Do Computer Science Students Understand Their Programming Task ? — A Case Study of Solving the Josephus Variant Problem

The ability of students to problem solve begins with interpreting the problem. When they interpret the problem inaccurately, they will likely use ineffective strategies or fail to solve the problem. Studies reported students are often incapable of identifying and articulating the problem goal, requirements/constraints, and expected output. In other words, students lack self-regulation skills, especially related to task understanding. In this study, two male and two female senior computer science students from Utah State University, USA, were recruited as research participants to learn more about their task understanding skills while engage in programming tasks. The participants were asked to answer five programming problems while thinking aloud, and their responses were videoand audio-recorded. This report focuses on one of the problems, which was a variant of the Josephus problem. Three research questions were used to guide the analysis: (a) what were the participants’ initial task understanding; (b) how did it change during the problem-solving endeavor; and (c) why did it change. All participants identified the problem goal inaccurately and as a result, selected ineffective problem-solving strategies. The analysis suggested their inaccurate task interpretations were caused by their confidence bias (i.e., a systematic cognitive error), in which they drew knowledge and strategies from irrelevant experience. Out of four participants, only one was able to defeat the confidence bias and acquired an accurate task understanding; the influencing factors and possible interventions to overcome confidence bias are discussed.


Introduction
Numerous technologies seamlessly support our daily activities in this digital age.Presently, job automation and technology integrated solutions are becoming more common (Bui, 2015;Hambrusch, Hoffmann, Korb, Haugan, & Hosking, 2009;Henderson, 2009), and the demand for competent computer scientists is increasing (Lacey & Wright, 2009).Unfortunately, many undergraduate students are struggling to adapt to the expectations of computer science (CS) education.Various CS departments reported 30% to 50% dropout rate of undergraduate students (AAA Utah State University, 2016; Beaubouef & Mason, 2005;Howles, 2007;Kori et al., 2015).While many factors may influence students' decision to leave their major, numerous studies reported the immense challenges in learning computer programming during the first year as the leading dropout reason (Anderson & Skwarecki, 1989;Guzdial et al., 2015;Howles, 2007;Kori et al., 2015).
Students' learning impediment and high dropout rate can also be caused by their inadequate self-regulation (SR) skills.Falkner, Vivian, & Falkner (2014) reported some students are incapable of considering and addressing the assessment criteria during their problem-solving enterprise.Peng, Wang, & Sampson (2017) reported students are unable to identify the problem goal and expected output correctly.Although these reports suggest a deficiency in SR strategies, it is still unclear which SR aspect the students lack.Nevertheless, out of various SR aspects (e.g., knowledge about self, task interpretation, or planning), task interpretation or understanding of the problem is the most critical because it shapes the rest of the problem-solving endeavor (Butler & Cartier, 2005).Thus, students' self-regulation, especially their task interpretation became the focus of this study.
Since 1996, various researchers, such as Zimmerman, Winne, Hadwin, Pintrich, Butler, and Cartier, have tried to capture the complexity of students' SR in a single framework (Santoso, 2013).Butler and Cartier's model (BCM) of SR was chosen for the study presented in this paper because it emphasizes the significance of various contexts in any regulatory activities.Precisely, the BCM imposes that all self-regulation activities are influenced by multiple layers of context (Butler & Cartier, 2004, 2005;Butler et al., 2017;Cartier & Butler, 2004), such as students' awareness of themselves (e.g., their experience or strengths), academic culture, computer science (CS) as a discipline, and concepts, standards, and best practices in programming.This contextual characteristic makes BCM flexible because it can be and has been used to describe CS and engineering students' SR (Febrian, Lawanto, & Cromwell, 2015;Lawanto, 2010;Lawanto et al., 2013;Lawanto, Butler, Cartier, Santoso, & Goodridge, 2013;Santoso, 2013).
The BCM describes three elements of SR including the multiple layers of context, the learning or problem-solving environment, and students' engagement with the environment (Butler & Cartier, 2004, 2005;Butler et al., 2017;Cartier & Butler, 2004).The problem-solving environment refers to the given task, available resources and supports, and provided feedback.Students' engagement with the learning environment refers to their activities of (1) understanding or interpreting the task, (2) developing a plan to solve the task, (3) enacting the plan, (4) monitoring their progress and problem-solving activities, and (5) making adjustment as necessary.Adjustments can occur in their task interpretation (TI), plan, or enactment strategies based on their monitoring results.Additionally, the cycle of strategic action taken by a student (i.e., TI, planning, enacting, monitoring, and adjusting) is influenced by emotions and motivations.Butler andCartier (2004, 2005), Butler et al. (2017), and Cartier and Butler (2004) provide a more detailed discussion of BCM.Butler (1998) describes students' TI as their understanding of the given task and the associated processing demand to complete it.However, this definition is too broad to be operationalized.Thus, this study complemented the BCM with Hadwin's model of TI.Hadwin (2006) argues students' understanding of a problem can be categorized as explicit or implicit TI.Explicit TI refers to information that is plainly presented in a task description (Hadwin, Oshige, Miller, & Wild, 2009), such as the task goal.Implicit TI refers to any extrapolated information from the task description (Hadwin et al., 2009), such as relevant concepts, knowledge, and experience.These definitions imply that if the goal needed to be extrapolated from the task description, then it was part of the implicit TI.Likewise, if the task description listed the relevant concepts, then it was part of the explicit TI.In other words, how students get the information (i.e., by identifying or extrapolating) determines how the information is categorized.
Task interpretation is the first step in any SR activity (Butler & Cartier, 2005).Thus, any inaccurate explicit or implicit TI may inform students to select and employ ineffective problem-solving approaches (Butler, 1995).Fortunately, TI changes during the problem-solving enterprise (Rivera-Reyes, 2015;Rivera-Reyes, Lawanto, & Pate, 2017), suggesting that even though students may start with inaccurate explicit and implicit TI, they may gain the correct interpretation while solving the task, providing they continuously monitor themselves and are open to necessary adjustments.Isomöttönen & Tirronen (2013) argues that having relevant knowledge and skills on the given task is necessary for accurate and efficient self-monitoring activities.Further, when students are familiar with the discipline-related knowledge, values, skills, and expertise, they tend to have more accurate TI and be more competent of selecting effective domain-specific strategies (Butler & Winne, 1995;Hadwin et al., 2009).In other words, SR skills have a positive influence toward students' problem-solving endeavor (Lawanto, 2010;Lawanto & Johnson, 2009;Pintrich, 2002), and insufficient SR may endanger their problem-solving effort (Schoenfeld, 1983).

