Undergraduate students’ beliefs about diverse approaches to making engineering design decisions: Exploring change during a capstone course

Well-structured, de-contextualized problems that can be solved using solely technical approaches remain a large component of the engineering education curriculum. As a result, students may mistakenly believe that all engineering work can be done the same way—without the use of other approaches. Capstone design courses are an established way of exposing undergraduate students to ill-structured design tasks that more realistically reflect engineering practice. Yet, little is known about the influence of their capstone design experiences on their beliefs about how engineering design decisions are made. Our study compared students’ beliefs about four diverse approaches (technical, empathic, guess-based, and experience-based) to making engineering design decisions at the start of their capstone to their beliefs held at the end of their capstone. We conducted and analyzed qualitative transcripts from one-on-one, semi-structured interviews with 17 capstone students. We found little evidence that students’ experience in capstone courses changed their beliefs about diverse approaches to making engineering design decisions. The minimal change that we did find in students’ beliefs was primarily about guess-based approaches, and that change was not uniform amongst the students who did demonstrate change. Our findings point to the resiliency of students’ beliefs about approaches to design decisions throughout an engineering capstone design experience. Therefore, we recommend instructors foster reflexivity within their classrooms to disrupt these limited, normative beliefs about the approaches needed to make engineering design decisions.


Introduction and background
Engineering education focuses heavily on well-structured problems that emphasize the use of rationalistic approaches. Rationalistic approaches are systematic approaches that allow engineers to numerically compare options to select a single, optimal choice 1 3 (Jonassen, 2012). Throughout their education, engineering students primarily engage with well-structured problems that can be solved using solely rationalistic approaches (Douglas et al., 2012;Dym et al., 2005). Further, the middle years of engineering curricula emphasize well-structured problems to introduce engineering concepts that are based on finding a single, right answer (Dym, 2004;Han et al., 2018;Kotys-Schwartz et al., 2010). While some institutions have adopted a "design spine" or curricula that advances beyond engineering sciences (see Stevens University and the University of Indianapolis), the emphasis on well-structured problems remains common at institutions that have continued to use "bookends" curricula (Kotys-Schwartz et al., 2010). The emphasis on well-structured problems incorrectly signals to students that engineering requires only technical skills to find the single, right answer and that engineering problems can be solved using solely rationalistic approaches (Schon, 1984).
Real engineering design problems are complex, ill-structured, and inseparable from sociocultural contexts that require diverse approaches to decision making. Design, at its core, has been theorized as a series of decisions (Akin & Lin, 1995;Strobel & Pan, 2011) and, by nature, necessitates the use of diverse decision-making approaches beyond just rationalistic ones (Jonassen, 2000(Jonassen, , 2012Jonassen et al., 2006;Ullman, 2001). In fact, scholars have shown that solving real-world problems requires engineers to use different skill sets and expertise throughout the process, beyond just rationalistic approaches (Strobel & Pan, 2011). Based on decision making and human behavior literature, intuition is a way engineers can approach their decision making by leveraging their prior experiences in complex situations (Badke-Schaub & Eris, 2014;Dringenberg & Abell, 2018;Klein, 2008). For example, intuition has been empirically documented as being a component of expert engineers' decision-making and design processes (Baird et al., 2000;Cross, 2001;Gainsburg et al., 2016;Girod et al., 2003) and even argued to be the dominant mode of judgment (Young, 2018). Further, because engineering problems cannot be separated from the contexts in which they are embedded, empathic approaches are also crucial to engineering decision making. Specifically, empathic approaches are important to consider people and their needs within engineering design (IDEO, 2015;Zhang & Dong, 2009), as well as the societal impact of engineering projects (Gunckel & Tolbert, 2018;Walther et al., 2017).
