self-efficacy beliefs through social persuation, that is, emphasizing that learners’ performance on learing tasks can be enhanced through effort, which is also consistent with research supporting Dweck’s (2008) theory. Considering that empirical research on attribution feedback mostly focused on face-to-face settings (Dresel & Haugwitz, 2008) and that teacher feedback in the classroom is sparse (Hattie & Timperley, 2007), feedback provided in an online environment is promising as it can be customized in terms of frequency and type to achieve the desired effect on self-efficacy development. In addition, although example-based research evidence recommends the pairing of an example with a similar problem to faciliate learning (Van Gog et al., 2011), the design of the feedback to the paired practice problems has not been emphasized in this line of research.

Affective states: Math anxiety coping strategy

The final feature added to our online statistics lesson is affective state in the form of math anxiety copying messages. Physiological and affective states are another source of information affecting self-efficacy. Anxiety toward a particular academic subject has often been used as an indicator of physiological and affective states (Bandura, 1997; Usher & Pajares, 2009), and anxiety in academic settings has been identified as a source of poor self-efficacy (Bandura, 1997; Usher & Pajares, 2008).

Anxiety consists of two dimensions, that is, the affective dimension (unpleasant feelings such as fear and apprehension) and the cognitive dimension (worry concerning performance; Ho, Senturk, Lam, & Zimmer, 2000; Wigfield & Meece, 1988). Anxiety coping toward learning mathematical content could be achieved through exposure to affective or cognitive coping messages (Shen, 2009). With regard to affective coping messages, recent empirical research in computer-based learning environments has shown emerging evidence of the promising effect of such messages in reducing anxiety or improving performance in the context of college students learning mathematical tasks (Huang & Mayer, 2016; Im, 2012; Shen, 2009). The effect of cognitive anxiety coping messages in mathematics has also been documented (Im, 2012). Specifically, it has been found that coping messages based on Dweck’s (2008) implicit theories of intelligence in an attempt to develop students’ growth mindset effectively enhanced college students’ self-efficacy in mathematics. This seems a viable approach that calls for additional empirical investigation, especially in online mathematical learning environments. Previous research has established the link between math anxiety and perceptions of math ability: People with high math anxiety perceive their math ability negatively (Ashcraft, 2002; Maloney & Beilock, 2012). Imagine high anxious math learners with negative self-perceptions in their ability. If math learners—especially those with high anxiety and low self-efficacy—were supported with an explicit coping message that math ability is not unchangeable, but instead, will improve with continuous effort and repeated practice, it is likely that they may become more focused on the learning tasks at hand rather than their anxious thoughts on not performing well. This idea is the fourth element investigated in the present study.

Integrating Self-Efficacy Strategies in an Online Example-Based Environment: Predictions for the Present Study

Despite the importance of the four sources of self-efficacy, little research has systematically applied and tested a combination of instructional strategies targeting all four sources of self-efficacy. A technology-based learning environment lends itself well to the exploration of an integrated model of self-efficacy interventions. In this study, strategies related to the four sources are implemented in an online example-based learning environment, including (a) a strategy on vicarious experience through expert modeling examples, (b) a strategy on mastery experience through mental practice where students mentally rehearse the example procedures before moving to the paired practice problems, (c) a strategy on social persuasion through the provision of effort feedback to student practice problems, and (d) a strategy on physiological or affective states through math anxiety coping messages before having students study the modeling examples and solve the paired practice problems. It has been pointed out that gender, ethnicity, and learning domain influence how students rely on the sources of self-efficacy (Usher & Pajares, 2008). Nevertheless, employing all four sources of self-efficacy information in an educational intervention has the most potential to address the needs of diverse learners (Zeldin et al., 2008).

The overall research question of the study is as follows: In an online example-based statistical learning environment, what is the effect of adding a package of self-efficacy features related to the four sources of self-efficacy on learning outcome performance, self-efficacy, and task anxiety? According to Bandura’s model of the four sources of self-efficacy, we predict that adding the self-efficacy features to the example-based statistical lesson will result in improved learning performance, including performance on a practice activity, a retention test, and a transfer test (Prediction 1), reduced task anxiety (Prediction 2), and increased self-efficacy on the statistical learning tasks (Prediction 3). We are also interested in exploring whether the same pattern of results holds for men and women as gender could influence how students rely on the sources of self-efficacy (Usher, 2009; Usher & Pajares, 2008). For example, a qualitative review of the literature on sources of self-efficacy reported studies that found gender differences in the strength of the sources in mathematics and science domains (Usher & Pajares, 2008).

In addition, a secondary question of the study is as follows: What are the relations among the outcome variables of performance, task anxiety, and self-efficacy? We predict that there would be intertwined relations among the aforementioned variables, with self-efficacy serving a mediating role between performance and the other variables (Prediction 4). In addition to the primary goal of this study, that is, incorporating a suite of self-efficacy features that lead to enhanced test performance, we expect that the self-efficacy intervention will reduce task anxiety and increase self-efficacy, which in turn will improve learning performance. The proposed mediating role of self-efficacy and anxiety is also consistent with Bandura’s position on the role of self-efficacy as “mediating between the sources of its creation and subsequent outcomes” (Pajares & Kranzler, 1995, p. 427).