Self-Regulation in Computer Programming
Developing a computer program requires the ability to translate and model one's way of thinking, the problem, and the solution in natural language into the selected programming language (Renumol, Janakiram, & Jayaprakash, 2010).Each programming language has its unique syntax and structures that help students organize their code and focus their attention on solving the problem (Lee, 2014).Further, students use various cognitive skills to comprehend, design, and interlink various types and levels of abstraction while programming (Renumol et al., 2010;Wing, 2008).Self-regulation is therefore essential during such complex endeavor.Unfortunately, there is limited literature on this topic in CS education.Alharbi, Henskens, & Hannaford (2012) reported typical CS students are visual, sensing, reflective, and sequential learners, suggesting that they learn best when exposed to visual representation and facts sequentially.CS students may also prefer to solve problems sequentially and to develop a visual interpretation of the problem.As reflective learners, CS students may frequently monitor and reflect on their learning progress (Felder & Soloman, n.d.).Lye & Koh (2014) argue that reflections can help students better understand various CS concepts and principles.In other words, most CS students are equipped with some characteristics that could help them be successful in this discipline.Kumar et al. (2005) reported that using various SR skills enhances students' performance in programming.Since using discipline-specific strategies during a problem-solving endeavor is more efficient (Falkner et al., 2014), it is possible that self-regulated students are more competent in selecting and applying CS discipline-specific strategies, thus enhancing their performance.Bergin, Reilly, & Traynor (2005) reported that students with high intrinsic motivations and task value (i.e., able to appreciate the importance of a given task) tend to employ various SR strategies more frequently, and possibly perform better in programming, compared to their counterparts.
Studies also discussed SR deficiencies of CS students.Havenga (2015) reported that although students are aware of their fragmented knowledge of, and potential misconceptions on, various object-oriented programming concepts, they tend to jump into solving a given task instead of addressing their fragmented knowledge and confirming the potential misconceptions.This report suggests that some CS students are incapable of self-regulating themselves properly.Falkner et al., (2014) reported some CS students are incapable of considering and addressing parts of the assessment criteria during their programming endeavor, suggesting an inadequacy of students' TI skills.