Because design is complex and integral to engineering, design experiences are an established part of undergraduate engineering education. A key component of capstone education is the opportunity to work on team-based design projects (Dutson et al., 1997), with the intention of developing students' decision-making abilities (Beyerlein et al., 2003). Historically, capstone programs were developed in response to and critical in addressing industry critiques of universities graduating ill-prepared engineers (Dym et al., 2005). Capstone education is expected to expose students to the realities of engineering design and provide them with the opportunity to learn the skills that are necessary for engineering practice (Dym et al., 2005;Todd et al., 1995). Although the technical skills necessary for practice may differ based on the program, design is a shared skill across engineering disciplines. For example, ABET includes the following objective (criterion 4) for students' decision-making skills, referred to as "judgments": "[Students must attain] an ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts" (ABET, 2020, p. 5) Although capstone has the objective to introduce students to the reality of design, we do not yet understand what influence a capstone experience has on students' beliefs on how engineering decisions are made. This is not to say that decision making has not been studied within capstone design, as there have been several publications on frameworks or systems to guide decision making (e.g., Gidel et al., 2005;Kim & Xirouchakis, 2010;Steingrimsson et al., 2017). However, there appears to be no prior work in the context of engineering design that has evaluated how capstone has influenced students' decisionmaking skills or beliefs. Furthermore, while change is complex, scholars have established that students' beliefs are capable of being addressed through instruction (Chi & Roscoe, 2002). Simple incorrect knowledge that students possess may be addressed quickly through intervention, while more deeply held misconceptions may require a longer, more concerted effort to produce conceptual change (Chi & Roscoe, 2002). It is important that we understand how students' beliefs about decision making are influenced through their formal capstone education for several reasons. First, we know beliefs are an important construct because beliefs are central to our reasoning (Kuhn, 1991) and serve to inform our behaviors (Fishbein & Ajzen, 2015;Nespor, 1987;Pajares, 1992;Rosenthal & Jacobson, 1968). While beliefs cannot be fully equated to the behaviors that we may exhibit (Fishbein & Ajzen, 2015;Guanes et al., 2021), they provide meaningful insight into predicting how we will behave. In engineering design specifically, we know that beliefs play a fundamental role in how we enact decision making (Jonassen, 2008). Most importantly, we know that beliefs can act as a barrier to meaningfully instructing students about diverse approaches to engineering decision making Walther et al., 2017). Beliefs have also been identified as a construct of interest specifically within engineering capstone design research. For example, Lutz and Paretti, (2017) have previously studied students' beliefs about capstone design outcomes, Cross et al., (2013) studied students' beliefs about learning communication skills and Csavina et al., (2017) studied students' and instructors' beliefs about reflection within the context of capstone design.
From the existing work on students' beliefs about decision making, we see that students largely believe that technical approaches are the dominant method used to make engineering decisions and that empathic and intuitive approaches may only play a supplementary role, if any . This aligns with prior literature that found that engineering students focus on the technical feasibility of their designs when discussing their decision-making approaches to design (Toh & Miller, 2019) and report relying primarily on technical approaches when tasked with making decisions when presented ethical dilemmas (Bodnar et al., 2020). We also know that the beliefs that students hold about technical approaches being dominant and intuitive approaches serving only a supplementary role are different than those held by faculty members with industry experience, who instead saw technical approaches as limited and expressed the need for intuitive approaches . It was also found that, in general, students perceive empathic approaches as outside the scope of engineering work (Fila & Hess, 2016) and struggle to draw connections between empathic approaches and engineering problem solving (Walther et al., 2020). Even when students espouse the belief that empathic approaches are important in engineering design, they do not report translating that belief to their actual design decisions . Similarly, it was also found that students held the belief that empathic approaches are a valuable add-on when making engineering decisions, but as an approach that can enhance decision making and is not necessary in all contexts (Guanes et al., 2022). While these studies give us the general idea of what students believe about the role of diverse approaches, they have not looked for evidence of change in students' beliefs as a function of their capstone experience.
To address this gap, our study explicitly investigated the beliefs that undergraduate engineering students hold about diverse approaches to making engineering design decisions both before and after a capstone design experience. Specifically, we answer the following research question: How do undergraduate engineering students' beliefs about diverse approaches to design decisions at the start of their capstone course compare to their beliefs at the end of their capstone course? This contribution is important because by understanding how students' beliefs change or don't change over time, instructors can have a better idea of how they could better prepare students for what they will encounter in their professional careers.