Method

Participants and Design

The participants were 147 students recruited from two sources: 77 were lab participants from a mid-western university in the United States who completed the study in a lab setting facilitated by an experimenter, and 70 were online participants recruited from Prolific, an online crowdsourcing platform for research, who completed the study in an online environment at a place of their choice. The inclusion of online participants was to increase the sample size, broaden the representativeness of the sample, and maximize the statistical power. Four lab participants and one online participant were excluded for failing two out of the three attention check criteria (as described in the Method section), leaving 142 participants in our final data set. Of the 73 remaining lab participants, 35 served in the treatment group and 38 served in the control group; and of the 69 remaining online participants, 36 served in the treatment group and 33 served in the control group. The experiment used a 2 × 2 × 2 between-subjects design with the first factor being whether or not the online instruction included features intended to enhance the learner’s self-efficacy (treatment vs. control), the second factor being participant gender (male vs. female), and the third factor being the source of the participants (lab vs. online).

All participants were prescreened to meet the requirements of being at least 18 years old or older and having no prior knowledge of either of the statistical rules covered in the experimental materials. In addition, lab participants at the university were restricted to undergraduate students. Since the demographic information of the participant pool from the online crowdsourcing platform was much more diverse, the following prescreening criteria were added for this group of participants: (a) their first or primary language was English and (b) their current education level was between secondary school and undergraduate degrees. Furthermore, to better ensure the quality of the online participant recruitment, only the participants who had a 90% approval rate or higher for their previous research participation via the platform were qualified to participate in the present study. The online participants came mainly from the United States (66%) and Europe (25%). The mean age of the participants was 21.47 years (SD = 4.21), and there were 72 women and 70 men. The majority of the participants were Caucasian (71.1%), followed by African Americans (12.7%), Asian (6.3%), Latino or Hispanic (4.2%), mixed (3.5%), and other (2.1%).

Instructional Materials

The instructional materials consisted of a control version and a treatment version of a self-paced online lesson on two statistical rules, Chebyshev’s rule and the Empirical rule. As shown in Figure 1(a), for both versions, the learning content contained the following sections in sequence: (a) demographic survey and self-efficacy premeasure, (b) introduction and review of prerequisite knowledge, (c) introduction to the Empirical rule and Chebyshev’s rule, (d) condition-dependent practice in the form of a set of five example-problem pairs, (e) self-report materials (e.g., task anxiety and self-efficacy), and (f) posttest consisting of a retention test and a transfer test. Both versions were designed and delivered via a specially designed web site on Qualtrics that also recorded learner responses and time on task. The control version and the treatment version were identical except for the practice activity. As shown in Figure 1(b), in the control version, the practice consisted of five written worked examples paired with the corresponding problems for the participants to solve; the treatment version differed in that the practice activity was enhanced with four strategies corresponding to the four sources of self-efficacy to boost participants’ confidence in performing the statistical tasks, that is, modeling examples aligned with the vicarious experience source, anxiety coping aligned with the physiological state source, mental practice aligned with the mastery learning source, and effort feedback aligned with the social persuasion source.

Figure 1.

An overview of the structure of the instructional materials (a), including the differences between the treatment version versus the control version of the instructional materials (b).

Figure 2 illustrates the four strategies integrated into the example-problem practice activity for the self-efficacy treatment. First, to enhance self-efficacy based on the vicarious experience source, the five examples were presented in the format of video modeling examples where an animated expert pedagogical agent demonstrated and verbalized the correct process of problem solving for each example problem. The pedagogical agent was presented as a senior male instructor who sounded confident and authoritative in his verbalization. As a comparison, the control version included the five examples in the format of written, step-by-step worked examples for participants to study. Figure 3 provides a screenshot of a modeling example (treatment version) versus a written worked example (control version) used in the study.

Figure 2.

An overview of the four strategies corresponding to the four sources of self-efficacy integrated into the practice activity in the treatment condition.

Figure 3.

An expert modeling example in the treatment condition (a) versus a written worked example in the control condition (b).

Second, to enhance self-efficacy based on the physiological state source, a math anxiety coping message was inserted at the beginning of the practice activity in the form of practice instruction. Participants were told to listen to the message to better prepare them to work on the activity. The message was delivered verbally in a video by another pedagogical agent serving a motivating role. The pedagogical agent was represented as a young female who delivered the anxiety-coping message in a calming tone. Figure 4 shows a screenshot of the video. The message was adapted from a previous study (Huang & Mayer, 2016), with a new focus on fostering a growth mindset in an attempt to reduce participants’ anxiety level in learning the statistical rules. Below is the complete transcript of the message:

For this practice, you will work on 5 example-problem pairs. For each pair, you will study the example first, and then solve the paired problem. You will get immediate feedback for your problem solving. Do not give up if you encounter any difficulty. As long as you work hard, your effort will pay off. As Albert Einstein once said, “It’s not that I’m so smart, it’s just that I stay with problems longer”. Your ability in solving the problems will grow with your continuous effort. If you make a mistake, do not feel discouraged. What is important is to learn from your mistake and improve as you go through the example-problem pairs. Through repeated practice we can improve our skills and feel confident while using them. The 5 example-problem pairs to be presented next will focus on engaging you in the repeated practice. Your goal is to study an example first, and then solve the paired problem following the similar procedure. Whether studying the example or solving the paired problem, just focus on what has to be done, one step at a time, and eventually, you can reach the mastery level on these problems. Now, click the Next button to start working on the example-problem pairs.

