"Making Math More Meaningful: Peer-Led Workshops Use Context to Connect First-Year Engineers to Content and to Society"

Research Paper Recommended citation: Evans, C. A., Sauve, R., & Schneider-Bentley, L. (2025). "Making Math More Meaningful: Peer-Led Workshops Use Context to Connect First-Year Engineers to Content and to Society". In Kangaslampi, R., Langie, G., Järvinen, H.-M., & Nagy, B. (Eds.), SEFI 53rd Annual Conference. European Society for Engineering Education (SEFI), Tampere, Finland. DOI: 10.5281/zenodo.17631251. This Conference Paper is brought to you for open access by the 53rd Annual Conference of the European Society for Engineering Education (SEFI) at Tampere University in Tampere, Finland. This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License. MAKING ENGINEERING MATH MORE MEANINGFUL: PEER-LED WORKSHOPS USE CONTEXT TO CONNECT FIRST-YEAR STUDENTS TO CONTENT AND SOCIETY C.A. Evans a,1, R.T. Sauvé b, L.M. Schneider-Bentley c, a Cornell University, College of Engineering, Ithaca, USA, 0009-0001-3528-2146 b Cornell University, College of Engineering, Ithaca, USA, c Cornell University, College of Engineering, Ithaca, USA, Conference Key Areas: Dialogue between engineering and society-effects on education, Diversity, Equity, and Inclusion in our universities and in our teaching Keywords: Peer educators, context, relevance, math, society ABSTRACT Research shows that framing math content using real-life and social context can improve understanding, engagement, and retention, and expose engineering students to social and engineering relevance of otherwise abstract seeming concepts. At large institutions, peer-led learning in the form of supplementary workshops associated with first (and second) year courses may be taken by a large proportion of students. Trained peer educators have been shown to be effective facilitators and mentors as they build community and engage students in small group collaborative problem solving. This study examined the efficacy and the challenges of incorporating contextualized problems into peer-led engineering math workshops that parallel large lecture courses. Results suggest peer educators can effectively develop and implement contextualized math problems as part of their workshops. The problems, overall, increased content understanding, introduced new engineering and social relevance, and for many students were enjoyable and challenging. Data show that there are some important gender and ethnicity differences in the perception of the value of the problems which will need to be addressed with structure and pedagogy as we analyze the problems and facilitator experience going forward. 1 Corresponding Author C.A. Evans [email protected] 1 INTRODUCTION Introduction The role of contextualized problems in Engineering Education Tangible, real-life context of the problems engineers tackle in their work are often excluded in engineering courses, particularly early in curricula (Leydens and Lucena, 2017). The lack of relevant context in the problems engineering students practice may result in students’ incorrect framing of engineering as a completely technical profession, rather than one that serves people and always has implications for society (Leydens et al. 2021). Ostensibly, one result of this is that students who are inspired to become engineers to do social good, make change, or because it is in line with their personal values, meet with few opportunities to learn how the skills they gain in the early curricular courses (i.e. mathematics series) can be used in real world contexts toward valued purpose. Wint (2022) analyzed the digital stories of 82 engineering students describing why they chose to study engineering. Forty-one percent of the students articulated their interest in engineering was associated with a desire to serve society, 21% mentioned working toward sustainability, and 16% discussed social justice as their motivation. In contrast, others reported being interested in engineering because they have strong skills and comfort with mathematics. These students may not be comfortable or aware of the way in which these skills are applied in engineering work (Wint 2022). In both cases, these reasons motivate the value of exposing early engineering students to relevance and social context into seemingly abstract math content. Exposing engineering students to ethical discussions and dilemmas including social issues (Leydens et al 2021) is valuable because of the persistent student belief that engineering is dominantly a technical profession. Cech (2013) found that engineering students (326 students from 4 US Universities) belief in the importance of several measures related to social/public welfare components of engineering decreased over the course of their education. Engaging students whose ways of knowing are strongly influenced by sense-making (Danieliak et al, 2014), and building opportunities for students to see their own (marginalized) identities reflected in applied engineering problems (Ozkan and Andrews, 2022), may positively impact a sense of belonging which can improve retention of a more heterogeneous group of thinkers and diverse student body (Walton and Cohen, 2011). Women engineering students may also value social consciousness more than the technological leadership (Cech, 2014), therefore, exposing women students to more contextualized questions may engage their interest and support this classically under-represented population. The potential of peer education to improve student experience and achievement in engineering programs A growing body of research supports the idea that peer-led learning models can significantly benefit student learning (Bengasai et al, 2023; Lewis, 2011,) At large universities using peer-led learning, high proportions of first year students take advantage of peer-led workshops (Sauve et al, 2024), thus there is potential for strategies enacted in these learning spaces to impact a high proportion of first year students. In the College of Engineering at Cornell University, USA, in Academic Years 2021-2022 and 2022-2023 between 40 and 45 % of first year students enrolled in at least one peer-led Academic Excellence Workshop. Over 90% of students in peer-led workshops ‘agreed or strongly agreed’(anonymously) that they felt respected, and greater than 70% of students reported