Research design
The data analyzed and presented in this paper came from a larger project studying the beliefs students hold about diverse approaches to engineering decision making in the context of engineering design. We took a qualitative and exploratory approach to collecting and analyzing data from engineering students at the start and conclusion of their capstone design experience.

Theoretical framework
We conducted our data collection and analysis using a framework, provided in Fig. 1, which we adapted from the empirical framework of Sadler and Zeidler (2005) for patterns of reasoning used by students to make sociotechnical decisions. We iterated on this framework in the earlier stages of our research on students' beliefs about diverse approaches to engineering decision making and made further revisions for the use in this study based on decision-making literature and our own empirical pilot study results (see for details, Dringenberg et al., 2021;Guanes et al., 2019). Within our framework, we theorized four distinct Fig. 1 Framework for approaches to decision making approaches needed to make engineering design decisions: technical, empathic, experiencebased, and guess-based. Besides aligning our work to literature about decision making, our motivation behind providing students with a framework with four specific approaches was to allow students to talk through their design decisions more clearly. In this section, we will discuss the definitions of each of these approaches and the basis for why we included them.
The four approaches within our framework are split into the categories of effortful and automatic approaches, which align with the dual-processing orientation theorized by Kahneman (2011) and have been applied to engineering design (Kannengiesser & Gero, 2019). Effortful approaches are considered slow, conscious processes that can be done from a technical or empathic standpoint. Automatic approaches are considered fast, subconscious processes that come as a gut feeling based on previous experiences or an attempt at guessing.
The categories of effortful and automatic approaches each include two distinct subapproaches. Within effortful approaches, we define (1) technical approaches as analyzing the decision to be made from your own engineering perspective and (2) empathic approaches as analyzing the decision from the perspective of others and how your decision would affect them. An example of technical approaches would be comparing the cost and benefits of different materials for a given project. An example of empathic approach would be considering how the material selected would affect the user or other stakeholders. Together, these approaches illustrate how engineers could consciously consider decisions from multiple perspectives. While we do not mean to reinforce the false notion of a sociotechnical divide (Cech, 2013;NAE, 2017;Swartz et al., 2019), our decision to separate technical and empathic approaches as two distinct effortful approaches was based on what is understood about how engineers conceptualized their work (Dringenberg & Abell, 2018) and the ways that students in our pilot interviews described their decision making (Guanes et al., 2019).
We provided the definitions of each approach in our framework and an example to our student participants verbatim at the start of each interview, along with the visual representation of our framework for these approaches shown in Fig. 1. Within automatic approaches, we define (1) experience-based approaches as having a gut-feeling about the decision due to previous experience, which can be informed by technical or empathic experiences, and (2) guess-based approaches as the attempt of supposing something without information. An example of an experience-based approach is having an immediate reaction that a certain material would be better for the task due to your experience working with it, seeing that it has worked in a similar context. An example of a guess-based approach would be picking a material based on a guess and seeing if it works for the task. Together, these approaches illustrate how engineers could make a decision in a fast and subconscious way. Both experience-and guess-based approaches are conceptualized as distinct aspects of intuition (see for details, Guanes et al., 2019). Experience-based approaches were included within our framework as prior literature framed intuition as a form of expertise (Dringenberg & Abell, 2018). Guess-based approaches were included based on pilot student interviews, which demonstrated that students framed intuition as guessing, due to a perceived lack of prior experience (Guanes et al., 2019).

Beliefs as construct of interest
Our research focuses on beliefs as the central research construct. For the purposes of this study, we operationalized beliefs as assumptions that participants make about reality, or their beliefs about how the world is (Kuhn, 1991). While beliefs may exist at a conscious or subconscious (Connors & Halligan, 2015;Smith, 2016) level, we note that our method of asking individuals to explicitly state their beliefs about diverse approaches to making engineering design decisions captures predominantly their espoused beliefs at the time of our interviews with them. Because of our broad conceptualization of beliefs, this included beliefs about how the four decision making approaches were used within their capstone project, how they believed that engineers use the four diverse approaches in the workplace, how they believe that engineers should use the four diverse approaches in the workplace, and their general beliefs about the application of the four diverse approaches within our framework.

Participants
We recruited 17 engineering capstone design students from a large, Midwestern, public, research-intensive university. We aimed to capture a variety of perspectives by recruiting students from multidisciplinary, interdisciplinary, and disciplinary capstone design courses because of the diverse ways that students are taught about decision making across these contexts. For example, during our pilot interviews, we realized that industrial engineers are likely taught to consider diverse stakeholders throughout their education whereas students in majors such as electrical engineering are often more engaged with the technical aspects of engineering projects. We were able to recruit students from seven out of eight of our targeted disciplines; the only targeted discipline we were not able to recruit students from was civil engineering. We accepted all students who volunteered to be a part of this study and had 17 total student participants (see Table 1 for details). We provide the information about their capstone projects in Table 1 as we recognize that much of capstone is centered on working on a specific project. The specific project that students worked on is likely to influence the ways in which they believe decisions are made in practice. We also include this information as we recognize that projects may differ widely between courses, disciplines, and institutions. In addition to providing a summary of the capstone project, we also include the project type which refers to whether the project sponsor was within the university (academic), or if the sponsor was an external company (sponsored). All the capstone projects that the student participants worked on had a sponsor that they coordinated with.
To maintain participants' confidentiality, we did not collect information on if participants were in the same group as others in the study. For example, while we know that Nina and Mark worked on the same larger project, the multidisciplinary capstone course is structured so that four teams of four students work on the same larger project. We do not know if they worked together on the same aspect of the project or were on the same smaller team. Further, because the description of students' capstone projects was derived from an open-ended question during the interview, we do not have all the details about the types of projects that students completed as part of their capstone design course but were able to provide a brief synopsis of the project where possible.
Of the 17 students involved in this study, 14 had a year-long capstone design experience, while the remainder only engaged in a single semester-long capstone course. The demographic information of the 17 students involved in this study is provided in Table 2.

Researcher positionality
As authors, we recognize that our positionalities influence the research process, particularly how we interpret the results of this work. Aside from the third author, who spent just nine months working in an engineering design setting at a global corporation, our collective experience with engineering design decisions has occurred within educational settings. Our shared academic orientation means that we approached this work through the lens of understanding student beliefs about diverse approaches to engineering decision making through a theoretical lens. Further, while we have all taught in undergraduate engineering contexts, none of us have worked as capstone instructors. Therefore, our interpretation of the results and conclusions that we draw from them, along with the recommendations that we make is influenced by our positioning as "outsiders" and lack of contextual knowledge about teaching a capstone design course. However, all authors have been students in a capstone design course and understand the basis of this context.