Figure 4.

A screenshot of the motivating pedagogical agent delivering the anxiety coping message.

Third, to enhance self-efficacy based on the mastery learning source, a mental practice activity was added after each modeling example before the paired problem-solving activity. The instruction for the mental practice activity was presented on a separate page as textual information presented by the same motivational pedagogical agent. Participants were asked to mentally practice the procedure required to solve the problem presented in the previous modeling example. Figure 5 shows a screenshot containing an example of the instructions for a mental practice. To ensure that the mental practice served as a mastery learning source of self-efficacy, we emphasized the role of the modeling examples in helping learners master the material and we emphasized a sense of success by specifically instructing the participants to go back and review the video example previously presented if they had difficulty mentally performing the procedure.

Figure 5.

Example of instruction for a mental practice activity.

Fourth, to enhance self-efficacy based on the social persuasion source, a set of five pairs of customized effort feedback messages corresponding to the problem-solving items was inserted, in addition to score feedback (e.g., you received x out of y points) that the control group also received. After the participant solved each problem, depending on whether the participant in the treatment group answered it correctly or incorrectly, the participant received a feedback message either praising his or her effort (for a correct response) or encouraging him or her to spend more effort on the next example-practice pair (for an incorrect response). Each effort feedback message was customized so that no participant would receive the same feedback twice. For example, if the participant did not solve all of the questions correctly in the first practice problem, the effort feedback would be: “Your answer is not 100% correct. Don’t give up. Focus on the next example-problem pair. Study the example carefully. With hard work, your performance will improve”; while for the second practice problem, the effort feedback for incorrect answers would be, “Keep on trying, and your effort will pay off.” Each effort feedback message was presented as textual information by the motivational pedagogical agent right below the score information shown to the participants for that problem. Figure 6 shows examples of feedback to correct and incorrect responses to one of the problems, respectively.

Figure 6.

(a) Example of effort feedback for correct response. (b) Example of effort feedback for incorrect response.

Outcome Measures

The practice activity included five problems (paired with five examples, respectively) for students to solve (α = .91). Each problem (e.g., “A sample of size n = 80 has mean M = 25 and standard deviation SD = 2. Find the approximate number of observations in the data set that lie between 21 and 29.”) contained four subquestions (e.g., “How many standard deviations are 21 and 29 away from the mean?”). The total score of the practice activity was the sum of scores of correctly answered items (maximum score = 20), based on a scoring key.

The posttests included a 6-item retention test (α = .84) and an 11-item transfer test (α = .94). The retention test (maximum score = 6) required the participants to either recall or recognize statements concerning the Empirical rule or Chebyshev’s rule, such as “Which rule applies to bell-shaped data distribution?” The total score of the retention test was tabulated by adding up the scores of correctly answered items, based on a scoring key. The transfer test (maximum score = 66) consisted of both near transfer questions (n = 6) and far transfer questions (n = 5). Each near transfer question contains three subquestions, ranging from one to two points each, based on a scoring rubric. Each far transfer question contains three or four subquestions, ranging from two to three points each, based on a scoring rubric. The near transfer problems required the participants to apply one of the two rules to solve six problems that were similar to the problems presented during the practice activity, such as “A sample of size n = 150 has mean = 6 and standard deviation = 2. Please determine the following: How many standard deviations are 0 and 12 away from the mean?” Far transfer problems required the participants to apply the rules to solve five problems in a real-life scenario context that were different than those presented during the practice, such as “200 students took an IQ test. The scores showed a bell-shaped distribution with a mean of 100 and a standard deviation of 17. Please determine the following: Approximately how many people have an IQ score between 66 and 134?” The total score of the transfer test was tabulated by adding up the scores for individual items on the test.

Self-report materials consisted of a self-efficacy scale, task anxiety scale, and demographic survey.¹ Self-efficacy was measured by a 100-point rating scale (0 = no confidence at all and 100 = extremely confident; Bandura, 2006; Pajares, Hartley, & Valiante, 2001) asking the participants how confident they were on performing six tasks requiring the knowledge and application of the two statistical rules. The six tasks are aligned with the learning objectives of the online module. Self-efficacy was measured both at the beginning of the study (α = .96) and at the end of the example-practice activity (α = .96).

Task anxiety was measured by a 1-item, 9-point Likert scale (1 = very, very low anxiety and 9 = very, very high anxiety) asking the participants to report the amount of anxiety they perceived while studying the example-problem pairs.