Research Questions and Design
The objective of this qualitative study was to investigate the task understanding skills of four senior CS students solving a variant of the Josephus problem.Three research questions were used to guide this study: (1) what were the students' initial explicit and implicit TIs; (2) how did their initial TI change during the problem-solving; and (3) what were the factors that influenced those changes.Multiple qualitative case study design was used to answer the research questions because of its alignment with the golden standard for conducting SR research (Butler & Cartier, 2005, 2018;Dinsmore, Alexander, & Loughlin, 2008) where the researchers collected multiple, in-depth data of the participants' (or cases') SR activities while solving programming problems.This qualitative study consisted of two units of analysis, which were related to object-oriented and algorithm design.Both issues require the participants to work on various levels of abstraction.In this report, the researchers only focus on the algorithm design; the object-oriented design is discussed elsewhere.

The Participants
In selecting the participants, Creswell (2012) argues that the cases need to represent as much diversity as possible.
To establish diversity in this study, two male and two female senior CS students that represented higher-and lower-performance based on GPA were selected.Male and female students were selected based on studies that reported that males and females think, perceive, and self-regulate differently (Irani, 2004;Lawanto, Cromwell, & Febrian, 2016;Madigan, Goodfellow, & Stone, 2007;Pivkina, Pontelli, Jensen, & Haebe, 2009).Higher and lower performing students were selected because a higher GPA might reflect competent self-regulated students and vice versa, lower GPA might reflect incompetent self-regulated students.This interpretation was based on reports by Butler and Cartier (2005), Coutinho (2007), and Dent and Koenka (2016) that suggest competent self-regulated students tend to have excellent academic achievements.
Two male and two female senior CS students at Utah State University, USA consented to participate in this study.Each of the four participants selected an alias to be used in this study.The higher-performer participants were Jake and Anne with GPAs of 3.96 and 3.62 on a 4-point scale, respectively.The lower-performer participants with GPAs of 3.10 and 3.36 on a 4-point scale were Rusty and LStew.Although all participants were academically successful, they used relatively diverse problem-solving and self-regulation approaches, as expected in this study.
All participants were Caucasian and familiar with imperative and object-oriented programming paradigm.The male participants were also familiar with logic programming.As seniors, they had completed various CS core courses, such as introduction to programming, algorithm and data structure, calculus, discrete mathematics, software engineering, and event-driven programming.Jake, Anne, and LStew were taking the Advanced Algorithms course.Thus, they were equipped with more than the required knowledge to solve the Josephus problem.Further, Jake, Rusty, Anne, and LStew spent around 5800, 4160, 2000, and 2100 hours, respectively, developing their programming skills, suggesting they had ample time to hone their skills.
As women, Anne and LStew struggled with the CS stereotype, and a sense of not belonging, especially prior to their senior year.This phenomenon aligns with various reports on women in computer science (Falkner, Szabo, Michell, Szorenyi, & Thyer, 2015;Graham & Latulipe, 2003;Irani, 2004;Lewis, Anderson, & Yasuhara, 2016;Outlay, Platt, & Conroy, 2017;Wang, Hejazi Moghadam, & Tiffany-Morales, 2017).Lewis, Anderson, and Yasuhara (2016) describes this stereotype as "singularly focused on CS, asocial, competitive, and male" (p.30).Both Anne and LStew often felt discouraged when comparing themselves with their peers.Anne shared that she frequently considered quitting her study, and was concerned with the impostor syndrome, which made her think: "I know I am not as good as other people think I am, and as soon as they find out how bad I am at programming, then they will realize that I should not be here." LStew reminisced how the self-comparison game tended to lower her self-esteem and impacted her programming performance.Fortunately, both of them overcame this challenge in their senior year.Anne said during the interview, "For the last four years, I thought that I am not as smart as you guys [her peers] but that was all made up in my head."She further explained, "Because there are not as many women [in CS], you do not have as many people to gauge it off … It is harder to know where you really stand with people." Each participant completed all the research tasks and received a $40 gift card and a personalized SRL report as a token of appreciation.The personalized reports were written with minimum jargon and described each participants' strengths and weaknesses and some strategies to improve their task interpretation skills.All participants responded positively towards their report.