Data collection
We conducted semi-structured, one-on-one interviews at two points in time: the beginning and end of the participants' capstone experience. Our interviews with students were led by either a graduate research associate (author Guanes) or an undergraduate research associate. For anonymity purposes, we asked our participants to select a pseudonym given the first letter. We conducted and recorded each interview either in person or through an online video platform. Our final data set was composed of the pre-and post-interview transcripts with 17 undergraduate engineering student participants, for a total of 34 interview transcripts.
The objective of the larger project that this project stems from was to learn about the participants' beliefs about diverse approaches to engineering decision making. To achieve this goal, we used a retrospective interview approach-description of past situationsbecause it allows researchers to learn about participants' beliefs (McNeill et al., 2016; Van  Gog et al., 2005). This approach is more "belief-driven" because participants are retrieving information that is meaningful to them, rather than providing detailed descriptions of what occurred (Robinson, 2014). Students were asked to describe a concrete decision that they made in their design project that did not have a clear answer and was important for their final design. Then, students were asked what role each of the diverse approaches included in our theoretical framework (technical, empathic, experience-based, and guess-based) played in that decision, their beliefs about the role of each approach for design decisions in engineering practice, and their beliefs about how engineering decisions should ultimately be made. We conducted all our interviews using the same interview protocol. Our full interview protocol can be found in Appendix A.

Data analysis
We analyzed the data in three key phases, as shown in Fig. 2 and described in detail in the following sections. Prior to our analysis, all interviews were professionally transcribed and then de-identified and checked for accuracy by a member of the research team.

Phase 1
We conducted the first phase of our analysis on the data generated from the interview questions that asked students about the role of each approach in actual engineering design decisions in practice and their beliefs about how engineering decisions should be made. This strategy enabled us to directly compare the students' pre-and post-interviews about students' beliefs about how decisions should be and are made by engineers. We utilized the retrospective portion of the interview as needed to make sense of absent and conflicting changes. We began our analysis of the data by using a priori coding to perform data condensation on each of the student transcripts (pre-and post-capstone interviews for each participant); we applied a codebook, see Appendix C, that had been developed from responses to the same interview protocol Saldaña, 2016). Each code we applied represents a belief that students held about the use or meaning of the four diverse

Phase 1
•All student pre-and post-interviews were coded using an established codebook.

•Product: Students' beliefs
Phase 2 •Pre-and post-interview codes were compared for each student and generation of categories of change.
•Product: Comparison of students' beliefs and categories of change Phase 3 •Instances of change in students' beliefs were examined in further detail.
•Product: Generation of sub-categories of change that occured Fig. 2 Analysis phases approaches included in our theoretical framework. For example, a common code or belief that we found was that technical approaches are the dominant approach used in engineering. To ensure quality, the first and second authors independently applied the codebook to each transcript, then met to discuss any discrepancies in the applications of codes and converge on the final code application for each transcript. During this process, the authors remained open to any emergent codes that may not have existed in the original codebook.
To further ensure quality and accurately interpret the beliefs that participants held, we utilized the constant comparison method; we frequently took the results of our analysis back to the transcript to ensure that we were remaining close to our data in our code applications (Boeije, 2002). As part of our process, we were careful to capture only beliefs that were supported by the students' full interview transcripts. The result of this phase was the codes-the beliefs-that our students held about the roles and use of each diverse approach pre-and post-capstone. In our analysis we only looked at whether a belief was held and, as such, we did not categorize the strength of the belief held by students. This means that if a code was present in the student transcripts, we did not duplicate the code if the belief was expressed again.

Phase 2
After coding each transcript, we compared the presence of the pre-and post-capstone interview codes for a subset of the participants. We chose to start with a random subset of our students to explore if our analysis method sufficiently made sense of the trends we were noting. We directly compared the pre-and post-capstone interviews for several individual students to ascertain how each student's codes at the start of their capstone compared to their codes at the end. In cases where a code was present in only one interview, we closely examined the full transcripts to determine whether the same belief was supported in both interviews. If it was determined that the code was supported in the transcript that it did not appear, it was added as a code. As we compared the codes that students expressed in their pre-and post-interviews, we developed three emergent categories to describe the changes we were seeing between the pre-and post-interviews for each student:"change," "no change," and "absent." We tested the categorizations on another subset of our transcripts, met to discuss the application of these categories, and ultimately interpreted that these categorizations of changes were appropriate for representing our data. We then conducted this second-order analysis on our remaining transcripts. Presented as Table 3 is an example of our code application and categorization for Mark.

Phase 3
The third step of our analysis process was to look at the instances of change of beliefs and perform additional analysis on the pairs of transcripts that contained a comparison category of "change" to better understand the nature of the change that took place. Specifically, we looked to see whether a student became more or less open to the use of a particular approach that they seemed to have changed their beliefs about. To better understand possible instances of change, the entire pre-and post-transcripts were reviewed and compared. During this process, the first and second authors met frequently to discuss the trends that they noted during their individual passes through the data to arrive at the final categorizations of change.