A demographic survey was also included in the study, including questions about participant age, gender, ethnicity, self-reported skill level of basic math calculations (5-point rating scale, with 1 = extremely unskilled and 5 = extremely skilled; “Rate your skill level in basic addition, subtraction, multiplication, and division (up to 4 digits) with the aid of a calculator.”), and comfort level with computer-based instruction (5-point rating scale, with 1 = extremely uncomfortable and 5 = extremely comfortable; “Rate your comfort level with computer-based instruction.”).

For both versions of the lesson, three attention check criteria were used to better ensure the quality of the data: the total time on task, and two multiple choice questions embedded in the online module. The first attention check question was added to the first self-efficacy measure: “It is important that you pay attention to this study. Please write the number 25 in the blank next to this statement at the end of the scale.” The second attention check question was added to the questions for one of the problems in the practice: “It is important that you pay attention to this study. Please check the radio button next to ‘2’ below.” Each attention check question was designed to look similar to the other questions where it was embedded in terms of length and format (Oppenheimer, Meyvis, & Davidenko, 2009).

Procedure

Participants were randomly assigned to either the treatment group or the control group within gender through the web-based study site. The lab participants completed the study in groups of multiple participants in a 30-station computer lab at their university. The experimenter briefly introduced the study, collected student consent forms, and provided each participant a calculator, a piece of a scrap paper, and a set of earphones before the study. Participants were then instructed to access the web-based study site and follow the instruction there to complete the study. The average time for the lab participants to complete the self-paced study was about 46 min. The online participants completed the study in a setting of their choice. They accessed the study site through a link in the online crowdsourcing platform. In contrast to the lab sessions, participant consent information and instruction on getting ready for the study was embedded at the beginning of the web-based system. To better ensure the quality of the online delivery of the study, online participants were instructed to complete the study in a quiet place, asked to minimize distractions (e.g., turn off phones), and given other essential preparation information such as having a calculator and scrap paper ready before starting the study. The average time for the online participants to complete the study was about 57 min (including the time spent on reviewing the information on informed consent and getting ready for the self-paced online study, which, for the lab study, was facilitated by the experimenter face-to-face and was not recorded as part of the completion time). Once the study started, all participants in a given group (i.e., treatment or control), whether in the lab session or the online session, were presented with the identical condition-based instructional content on the two statistical rules. Each lab participant received a $15 gift card, and each online participant received £15 for completing the study. We followed guidelines for ethical treatment of human subjects and obtained institutional review board approval for the study.

Data Analysis

First, we conducted a series of tests, including a Chi-square test and independent samples t-tests, to determine if the treatment group and the control group were equivalent in terms of basic characteristics, including gender, ethnicity, age, comfort level with computer-based instruction, skill level of basic math calculations, and the initial self-efficacy level before learning the lesson. Second, we conducted three-way, 2 (Condition: treatment vs. control) × 2 (Gender: male vs. female) × 2 (Experiment setting: online vs. lab), between-subjects analyses of variance to examine the effectiveness of the intervention on practice performance, retention performance, transfer performance, task anxiety, and self-efficacy, respectively. IBM SPSS Statistics 23 was used to conduct the analyses. Third, we conducted Pearson product-moment bivariate correlations, a multiple-group path analysis, and a serial multiple mediator model to examine how task anxiety, self-efficacy, and performance relate to each other. SPSS 23, SPSS AMOS, and PROCESS macro for SPSS (Model 6; Hayes, 2013) were used to conduct the three types of analyses, respectively.

Results

Were the Groups Equivalent on Basic Characteristics?

First, participants were equally distributed within gender through the web-based system between the two groups, with 35 males and 36 females in the treatment group and control group, respectively. Second, a Chi-square test for independence indicated that there was no significant difference in the distribution of ethnicity (Caucasian vs. African American vs. Other ethnicities) between the two groups, χ² (2, N = 142) = 2.60, p = .273. Third, independent samples t tests showed that the two groups did not differ significantly on mean age (M_{control group} = 21.67, SD = 5.09; M_{treatment group} = 21.27, SD = 3.13, t(138) = −.56, p = .576), mean rating of comfort level with computer-based instruction (M_{control group} =4.26, SD = .81; M_{treatment group} = 4.37, SD = .74, t(139) = .83 p = .406), or mean rating of skill level of basic math calculations (M_{control group} = 4.56, SD = .58; M_{treatment group} =4.62, SD = .59, t(140) = .57, p = .568). However, we did find a significant difference for participants’ initial rating of self-efficacy level between the two groups (M_{control group} = 5.46, SD = 11.69; M_{treatment group} = 11.94, SD = 22.35, t(105.61) = 2.17, p = .033), thus it was included as a covariate in our comparison of posttreatment self-efficacy between the groups. Overall, we conclude that the groups were equivalent on most basic characteristics.

Did the Inclusion of the Self-Efficacy Features Enhance Learning Outcome Performance?