Data Collection Method
Four instruments were used in this study, including the initial TI survey, five programming problems, five problem-space maps, and semi-structured interview questions.All instruments had been pilot-tested and refined accordingly prior to the data collection.The initial TI survey consisted of five open-ended questions assessing the participants' initial explicit and implicit task understanding, such as their understanding of the task goal and the required steps to solve it.The five programming problems consisted of two practice questions, one object-oriented question (i.e., a unit of analysis), one break question, and an algorithm design question (i.e., another unit of analysis).The problem-space maps were used to track the participants' problem-solving endeavor, such as completed design issues and design changes.This technique was adopted from Johnson (2008) to enhance the observation quality of the participants' thought processes.The interview questions were used to confirm the researchers' observations during the problem-solving enterprise.For example, the researchers asked one participant to explain his justification of switching from using LinkedList to Array to store rebels-related information, and based on that justification, the researchers decided whether a revised TI influenced the design change or not.The semi-structured interview was selected because it enabled the researcher to adjust the interview process to further explore a particular phenomenon of the participants' self-regulation activities.
During the data collection, the participants had to (1) read the problem out loud; (2) complete the initial TI survey; (3) answer the problem out loud; and (4) answer the interview questions.There was no time limit set for solving the problems.Thinking aloud is commonly accepted as one of the best methods to assess how students think (Bainbridge & Sanderson, 2005).Unfortunately, this method is not without shortcoming.then met to address their differences.During the discussion, the experts also used the recorded videos and other collected data to resolve their disagreements.The experts produced 732 codes with a Kappa score of 1.00 for each Josephus-related transcription, suggesting a perfect agreement among coders (Viera & Garrett, 2005).
The initial TI survey responses were used to address the first research question, which was assessing the participants' initial TI.However, since the participants answered the survey questions in writing, some of their responses lacked details and contexts.Fortunately, the recorded videos/audios of their verbalization could complement the deficiencies of their written responses.Also, the participants' interview responses were checked in case they forgot to report some of their thought processes when answering the survey.
Table 1.Strategic actions of self-regulation

Strategic Action Definition
Task interpretation (TI) Students' understanding of a task and the associated processing demand to complete it (Butler, 1998).
Planning strategies (PS) Selecting appropriate strategies to complete the task (Butler & Cartier, 2005).

Enacting strategies (ES)
Students' cognitive activities employed as they engage in their work executing the design tasks, as planned, monitored, and adjusted through metacognitive activity (Lawanto, Butler, Cartier, Santoso, Goodridge, et al., 2013).

Adjusting (A)
Students' activities of adjusting goals, plans, or strategies based on self-perceptions of progress or feedback (Butler & Cartier, 2005).
The second research question, which was about the participants' initial TI revision, was answered by analyzing the coded-transcriptions and determining any changes in their initial TI.For each identified revision, the researchers traced it back to associated initial interpretation and examined the associated codes along the trace-path.
To address the third research question, which was identifying the factors that influenced these changes, all collected data and other analysis results were used.The influencing factors were mostly inferred from the coded-transcription by using the trace-path.Some other influencing factors were discovered in the participants' interview responses and recorded video of their initial task interpretation survey responses.

Findings
As previously discussed, this paper focuses on the results of the Josephus problem, one of the five programming problems provided to the participants, and the discussion is organized by the three research questions.Table 2 shows the participants' overall performance.As shown in this table, all participants started with an incomplete TI.While LStew failed to submit any solution due to facing challenges during the problem-solving endeavor, the other participants submitted inaccurate solutions.During the problem-solving enterprise, only Rusty was able to change his task understanding and acquire an accurate task interpretation.