Summary of previous study findings
As this study was a continuation of existing work, we aim to orient readers in the findings from this previous work. Our previous study evaluated students' post-interview beliefs and found that students held a variety of beliefs about diverse approaches to engineering decision making (Guanes et al., 2022). At a high level, this study found 10 broad categories of beliefs that students held; these categories have been included in Table 4 located in the findings section (Guanes et al., 2022). Notably, while students largely believed that technical approaches to design are dominant in engineering, half of the students also recognized that technical approaches are in some way limited (Guanes et al., 2022). The study also revealed that students believed that empathic approaches serve as an add-on to engineering design, seeing the approach as being valuable in considering those inside and outside of the design team, but ultimately being optional (Guanes et al., 2022). This work also revealed that students believed the use of both experience-and guess-based approaches limited to specific scenarios, while some saw these approaches as wholly unacceptable within engineering practice (Guanes et al., 2022). Only a small number of students saw guess-based approaches as being an accepted approach within engineering design (Guanes et al., 2022).

Findings
The results of our coding are presented in Table 4. In Table 4, we also present the number of students expressing certain codes in the pre-and post-interviews, along with the categorizations of change. A breakdown of the code distribution of each student transcript has been provided in Appendix B. In summary, we found that the ways in which students' beliefs before and after capstone compared to one another fell into three broad categories: no change, absent, and change. To begin, we will provide a broad answer to our research question by comparing the pre-and post-interview codes and categorization of change. In

Summary of findings
Our data analysis revealed that the beliefs that participants held about diverse approaches to engineering decision making at the beginning of their capstone experience remained largely unchanged at the conclusion of their capstone experience. Across the different decision-making approaches, we see that most of the categorizations we made were "no change." "Absent" relationships were also noted across all elements of our framework, while change was only recorded within the automatic approaches, centered mostly around guess-based approaches. In most circumstances, the rate of "absent" or "change" categorizations between the two interviews did not shift by more than one or two students. However, in the case of the belief that technical approaches are used to convince others, we saw that six participants expressed such belief in their post-interview but did not in their pre-interview. Further, we also saw that more participants expressed the general belief that guess-based approaches are accepted or not accepted instead of focusing on specific circumstances that such approach can be appropriate to use, such as during brainstorming. It appears that in addition to minimal change being centered on guess-based approaches, the changes also appeared to diverge, as we see overall instances of both "not accepting" and "accepting" increase from the pre-to post-interview.

No change
We found that most of the coded beliefs that participants held about how different approaches to decision making are and should be used within engineering ultimately stayed the same and were categorized as no change. Although students did not often say the same statements line by line, we categorized "no change" beliefs as those that encapsulated the same idea in the pre-and post-capstone interview. In other words, our category of no change indicates a lack of evidence that the beliefs that students held changed in any way, even though the exact language they used to describe them may have varied. For example, at the beginning of his capstone experience, Quetzalcoatl believed that guessbased approaches were used to keep the engineering design process moving and acceptable to use in circumstances where there were unknowns. He stated in his pre-interview that guess-based approaches were used to compensate for a lack of knowledge when encountering a new or unfamiliar problem and stated that "there's a lot of guesswork involved if you're unfamiliar in the environment and you're encountering an unfamiliar problem." In his post-interview, this belief was articulated again as he stated that "when you really are lacking information, then I think [guess], just picking some direction and trying it for a bit […]" is a valid approach. We also found instances where students did express the same belief using almost the exact same language during the pre-and post-capstone interview prompts. For example, when asked about the role of empathic-based approaches, White saw them as primarily being used to consider teammates or other engineers in the project instead of end-users or those outside the team. In his pre-interview, he stated, "If you work in a team, of course, the empathic decision is pretty important, because you need to think about others' feelings and others' opinions." In his post-interview he also shared the belief that empathic-based approaches pertained to the team, stating "empathic [-based

Absent
We also found many instances of what we categorized as "absent" beliefs, or beliefs that were discussed in one of the interviews but not in the other interview. While we cannot draw concrete conclusions about whether students retained or lost these beliefs, they do provide us insight into what was on the forefront of students' minds during these interviews. For example, Nina stated at the beginning of the capstone course that experience was valuable for making quick decisions, something that engineers with applicable experience could use as a "time saver." In her post-interview she did not mention that experience-based approaches could be used to save time; instead, she focused on the general acceptance of the approach, stating that experience-based approaches should only be used for "the less important things," although she did state they likely play more of a role than "most people are able to realize." Another example of "absent" beliefs manifested in Henry's interviews. During his precapstone interview, he expressed the belief that technical approaches "eliminate some biases" and allow us to separate out "the choice we would personally want." While he still argued that technical approaches were important to mitigate bias in his post-capstone interview, Henry also expressed a new belief that he did not share in this pre-capstone interview, that technical approaches are limited, stating "I don't think it's the best way to have everything done from a purely technical approach because it [is] kind of is lacking for how the actual real world is." He goes on to argue that technical approaches cannot be the sole approach because it would take an "absurd amount of time for you to get something done and you'll probably get in trouble with your manager or whoever's your supervisor."