The major prediction of this study is that inclusion of self-efficacy features in a computer-based lesson would enhance performance. To address this prediction, 2 (Condition: treatment vs. control) × 2 (Gender: male vs. female) × 2 (Experiment setting: online vs. lab) between-subjects analyses of variance was conducted to examine the group differences on the practice, retention, and transfer performance, respectively. The first nine lines of Table 1 show the mean score and standard deviation for each group on practice, retention, and transfer performance, respectively. As shown in Line 1 of Table 1, the treatment group (M = 16.79, SD = 4.14) performed significantly better on the practice problems than the control group (M = 15.18, SD = 4.76), F(1, 134) = 4.48, p = .036, d = 0.36. Similarly, as shown in Line 4 of Table 1, the treatment group (M = 4.93, SD = 1.65) performed significantly better than the control group (M = 4.25, SD = 1.87) on the retention test, F(1, 134) = 4.32, p = .040, d = 0.39. Finally, as shown in Line 7 of Table 1, the treatment group (M = 50.27, SD = 16.29) performed significantly better than the control group (M = 42.94, SD = 18.67) on the transfer test, F(1, 134) = 5.66, p = .019, d = 0.42. No main effect for gender or experiment setting was found on the practice items, retention test, or transfer test; neither were there any significant interactions involving these factors, ps > .05. The same pattern of significant results differences was found when we included initial self-efficacy as a covariate. Overall, this pattern of significant differences in learning and learning outcome measures constitutes the major empirical contribution of this study. We conclude that inclusion of self-efficacy features in a multimedia statistics lesson caused an improvement in learning outcomes.

Table 1.

Descriptive Statistics for the Outcome Measures by Condition.

Measures	Treatment group		Control group
Measures	M	SD	M	SD	Cohen’s d
Practice^a (20)	16.79	4.14	15.18	4.76	0.36
Males	17.60	3.81	15.09	5.25
Females	16.00	4.34	15.28	4.31
Retention^a (6)	4.93	1.65	4.25	1.87	0.39
Males	5.14	1.63	4.40	1.90
Females	4.72	1.67	4.11	1.86
Transfer^a (66)	50.27	16.29	42.94	18.67	0.42
Males	52.20	15.66	45.80	18.40
Females	48.39	16.89	40.17	18.76
Anxiety^a,b (9)	3.82	1.99	4.75	2.17	-0.45
Males	3.83	2.22	4.26	1.85
Females	3.81	1.79	5.22	2.37
	Adjusted M	SE	Adjusted M	SE
Self-Efficacy^a (100)	76.93	3.40	65.14	3.39	0.44
Males	81.23	4.90	63.36	4.73
Females	72.62	4.72	66.92	4.82

Note. Values in parentheses indicate maximum scores.

^aTreatment group significantly outperformed control group at p < .05.

^bSignificant Gender × Experiment Setting difference at p < .05.

Did the Inclusion of the Self-Efficacy Features Reduce Task Anxiety?

A second major prediction is that adding self-efficacy features to a multimedia statistics lesson would reduce the learners’ level of anxiety. The tenth line of Table 1 shows the mean rating of anxiety (and SDs) for the two groups. The treatment group (M = 3.82, SD = 1.99) reported significantly lower anxiety than the control group (M = 4.75, SD = 2.17), F(1, 134) = 9.09, p = .003, d = −0.45. There were no significant interactions involving group. The same pattern of results was obtained when we included initial self-efficacy as a covariate. Overall, we conclude that the treatment was effective in reducing anxiety for students learning from a multimedia statistics lesson. This is the second major empirical contribution of this study.

In addition, a significant Gender × Experiment Setting interaction was revealed, F(1, 134) = 5.28, p = .023. Follow-up analyses indicated that for the online participants, men reported significantly lower anxiety (M = 3.75, SD = 1.91) than women (M = 5.04, SD = 2.56), d = −0.57, whereas men (M = 4.54, SD = 2.19) and women (M = 4.23, SD = 1.96) did not differ significantly on anxiety ratings for the lab participants, d = 0.15. This pattern suggests that women may find online learning environments more anxiety-evoking than men do.

Did the Inclusion of the Self-Efficacy Features Enhance Perceived Self-Efficacy?

A third major prediction is that adding self-efficacy features to a computer-based multimedia statistics lesson will increase self-reported self-efficacy after learning. As the treatment group started with higher self-efficacy (M = 11.94, SD = 22.35) than the control group (M = 5.46, SD = 11.69), p = .049, initial self-efficacy score was used as a covariate, and adjusted means and standard error were reported for post self-efficacy. The thirteenth line of Table 1 shows the adjusted mean for the self-efficacy rating (and SE) given after the lesson for the two groups. As shown in Line 13 of Table 1, the treatment group (adjusted M = 76.93, SE = 3.40) reported significantly higher post self-efficacy than the control group (adjusted M = 65.14, SE = 3.39), F(1, 133) = 5.94, p = .016, d = 0.44, partial η²= 0.04. There were no significant effects or interactions involving experiment or gender, ps > .05. We conclude that adding self-efficacy features to a computer-based multimedia statistics lesson was successful in improving self-reported self-efficacy.

How Did Task Anxiety, Self-Efficacy, and Performance Relate to Each Other?