an increase in sense of belonging to the college community (Sauve et al,2024). Women, Black, and Hispanic students enroll in workshops in a higher proportion relative to their representation in the lecture courses that workshops parallel. As a result, the effects of workshops on learning outcomes have the potential to disproportionately impact these populations, making it even more critical to understand students varied responses to the structure and function of these learning communities (Sauve et al 2024). When undergraduate peer educators are trained to use evidence-based facilitation practices and to employ strategies that build community, they create a sense of belonging and improve the confidence and understanding of challenging engineering material (Sauve et al, 2024, Luckie et al 2019; Schneider and Terrell, 2010). Engaging students in the teaching and learning process, careful structuring and guiding of students during collaborative work, and providing opportunities for students to reflect (‘auxilliary questions’) on both the math and the social context can lead to ‘meaningful’ learning in math (Koskinen and Pitkaniemi, 2022). This exploration of introducing contextualized problems (CPs) into peer facilitatordesigned workshops is the first step in understanding the potential to use and enhance peer educators’ skills to make opportunities to embed more social context into engineering programs outside of the formal curriculum. Ultimately, if we can determine the various ways that setting engineering math problems in a broader context can impact student learning and motivation (including for diverse demographics), and if we train peer educators to design and implement effective CPs in their learning environments, we will have yet another tool that can support student success. This would help to fill a noted gap in engineering curricula (Leydens et al., 2021). Research Questions Our overarching research goal was to determine if peer led workshops can play a positive role in exposing early engineering students to the real-life application and social context of some of the concepts they are learning in core engineering math courses. We asked: 1) What are the perceived values and challenges of incorporating contextualized problems in core math courses for engineering students, and 2) What are the perceived values and challenges of developing and facilitating contextualized problems for peer educators). Within each of these questions, considering the long-standing barriers to women and other persistently under-represented student populations in engineering programs, we were also interested in how the direction and strength of those outcomes are influenced by gender and ethnicity and their complex intersectionality. Note that we embrace that students have a broad range of gender identities. In our study (at this time) only 4 participants identified as other choices and thus we are not able to examine these data in the context of that broader, more realistic range of gender identities. For students in the workshops we explored the value and challenges of working on contextualized problems in relations to themes of motivation and engagement, understanding of course content, problem solving and critical thinking, relevance to careers and gaining new social perspectives and preparation for course exams. For peer educators, who developed the workshop structure and problems, we will examine the experience of developing and guiding contextualized problem solving with respect to the same themes, as we move the work forward. 2 METHODOLOGY 2.1 Recruiting and selecting peer educators We limited data collection to workshops associated with core mathematics courses for engineers (single variable calculus n=2, multivariable calculus n=2, differential equations n=1, and statics n=1). Peer educators were invited to participate partially based on our knowledge of their skills and also based on their responses to answers to a discussion prompt after they had participated in a 1-hour presentation and question session entitled “Contextualizing Engineering/Math Problems” by Dr. John Leydens, engineering educator and researcher. A subset of experienced facilitators who expressed the belief that these problems had value in their own experience, or they felt they would be valuable for a variety of reasons were invited, with their cofacilitator, to participate. We asked these 6 teams to commit to developing and implementing at least 3 problems as part of at least three or more workshops during the rest of the fall semester. 2.2 Designing and implementing problems Peer educators were given free range with respect to the topic they chose to contextualize, and social context they chose for the problem. They were encouraged to choose 3-5 topics during the semester which would be most helpful or appropriate to develop a contextualized problem. Examples were provided. One to three reflection questions about the context were also developed and peer educators were encouraged to facilitate the problems in the middle of the workshops after retrieving concepts and practicing related non-contextualized problems, using the typical small group collaboration. Ten minutes were allotted for facilitation and discussion of the problems and reflections. 2.3 Data Collection In the six participating workshops over the course of 10 weeks, we collected 132 participant survey responses to 18 CPs. Variability in workshop size and student choice in completing surveys resulted in a range of survey responses/question (1 – 17) with a median of seven survey responses per question. After completing each CP, students immediately accessed an 8-question online survey (questions included in Table 1) that also asked them to identify gender and ethnicity. Four responses did not specify gender, thus they were not included in analyses that included gender effects or interactions. Peer educator pairs completed a survey together after each contextualized problem to reflect on their experience (data not analyzed in this paper). Peer educators uploaded the contextualized questions (as presented to the students) and the solutions into an online folder for characterization. At the end of the semester, we invited participating peer educators to a focus group to invite them to individually and collectively reflect on the experience. We collected written reflections and recorded and transcribed audio from a zoom meeting used only for the audio recording purpose (analysis not reported in this paper). 