Change
Our final category was "change," which captures instances where students espoused beliefs contradicted one another in the pre-and post-capstone interviews. In total, we found only six instances of change, which were spread across five individual students and concentrated in the 'guess' component of our framework. Amongst the evidence of change we found in students' beliefs about guess-based approaches, we found no clear pattern in the nature of the change that occurred; some students became more accepting of guess-based approaches being used in practice, while others were more critical of the use of guess towards the conclusion of their capstone course. To describe these changes, we separated this category into two subcategories that describe the nature of the change: narrowing and broadening.

Narrowing change
"Narrowing changes" are those where students displayed less accepting beliefs towards the end of their capstone course. In total, we found three instances of narrowing change. For example, at the beginning of her capstone experience, Emily believed that guess-based approaches had a place in the design process. She stated that guess-based approaches could be used in the beginning stages of design or in testing to see " [what] would work and what wouldn't in a process." However, at the end of her capstone experience, she expressed that guess-based approaches should not be used in engineering except in research settings and even then, only sparingly, stating that she did not think engineers "want to waste their time or resources just guessing and thinking of a random thing."

Broadening change
"Broadening changes" are those where students became more accepting of an approach to decision making over their capstone experience. In total, we found two instances of broadening change. For example, initially, Yan believed that guess-based approaches had a "very limited role […] in professional engineering." Yan stated that the role of guess-based approaches could be used in low-stakes circumstances where the repercussions of guessing wrong are tolerable, "I think, when it's not involving humans and not really … I guess, when the risk of it going wrong doesn't necessarily bear severe consequences." However, he acknowledged in circumstances like "picking a way to put an implant in someone's mouth […]" that guess-based approaches would be inappropriate to use. However, towards the end of his capstone experience, he argued that "a lot of what engineers actually do is guess," stating that "that's basically all we're [engineers] doing and then we're just seeing is this guess correct, is it close enough? I think that's basically what engineering is, just guessing until we get something that works." Overall, Yan became more accepting of the use of guess-based approaches in engineering design.

Discussion and recommendations
In this study, we explored the ways in which students' beliefs about diverse approaches to making engineering design decisions at the start of their capstone compared to their beliefs at the conclusion of their capstone experience. Our findings reveal that for the most part, our participants' descriptions of the role of diverse approaches remain the same over their capstone experience, and when they do change, we found no clear pattern in the nature of the change that did occur. Specifically, the only evidence that we found for change in our participants' beliefs between the beginning and end of their capstone design course was change in their beliefs about automatic approaches to decision making. We found one instance of change regarding experience-based approaches and the other five instances were about guess-based approaches. We interpret our findings as a piece of evidence that capstone design experiences for engineering students largely reinforce or do not challenge the beliefs that students hold about how engineers make design decisions when they start the course. In this section, we connect our findings to other areas of literature to provide possible explanations for why we found a lack of change in our participants' beliefs about diverse approaches to engineering decision making and start the conversation on the importance of this finding.