Another goal of the study was to examine the relations among the variables included in the study. We predicted that there would be interrelations between task anxiety and self-efficacy, and that self-efficacy would play a mediating role in predicting performance. Participant self-efficacy and task anxiety reported after the practice activity and the overall posttest performance (average of the retention and transfer tests) were used in these analyses.

Pearson correlations results

Table 2 presents the Pearson correlation results among the aforementioned variables by condition. As shown in the table, for both the treatment group and the control group, (a) self-efficacy was negatively correlated with task anxiety (r_{treatment group} = −.52, p = .000; r_{control group} = −.45, p = .000) while positively correlated with the posttest performance (r_{treatment group} = .73, p = .000; r_{control group} = .66, p = .000) and (b) task anxiety was negatively correlated with the posttest performance (r_{treatment group} = −.43, p = .000; r_{control group} = − .53, p = .000).

Table 2.

Pearson Correlations Between Task Anxiety, Self-Efficacy, and Performance for the Treatment Group (Above Diagonal) and the Control Group (Below Diagonal).

Measure	1	2	3
1. Self-efficacy	–	−.52**	.73**
2. Task anxiety	−.45**	–	−.43**
3. Performance	.66**	−.53**	–

^**p < .01.

Multiple-group path analysis results

To further analyze the relations among the outcome variables, a path analysis was conducted to examine if the relation of task anxiety to performance was mediated through self-efficacy. In this hypothesized model, task anxiety would influence performance through the mediation of self-efficacy; in addition, task anxiety would have a direct influence on performance. This model was tested using a multigroup approach comparing the paths for the control group and the treatment group.

As shown in Figures 7 and 8, for both conditions, self-efficacy mediated the relation between task anxiety and performance. In other words, task anxiety significantly predicted self-efficacy (B_{treatment group} = −6.76, p < .001; B_{control group} = −5.89, p < .001), which in turn predicted performance (B_{treatment group} = .48, p < .001; B_{control group} = .38, p < .001). In addition, for the control condition, task anxiety had a direct impact on performance (B = −2.64, p = .003) that was not observed for the treatment condition (B = −.58, p = .49). Taken together, these findings indicated that self-efficacy served as a full mediator for the treatment group while a partial mediator for the control group.

Figure 7.

Testing of self-efficacy as a mediator between task anxiety and performance for the treatment group. The numbers in parentheses are unstandardized coefficients. Dashed lines indicate nonsignificant regression coefficients; solid lines indicate significant regression coefficients.

Figure 8.

Testing of self-efficacy as a mediator between task anxiety and performance for the control group. The numbers in parentheses are unstandardized coefficients. Dashed lines indicate nonsignificant regression coefficients; solid lines indicate significant regression coefficients.

Serial multiple mediator results

The multiple-group path analysis results presented earlier indicated an interesting pathway from task anxiety to self-efficacy to performance for the treatment group and for the control group. We next conducted a multiple mediator model, with condition as a predicting variable, task anxiety and self-efficacy as two mediators, and performance as an outcome variable. We hypothesized that the relationship between condition and performance would be mediated by task anxiety and self-efficacy in sequence. Specifically, we hypothesized that the intervention would predict reduced task anxiety, which, in turn, would predict increased self-efficacy, which, in turn, would predict enhanced performance. This hypothesis was tested using a serial multiple mediator model in the PROCESS macro for SPSS (Model 6; Hayes, 2013). The outputs included direct effects, indirect effects, and bootstrapped confidence intervals (CIs; 5,000 bias-corrected resamples) for each indirect effect. A CI not containing zero would indicate a significant mediation (Hayes, 2013). As condition is a dichotomous variable, unstandardized rather than standardized coefficients were reported per Hayes’ recommendation.

As predicted, there was a significant total effect (without the two mediators) from condition to performance (B = 8.00, p = .01). We then sought to determine if task anxiety and self-efficacy mediated, sequentially and uniquely, this condition → performance relationship by examining the direct effect predicting performance from condition, task anxiety, and self-efficacy simultaneously as well as all the indirect effects in the model. Figure 9(a) shows that there is a direct relation between treatment and performance, when no mediators are included in the model. However, consider what happens when self-efficacy and anxiety are added as mediators, as shown in Figure 9(b). First, when task anxiety and self-efficacy were included in the model, the direct effect from condition to performance became nonsignificant (B = 1.29, p = .58), supporting the mediating role of task anxiety and self-efficacy in the relationship between condition and performance. Second, consistent with our prediction, the sequential indirect pathway of condition → anxiety → self-efficacy → performance was significant, B = 2.43, SE = 1.09, 95% CI = [.76, 5.11]. Specifically, condition significantly predicted task anxiety (B = −.93, SE = .35, p = .009), which significantly predicted self-efficacy (B = −6.29, SE = .96, p = .000), which in turn significantly predicted performance (B = .42, SE = .05, p = .000). Third, the indirect pathway of condition → anxiety → performance was significant, B = 1.63, SE = .89, 95% CI = [.32, 4.03], indicating that task anxiety uniquely mediated between condition and performance: condition significantly predicted anxiety, which then significantly predicted performance (B = −1.75, SE = .62, p = .006). Fourth, the indirect pathway of condition → self-efficacy → performance was not significant, B = 2.65, SE = 1.70, 95% CI = [−.64, 6.05]. Although self-efficacy significantly predicted performance (B = .42, SE = .05, p = .000), condition did not significantly predict self-efficacy when task anxiety was in the model (B = 6.36, SE = 4.08, p = .12). In summary, the results demonstrated the significant sequential task anxiety → self-efficacy mediation effect between condition and performance as well as the unique mediation effect of task anxiety between this relationship. These analyses provide support for the idea that self-efficacy features cause changes in learning outcomes by reducing task anxiety and increasing self-efficacy, and point to the crucial role of interventions aimed at motivational and affective aspects of an online lesson.