Answering Research Question 1: What Was the Participants' Initial Explicit and Implicit Task Interpretation?
The explicit aspects of the Josephus problem were related to the goal and provided requirements/constraints.Its implicit aspects were related to relevant programming concepts, extrapolated requirements/constraints, and the participants' relevant experience and steps to solve it.
All four participants had an incomplete initial understanding of the problem goal.LStew's understanding represents the other participants' interpretation, in which she thought the goal was "to write pseudocode that figures out what position Josephus should be at, in order to survive."This understanding was incomplete because they were not cognizant to print the pseudocode's state each time a rebel perished.Later, this inaccurate understanding led to other wrong interpretations and the section of ineffective approaches.
LStew identified the provided requirements/constraints as the pseudocode would "take an input, run through the formula, and return the output."The formula referred to a simplified mathematical model of the provided suicidal method.Rusty also had a similar interpretation, saying, "The algorithm must return the correct position."Both interpretations suggested the pseudocode did not have to print its states.These understandings were influenced by their incomplete interpretation of the task goal.Encouragingly, LStew also accurately identified "there will never be an input of zero or one because then the problem would not exist."Likewise, Rusty was capable of identifying "the chosen number cannot die." While Rusty and LStew focused on the provided requirements/constraints, Jake's and Anne's interpretation centered on extrapolated information.Since the problem asked for pseudocode, Jake concluded it was unnecessary to think about the speed and memory used by the algorithm.However, he acknowledged the algorithm should be mathematically correct, in that the algorithm should generate the correct output for every given input.As if complementing the others' interpretations, Anne deduced the number of people is "given with function call."Both Jake's and Anne's extrapolated requirements/constraints were correct and supported the idea that an incomplete task interpretation of an aspect of a problem might not harm all follow-up task interpretation activities.
Related to the relevant programming concepts, all participants understood that having basic programming knowledge was necessary to answer the given problem.Among the participants, Anne did not explicitly mention this qualification although she was aware of it, which suggested two interpretations.First, the nature of the Josephus problem implied the need to have programming skills, and thus it was unnecessary to state it plainly.Second, she was not mindful of her implicit connection between the problem and basic programming knowledge.
Unfortunately, the researchers did not confirm either possible interpretation.On the other hand, Rusty specified he especially needed the skills of using "Arrays with conditional operators and if statements."Further, Jake and LStew added the necessity to have a competency in "making algorithms out of behaviors."Anne even considered "creative problem-solving" skills as part of the needed qualifications.These observed behaviors suggested the participants were competent in identifying relevant programming concepts to solve the Josephus problem.The finding also supported the idea that having an inaccurate explicit TI might not negatively influence the implicit task understanding.
Jake, Rusty, Anne, and LStew mentioned solving discrete mathematics course assignments as relevant experience to solve the Josephus problem.Interestingly, Rusty did not mention this course during his initial TI, but he did mention it during the interview.However, Rusty's previously discussed problem-solving steps were informed by it, indicating he was unconsciously drawing strategies from that experience.On the other hand, Jake, Anne, and LStew shared they had worked on the "math proof of this problem [but] with a twist" during the course final examination.Naturally, their problem-solving steps were informed by this experience.
All participants' approaches to solving the problem were relatively similar, in that they needed to (1) determine a working pattern by simulating the provided suicidal method manually; (2) program the solution based on the identified pattern; and (3) verify the solution's accuracy.Although she enacted it, LStew did not mention these steps during her initial TI, which suggested she was aware of her problem-solving approach but failed to report it.Plausibly, she often solved similar problems using a similar strategy and was able to retrieve and select it instantaneously when working on the Josephus problem while also being oblivious about it.Such phenomenon is known as tacit expertise and can be acquired through continuous practices (Johnson, 2008).
Two issues emerged from the participants' approaches.First, the participants determined they needed to find a pattern.Rusty and LStew further elaborated the pattern for odd and even number of people might be different.However, finding a working pattern was an unnecessary step since they could easily convert the provided algorithm into pseudocode.Second, all participants assumed a working pattern could be identified after simulating some of the possible inputs manually.Consequently, with the exception of Jake, none of the other participants considered looking for alternative approaches during their initial problem-solving steps, which was a worrisome finding.
Studies reported students tend to solve a problem intuitively and then analytically (Abdillah, Nusantara, Subanj, Susanto, & Abadyo, 2016;Ball, Ormerod, & Morley, 2004;Kahneman, 2003).Further, the learner's experience influences their self-regulation (Butler & Cartier, 2004, 2005;Butler et al., 2015;Cartier & Butler, 2004).Thus, it was possible the participants' discrete mathematics experience significantly influenced their intuition and was reflected in their interpretation of the task goal and problem-solving approach.One of the typical discrete mathematics problems asks students to analyze (e.g., find a pattern) a number sequence and find a simple and succinct formula that could correctly generate the sequence.Plausibly, the participants relied on their experience of solving such problems.This analysis suggested drawing from irrelevant experience might harm the participants' TI.This finding was aligned with Butler's (1995) argument that students' may select ineffective strategies due to their misinterpretation.
When being asked about his wrong interpretation of the problem during the interview, Rusty explained he might have had "a little bit of overconfidence in thinking that I understood the problem," especially since he had "experience with the problem that I thought was similar but turned out to be very different."Similarly, after reading her personalized report, Anne said, "I got excited at the thought that I would have some background in solving that particular problem."Although studies reported that overconfidence is a common trait among students (Mata, Ferreira, & Sherman, 2013;Potgieter, Malatje, Gaigher, & Venter, 2010), the term itself is ambiguous.The finding suggested the participants' inaccurate task understanding was influenced by their decision to draw knowledge and strategies from solving various discrete mathematics problems.Such phenomenon is commonly known as confidence bias, which is defined as "a systematic error of judgment made by individuals when they assess the correctness of their responses to questions relating to intellectual or perceptual problems" (Pallier et al., 2002, p.258).The participants' confidence bias was also worsened by the desire to exhibit their skills or abilities.
As LStew explained, "I was trying to be smart and look/sound clever and focusing on what strengths I have that make me look smart (such as pattern recognition)." Aside from having a confidence bias, Rusty, Anne, and LStew assumed that they could find a working pattern after conducting a few manual simulations of the provided suicidal method.They were so confident that they did not make any alternative plans.During the interview, Rusty said, "Well, if they [educators] are asking this question, there has got to be a systematic way to approach it; there has got to be some underlying pattern."Rusty's belief suggested the participants had positive assumptions about the academic environment.In their study of an authentic and impactful problem, Saulnier & Brisson (2018) reported a similar finding.In their study, students were asked to design a stove to be used in a four-day expedition.Some students did not take this task seriously, and most of them were shocked when they had to use their designed stove during the expedition.Plausibly, students are too used to working with inauthentic problems.McNeill, Douglas, Koro-Ljungberg, Therriault, & Krause's (2016) report confirmed this suspicion.They reported students believe "classroom problems are more abstract and less complex because of the need to simplify in order to provide a general understanding in school" (p.547).