Making sense of the minimal change
Our findings revealed that our participants' beliefs about decision making largely stay the same over their capstone experience. In this section we explore two possible explanations behind our finding that student beliefs remain largely unchanged during capstone: (1) the pervasive effect of the normative culture of engineering education and (2) the lack of direct instruction to disrupt students' beliefs in capstone.
We posit that the pervasive nature of engineering curriculum as technical and rational (e.g., Cech, 2013;de Pillis & de Pillis, 2008;Faulkner, 2007;Picon, 2004) may play a significant role in the formation and resiliency of students' beliefs during their capstone experiences. Our previous contribution found that many of the beliefs that students held at the conclusion of their capstone experience mapped to the broader cultural expectations of engineers to be rational and utilize technical approaches and did not reflect those held by formerly practicing engineers . We now see that the beliefs that students hold at the close of their capstone experience are largely the same as those that they entered the course with. Despite the exposure to ill-structured problems that necessitate the use of diverse approaches within their capstone experience, our findings demonstrate that there does not appear to be a major change in the beliefs that students hold about decision making in the context of engineering design. The lack of change in beliefs maps to previous literature in the space that demonstrates the resiliency of our beliefs (e.g., Ambrose et al., 2010;Kloosterman et al., 1996;Lester, 2000;Murphy & Mason, 2006). For example, Downey and Lucena (2003) found that students resisted seeing design education as a primary component of engineering work as it conflicted with their understanding of engineering centering around scientific problem-solving. Because engineering education centers on well-structured problem-solving and the use of technical approaches (Douglas et al., 2012;Dym et al., 2005), it is probable that students are receiving implicit and explicit messages about their beliefs, potentially strengthening them over time through socialization (Harro, 2000;McLean & Syed, 2015). We find it to be no surprise that capstone, a course situated at the end of their educational journey, is not capable of disrupting their beliefs about decision making (Dym et al., 2005;Jocuns et al., 2008;Schon, 1984).
Second, we believe that the lack of direct instruction and assessment on diverse approaches outside of technical approaches contributes to the absence of change in the beliefs that students hold about diverse approaches to decision making. Capstone instruction still centers around technical approaches to design decisions (Brewer et al., 2015;Dringenberg et al., 2019), relying on decision-making strategies that heavily focus on the technical aspects of the design (Dringenberg et al., 2019). As such, capstone design instruction and assessment tend to not focus on covering other approaches to decision making. In fact, our previous work found that faculty struggled to teach approaches outside of technical approaches to their students (Dringenberg et al., 2019). While capstone courses expose students to ill-structured design problems (Jonassen, 2000), exposure to ill-structured problems does not lead students to gain an understanding of the role and value of diverse approaches to engineering. If the intention of capstone courses is to expose students to the ways that design and decision making is realistically made, further concrete work needs to be made to address misconceptions within the classroom. One concrete way to address the beliefs that students hold about the design and decision-making process is by explicitly exploring the misconceptions that students bring into the classroom (Ambrose et al., 2010;Chi & Roscoe, 2002). In other words, covering the concept over a lecture without addressing the misconception is likely insufficient to change students' beliefs (Ambrose et al., 2010;Chi & Roscoe, 2002). Another way to concretely address misconceptions about decision making within capstone courses is by leveraging concepts that are already being presented to students and explicitly connecting them to diverse approaches to decision making. For example, user needs, or stakeholder assessments, are often mentioned and assessed within the design process (Beyerlein et al., 2006;Dringenberg et al., 2019) but are not explicitly connected to "empathic approaches" within the classroom . Holding dialogues with students about how, realistically, decisions are made using methods beyond just technical approaches can allow students to recognize the value and role of such approaches within engineering work.

Change within guess-based approaches
As noted in our results, we found that the small amount of change present in our participants' beliefs was concentrated in their beliefs about the role of guess-based approaches in engineering design decision making. However, the nature of the changes that we found were inconsistent amongst students. Namely, we saw a divergent understanding of guess-based approaches and how they are utilized within the design process. Some students became more accepting of guess-based approaches, while others appeared to become less tolerant of their use. We posit that the tension between the curriculum and implicit messaging of engineering education (Douglas et al., 2012;Downey & Lucena, 2003;Dringenberg et al., 2021) and the reality of the design experience may affect the ways students make sense of the use of guess-based approaches to make design decisions and contribute to this finding.
It is well-established that the culture of engineering is constantly presenting explicit and implicit messages about technical approaches and how they are the engineering way of knowing (e.g., Faulkner, 2007;Holth, 2014;Picon, 2004). While empathic and experiencebased approaches to design may be rationalized as utilizing a technical base and be recognized as adhering to the cultural norms of the discipline, we believe that guess-based approaches may be more difficult for students to see as fitting with the culture of engineering. We believe that the curriculum of engineering education may further indicate to students that only technical decision-making approaches are valid in design. The curriculum of engineering heavily emphasizes well-structured problem-solving (Douglas et al., 2012) which may lead to the misconception that engineering problems can be solved using solely technical approaches. As Jonassen et al. (2014) stated, the focus on well-structured problems within engineering courses means that "learning to solve classroom problems does not effectively prepare engineering graduates to solve workplace problems" (pp. 103-104). Relatively little attention is given to ill-structured problem-solving that necessitates the use of diverse approaches, including scenarios in which engineers must make assumptions or guess in their problem-solving (Jonassen et al., 2014). On the other hand, students are being exposed to ill-structured problems in their capstone courses which may necessitate the use of guess-based approaches. The exposure to the reality of the design process may have served to disrupt some of the students' preconceived beliefs more aligned with broad culture (Ambrose et al., 2010).
The inconsistent change in students' beliefs about guess-based approaches could be seen as problematic in that students are walking away from a course with a clear set of outcomes with different takeaways, some of which do not match the reality of what they will encounter in the field. The reality of design is that engineering problems are ill-structured and require the use of diverse approaches (Jonassen, 2000(Jonassen, , 2012Jonassen et al., 2006;Strobel & Pan, 2011;Ullman, 2001) and practitioners do make assumptions and use their intuition in their problem-solving (Baird et al., 2000;Cross, 2001;Girod et al., 2003). We are in no way saying that guessing should be used or that it is valid in all contexts, but we do believe that students should accept that diverse approaches are needed within different contexts and situations within engineering design. Our work shows that currently, students are not receiving an explicit message about guess-based approaches since some became more accepting, while others became less accepting. In contrast to the other diverse approaches in this paper, we found the most change in guess-based approaches compared with the other approaches. While there was still very little change, we believe that targeted interventions and assessments pertaining to guess-based approaches to engineering decision making may be able to influence the nature of the change that occurs in students' beliefs about guess-based approaches.