Figure 9.

(a) Direct effect from condition to performance with no mediators. (b) Sequential mediation analysis (with task anxiety and self-efficacy as sequential mediators) of the links between condition and performance. Path values indicate unstandardized coefficients. *p < .05. ***p < .001.

General Discussion

Main Findings

A primary focus of the study is to test whether supplementing an online statistics lesson by adding four self-efficacy features based on Bandura’s four sources of self-efficacy would affect learning outcomes (including performance on practice, retention, and transfer tests). On all three measures of learning outcome, the treatment group (which received a lesson with added self-efficacy features) outscored the control group (which received the same lesson without added features) yielding an effect size of d = 0.36 on practice items, d = 0.39 on the retention test, and d = 0.42 on the transfer test. These findings provide evidence that incorporating self-efficacy features in an online statistics lesson caused better learning outcomes.

Another primary focus of the study is to test whether supplementing an online statistics lesson by adding four self-efficacy features based on Bandura’s four sources of self-efficacy would affect motivational outcomes (primarily based on ratings of self-efficacy) and affective outcomes (primarily based on ratings of task anxiety). The treatment group generated higher ratings of self-efficacy than the control group (with an effect size of d = 0.44) and lower ratings of task anxiety (with an effect size of d = −0.45). These findings provide evidence that incorporating self-efficacy features in an online statistics lesson caused the intended improvements in self-rated self-efficacy and anxiety.

In addition, a secondary goal of the study was to test the relation among the self-rating variables and combined learning outcome variables. For the experimental group and the control group, self-efficacy and task anxiety correlated with each other and with learning outcome performance. These patterns are consistent with the idea that self-efficacy and anxiety are related to one another and with learning outcomes. Importantly, a mediational analysis on the treatment group showed that task anxiety predicted self-efficacy which predicted learning outcome performance, with no significant direct connection between task anxiety and learning outcome performance. This analysis is consistent with a model in which the treatment helps reduce task anxiety, which increases self-efficacy, which results in improved learning performance. In contrast, a mediation analysis on the control group showed two paths—a direct path connecting task anxiety and learning performance and an indirect path connecting task anxiety to self-efficacy to learning performance. This suggests that task anxiety still is related to learning performance even when other variables such as self-efficacy are factored in for the control group but not for the treatment group.

Theoretical Implications

The findings of the study support the idea that developing intervention strategies based on the theory of sources of self-efficacy can successfully reduce anxiety, enhance learner self-efficacy, and increase performance on mathematical tasks. The research patterns suggest that reducing learners’ anxiety may play a key role in increasing their perceived self-efficacy, which subsequently has a positive impact on their performance. The agent-delivered anxiety coping message was developed with a focus on reducing the cognitive aspect of anxiety. It is reasonable to posit that the message was effective in anxiety coping in that (a) the treatment group perceived lower task anxiety than the control group and (b) task anxiety exerted a direct effect on performance in the control group, yet this direct effect was not observed in the treatment group. Taken together, the findings highlight the effectiveness of the four self-efficacy intervention strategies working together to enhance self-efficacy and performance as well as the indispensable role of reduced anxiety in promoting self-efficacious and effective learners. The fact that the four-component intervention succeeded in not only reducing task anxiety and enhancing self-efficacy but also improving test performance indicates the benefits of considering all four sources of self-efficacy information when designing self-efficacy interventions, especially in light of the limited effects of most previous interventions based on one or two sources of self-efficacy.

The uniqueness of this research lies in its integrated approach in designing a set of interventions in an online example-based environment based on Bandura’s four sources of self-efficacy while incorporating other research-based perspectives (e.g., example-based learning, pedagogical agents, and implicit theory of intelligence). No previous study has integrated the four strategies used in the present study into one framework and apply them in technology-based environments. The findings of the study contribute to our understanding of promoting efficacious and competent learners when it comes to learning tasks involving mathematical skills.

Practical Implications

Mathematics learning (including statistics) can prime high anxiety and low self-efficacy, especially in an online course that offers minimal personal support. This study addresses the practical problem of how to mitigate motivation and affective factors—such as high task anxiety and low self-efficacy—that can negatively affect learning with an online mathematics lesson. This study has practical implications for developing interventions to build self-efficacy and reduce anxiety when learning mathematical content in an online lesson. The findings are promising in informing other researchers, instructional designers, and classroom teachers of the strategies that are effective to increase self-efficacy, reduce anxiety, and foster learning. For example, paying special attention to reducing learner anxiety through anxiety coping messages is important to enhance self-efficacy and, subsequently, learning. In addition, the finding that women were more negatively affected by the online environment than were men in terms of anxiety suggests the need to focus on this particular group of learners and develop strategies to facilitate their online learning.