Answering Research Question 2: How did their Initial Understanding Change during the Problem-Solving?
This subsection focuses on Rusty's problem-solving approach because he was the only participant who had a revised TI.Rusty's approach is simplified as a flowchart in Figure 2. Unlike a typical flowchart, the first and last activities were assumed as the first and last boxes.Thus, Rusty began solving the problem by simulating the provided suicidal method manually for inputs (i.e., number of people) of 5 to 17.He made a table to visualize each input and the associated output and tried to generate a working pattern.Unfortunately, it was not as straightforward as Rusty initially thought, and instead found out he skipped simulating the result for input 16.Rusty then fixed that error and continued determining a pattern.Again, he was unable to find any useful mathematical pattern.Rusty then reread the provided example and noticed a mismatch between that and his simulation steps.Rusty's verification confirmed nothing alarming, so he unsuccessfully continued trying to identify a pattern.Rusty then considered stopping looking for a pattern and implementing the provided method as it is.However, before doing so, he concluded there was no harm in rereading the problem description.The review supported Rusty's idea of implementing the method as described.Then, by using his C++ expertise, Rusty developed, verified, and submitted the pseudocode.Unfortunately, his submitted solution was still inaccurate because he did not print out the pseudocode's states.However, Rusty said during the interview that the description presented "a possible visualization of what it [the pseudocode] was doing," which suggested he would be able to get a complete task understanding and submit a correct solution given enough time (e.g., allowing him to work on this problem for several days).
While solving the Josephus problem, Rusty was observed engaging in 13 planning strategies, 29 enacting strategies, 131 monitoring activities, and 7 adjustment strategies.Further analysis revealed that out of his 138 observed monitoring and adjusting activities, 12 were related to TI. Theoretically, Rusty's revised task understandings were captured in these codes.However, since participants might sometimes forget to think aloud, some of their revised TI might be identified as planning or enacting strategies.Fortunately, the follow-up analysis confirmed all Rusty's observed engagements were aligned either with his initial or revised task TI.Throughout his endeavor, Rusty was observed revising his TI one time.In Figure 2, this event was presented as the fourth box.Thus, Rusty's approach suggested he rarely revised his task understanding during the problem-solving enterprise.Plausibly, this behavior was influenced by his familiarity with the problem.which unfortunately was not verified.Nevertheless, this finding suggested Rusty's understanding of himself, and his awareness and reflection of past failures, helped him conquered his confidence bias.