Limitations
There are some limitations in how we approached and conducted our study that affect the transferability of our results. First, while we purposefully sampled students to ensure a variety of engineering disciplines and backgrounds were included, we were unable to recruit students from civil engineering and have no instructor-generated projects within our sample, meaning that all students had exposure to working with real stakeholders in their projects. As such, our findings may not apply to contexts where capstone projects are created by instructors. For example, students working on academic projects may not find the need to implement experience-or guess-based approaches in their work. Additionally, the participants in this work all come from a single institution that may have distinct curricula and cultures that we believe would influence the ways that students' beliefs would change over the course of their capstone experience. For example, institutions operating with a design spine may find that our work is not transferable to their local context. We encourage readers to carefully consider their own populations in contrast to ours and how our findings may transfer to their settings (Lather, 2007).
Second, it is important to recognize that students' beliefs about decision making are also formed outside of capstone courses. Capstone coursework is only a small component of the overall engineering curricula that students are exposed to. We recognize that beliefs are difficult to change in practice (e.g., Ambrose et al., 2010;Downey & Lucena, 2003;Kloosterman et al., 1996;Lester, 2000;Murphy & Mason, 2006) and that while progress can be made within capstone, a single or two-semester capstone sequence will likely not combat deeply held cultural beliefs that students hold about how engineers make decisions, especially those that are further reinforced by previous coursework. We believe that a more direct approach that centers on teaching diverse approaches to decision making is necessary if the intent of capstone is to change these beliefs.

Conclusion and recommendations
Although capstone education is purported to be the place where students begin to form the necessary skills for practice, including decision making, (ABET, 2020;Beyerlein et al., 2003;Dym et al., 2005), little attention has been given to how students' beliefs about how engineers should and do make design decisions are impacted by their capstone experience. Our findings show that our participants' beliefs remain largely the same and prioritize the use of technical approaches over all others. When change did occur in our participants' beliefs, we found it was mostly related to guess-based approaches to design decisions, and there was no clear pattern in the ways that our participants' beliefs changed. As beliefs are central to our reasoning (Kuhn, 1991) and impact the ways that engineers make decisions (Jonassen, 2008), it is crucial that we develop students' beliefs to match the reality of the field in that diverse approaches serve a significant role in engineering decision making (Jonassen et al., 2006). We believe that direct instruction can serve as a crucial next step in the formation of engineering students' beliefs about the use of diverse approaches (Ambrose et al., 2010;Chi & Roscoe, 2002). Future research is needed to explore how direct instruction on the role and application of diverse approaches relates to change in students' beliefs.
In conclusion, although one may assume that capstone impacts students' beliefs about how engineers work and make design decisions as it teaches them design skills, our work has demonstrated that students' beliefs remain static over the course of their capstone. As the beliefs that students hold do not fully match the beliefs of experts within the engineering field , our findings further support the notion of the school-towork gap and point to the need for additional instruction on decision making. In recognition of the minimal and inconsistent change that we found in students' beliefs about diverse approaches to engineering decision making, we offer several recommendations.
First, we believe that it is necessary for capstone faculty to talk with the students about their experiences in terms of the diverse approaches that they are using and how it maps back to the nature of the problems that they are being asked to work on. Specifically, we believe that instructors should explicitly teach and discuss the use of empathic, experience-based, and guess-based approaches to decision making along with the technical approaches. Because capstone is primarily a project-based course that may not involve many opportunities for direct instruction, we believe that project debriefs may serve as an opportunity for instructors to discuss decision-making approaches with their students. This is in alignment with Cech's (2013) recommendation that we must make "cultural space" and directly address our socialization to disrupt it.
Aside from discussing decision-making approaches in class, we also believe that explicit goals and student learning objectives should be created pertaining to how diverse approaches to engineering decision making such as empathic, experience-based, and guess-based approaches are utilized by practitioners. Literature has demonstrated the importance of setting explicit learning objectives for students (Ambrose et al., 2010), which we believe may provide capstone educators a path for shaping students' beliefs about diverse approaches to engineering decision making (Feisel & Rosa, 2005;Felder & Brent, 2003). We also believe that assessments of those learning objectives are critical in addressing students' perceptions as they would allow students to apply and receive feedback on that knowledge (Ambrose et al., 2010). While it has been recognized that the fluidity of engineering design makes it difficult to assess students and their work through the process (Bailey & Szabo, 2007), it is crucial that we develop assessment strategies that map to our expectations.

Interview protocol
Before beginning the interview, the researcher will go over the interview consent form with the participant.
All interviews aim to identify students' concrete decision-making behavior and their beliefs about the roles of different approaches to decision making. This will include the consistent use of follow-up questions such as, "why?" "why do you believe that?" "tell me more about that" and "what do you mean when you say that?".
We are interested in hearing about a decision that occurred when (1) you needed to make an explicit choice between multiple possible options, and (2) the choice had implications or mattered to your project.