The present study also contributes to the call to design programs focusing on developing self-efficacy involving mathematical learning tasks (Hill, Corbett, & Rose, 2010; Lent et al., 2005). By intentionally integrating a set of self-efficacy features in a multimedia lesson, the study highlights the potential of strategies concerning the four primary sources of self-efficacy that can be built into technology-based instruction to increase motivational and performance outcomes. Technology-based learning environments have enormous potential for delivering adaptive instruction integrating evidence-based strategies, making it ideal to explore and integrate best strategies and evaluate their impact on learning and motivational outcomes. The video modeling examples, the anxiety coping message, the mental practice activity, and the effort feedback tested in this research can be further customized in terms of frequency and the integral elements to meet the learning needs of various intended learners.

Limitations and Future Directions

One limitation of the study is that the four features related to the four sources of self-efficacy were implemented simultaneously, thereby making it impossible to pinpoint the exact feature(s) that had the biggest effect on enhancing learner self-efficacy and performance. Thus, it remains a question with regard to the relative effectiveness of each of the four strategies implemented. The inclusion of the measures on task anxiety and self-efficacy did shed some light on interpreting the study findings as discussed earlier. However, it is possible that more than one feature in the intervention (rather than the anxiety coping message alone) worked together to reduce learner anxiety, which then influenced self-efficacy and subsequent performance. Future research is needed to disentangle the effects of individual features, testing each strategy separately and systematically to better understand the mechanisms by which self-efficacy can be increased through such strategies.

In addition, the strategies implemented in this study are just four of many viable forms aligned with Bandura’s four sources of self-efficacy information. For example, regarding the mastery performance source, we chose the mental practice strategy, hence with a focus on mental performance instead of actual performance. Although Bandura (1997) indicated that it was possible to facilitate mastery experiences through nonactual performance (e.g., virtual mastery), such strategies serve as adjuncts to actual mastery experiences. Future research could focus on actual performance-based instead of performance-oriented strategies concerning the mastery experience source. Similarly, regarding the vicarious experience source, we chose modeling by a competent model who looked like an expert rather than a peer model gradually achieving mastery. This choice might be questioned by a reader who emphasizes both attribute and competence similarity between the model and the observer. However, Bandura (1997) supported the use of “highly competent” models, and he argued that model competence and the instructive value demonstrated in modeling are more important in self-efficacy development than model-observer similarity; after all, “[p]eople are not about to discard information that makes them more efficacious just because it comes from a dissimilar source” (p. 101). Despite that expert modeling is a viable form to operationalize the vicarious experience source, we acknowledge that it will be an interesting effort for future research to compare different forms of modeling in online learning involving mathematical skills.

We acknowledge that there could be potential confounding differences between agent-delivered modeling examples versus text-based worked examples, such as the delivery format of video versus text-based content. It may be argued that the video format is a more engaging medium than the text-based content, which contributed to the benefits of the online intervention in this study. While we could not exclude this possibility, our focus was on empirical strategies that could be integrated into online instruction to effectively increase self-efficacy and learning while reducing task anxiety. Future research may focus on whether the difference in delivery method will influence targeted outcomes by comparing an animated agent who models how to solve example problems with a text-based modeling example that includes a static image of the agent accompanied by a text message.

In addition, our findings were generated from quantitative data, including performance scores and self-reported rating scores. To further support our findings, it would have been helpful to collect qualitative data, such as participant interviews and think-alouds, to examine their perceptions of and experiences with the collection of self-efficacy features embedded in our multimedia lesson. This may allow us to check how participants interacted with and reacted to each feature, providing further insights to the study. It is also worth mentioning that there is overlap of the literature in self-efficacy and that in self-regulation. For example, self-efficacy can be examined under the umbrella framework of self-regulated learning (e.g., see a review by Panadero, 2017). Therefore, future studies could include measures of self-regulation. Another limitation of the study is that we focused on the college students in a short-experimental study in a controlled setting. It is not clear whether the set of tested features would produce similar findings for learners at different developmental stages or in different settings. It would be beneficial for future research to study younger learners at a larger scale with the intervention integrated into curriculum to understand the impact of the intervention in real classroom settings.

Footnotes

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by a Research & Creative Activities Program grant (RCAP#17-8003) at Western Kentucky University.

Note

Author Biographies

Xiaoxia Huang, PhD, is an assistant professor in instructional design in the School of Teacher Education at Western Kentucky University. Her research focuses on designing and evaluating technology-supported learning environments in various formal and informal settings to facilitate cognitive, affective, and motivational processes in learning.

Richard E. Mayer, PhD, is a distinguished professor in the Department of Psychological and Brain Sciences at the University of California, Santa Barbara. His research involves applying the science of learning to education, focusing on multimedia learning, e-learning, games for learning, and learning strategies.

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