Conclusion, Implication, and Limitation
As a qualitative case study, this research had a limited number of participants.While having four participants is commonly considered unacceptable in quantitative research, it is not the case in the qualitative case study (Creswell, 2012).A qualitative case study is not designed to produce generalized findings but to collect as much diversity as possible (Creswell, 2012).In this study, the diversities are related to the senior CS students' TI while solving a variant of the Josephus problem.The descriptions of the participants and their approach are necessary to allow readers to better interpret and relate to the findings and apply it in their respective contexts.
In this study, two male and two female senior CS students at Utah State University were recruited.Three participants had prior exposure to a variant of the Josephus problem during their discrete mathematics course.Interestingly, all participants considered their experience in that course as relevant and drew strategies to solve the problem from it.This confidence bias negatively influenced their initial TI, in that it swayed the participants from having an accurate understanding of the task goal and from selecting an effective problem-solving approach.This confidence bias was also preventing Jake, Anne, and LStew from monitoring and adjusting their task understanding throughout the problem-solving enterprise.Contrarily, Rusty was able to defeat his confidence bias and acquire an accurate understanding of the task.The analysis suggested his awareness of himself and that he sometimes misinterprets the problems, played a crucial part in his success.
Considering that all participants had confidence bias suggested it was a common phenomenon in problem-solving.It is possible that one reason for the students' incompetence to address some of the assessment criteria is because they have a confidence bias.Reflecting on Rusty's experience, it might be beneficial to design an instruction that can incite students' confidence bias and then address the issue.The instruction will need to be memorable and encourage students to reflect on their experience.Exposing students to varieties of programming tasks might also useful in enhancing their competency to distinguish different task types.Naturally, follow-up studies are needed to learn more about the nature of confidence bias in programming.
Regarding the participants' diversity, there were no notable differences between male and female participants' initial TI and problem-solving approaches.However, the researchers found male participants spent twice as much time programming compared to the females.A dissimilarity was also found among the higher-and lower-performers' TI of the task requirements/constraints.Both higher-performer participants focused their interpretation on the implicit aspect of the task, while the lower-performers focused on the explicit aspect.It was also worth noting that even though all participants inaccurately identify the goal of the problem, not all of their follow-up TI were incorrect.
Since this report only focused on the Josephus problem, its findings only captured a small portion of a diverse students' SR while engaged in programming tasks.Although some findings might be transferable to other programming problem, replication studies are still needed to bring to light the other portion of students' self-regulations.Further, Maksel & Plucker (2014) and Benson & Borrego (2015) argue about the importance of replication studies, such as it can help to verify the accurateness and applicability of educational research findings and interventions in different settings.When conducting a replication study, it is important to focus on verbal responses instead of written to get more elaborate and detailed insight into the participants' thought processes.

Table 2 .
The participants' overall performance