2.4 Data Analysis Student responses to survey questions were analyzed using contingency analyses Due to small sample sizes in some contingency tables, we calculated Fisher Exact probabilities (two-sided) for all outcomes. 3 RESULTS AND DISCUSSION 3.1 Student Overall Responses. The overall response to CPs were positive for each of the categories we examined. In over two-thirds of surveys, participants agreed or strongly agreed that the problems improved understanding of the concepts as compared to non-CPs. In greater than 50% of surveys, students agreed or strongly agreed that the problems introduced relevance associated with the material, and/or some new thinking about the social value of engineering. Lopez-Diaz and Pena (2022) also reported positive self-reported outcomes when real-world problems were included in a multivariate calculus course as a seminar between 2019 and 2021. In our population, approximately one-third of all responses reported enjoying working on the problems more than basic problems, and 43 and 21 percent reported equal or less enjoyment respectively. The contextualized problems were perceived as requiring more thinking (or different ways of thinking) than non-CPs (Table 1). Students who found the problems more enjoyable remarked about the value of working on something that seemed ‘real’, or enjoying the challenge of having to think differently - “(the problem was) more applicable and felt like I was working on something that seemed more ‘real’, was definitely more enjoyable”, and “This problem was a bit more challenging than usual problems.” Those who found the problems less enjoyable commented on a lack of preparedness with understanding the fundamental concepts, or having a difficult time understanding what the problem was asking, for example, ”It was hard to understand and I haven’t practiced this concept a lot outside of class.” These outcomes are consistent with learning strategies models that articulate the importance of scaffolding learning across phases (‘surface,’ ‘deep’ learning, and ‘transfer’ learning). The introduction of context to seemingly abstract math problems is beneficial when students have already learned the material at the surface level (Hattie & Donoghue, 2016) 3.2 Response By Gender, Ethnicity, and Intersectionality There is the potential for gender and ethnicity differences in the perception of the value of workshops for improving performance and for building confidence (Evans et al, 2024; Sauve et al, 2024). It is critical that as we consider adding CPs as a new feature, we learn more about the sometimes-complex responses in populations that have been systemically under-represented in engineering. A larger proportion of men students found CPs more enjoyable than did female students (p= 0.06, two-tailed). While both women and men students reported a benefit to understanding concepts and seeing relevance to their future, women students agreed significantly more than men that they learned something new about the social value of engineering (p=0.02, two-tailed) (Table 2.). The finding that more men find CPs enjoyable as compared to women appears to be a broad outcome for women, irrespective of ethnicity, and there were no gender or ethnicity differences regarding the greater challenge of such problems. Overall, content understanding was improved by collaborating on these questions, however 81% of Asian women ‘somewhat agreed’ with increased understanding as compared to a more evenly distributed range of responses by Asian men (Table 3.). Table 1.Summary table of student responses to survey questions following implementation of each contextualized problem. For questions 3-8, % Agree and % Disagree include the sums of strongly and somewhat (n=132 responses) Survey Question % More % Same % Less 1. Working on this contextualized problem was _________ enjoyable than a typical non-contextualized question of the same topic 36 43 21 % More or %Different % Same % Less 2. Working on this contextualized problem required_____________ 'thinking' than a non-contextualized problem on the same topic 85 39 8 % Agree and Strongly Agree % Neutral % Disagree and Strongly Disagree 3. This contextualized problem helped me understand the topic better than a non-conceptualized problem 69 20 11 4. The contextualized problem helped me see the relevance of the topic to my education, life, or future career 66 21 14 5. Working on the contextualized question helped me see something new about the social value of engineering in general 57 25 18 6. Working on this contextualized problem generated some good conversation about the context with my peers 64 21 15 7. Working on the contextualized question helped me feel more prepared for the course exam 50 31 19 8. Working on the contextualized problem was NOT beneficial with respect to preparing me for the course exam 22 25 53 Table 2. Table of significant differences in student response by gender questions 1 and 5. % Agree and % Disagree include the sums of strongly and somewhat %. Neither agree nor disagree is removed in the table for ease of interpretation, however all data were included in the contingency analysis (n=128). 1. Working on this contextualized problem was _________ enjoyable than a typical non-contextualized question of the same topic % Women % Men %All responses Fishers Exact Probability Twosided p value more 27 47 37 2.00E-03 0.06 less 25 19 22 the same 48 34 41 5. Working on the contextualized question helped me see something new about the social value of engineering in general? % Women % Men %All responses Fishers Exact Probability Twosided p value %Agree 71 44 57 6.40E-06 0.02 % Disagree 13 23 18 The strongest gender by ethnicity effect was in women who identified as White, compared to their men counterparts with respect to the questions about the benefit of CPs for revealing relevance and social value of these math topics in students. Fifty-six percent of White women strongly agreed that the CPs allowed them to see relevance to their education or future career, as compared to 13% of White men. A similar outcome for White women was seen for the other social value of engineering question. With respect to preparation for exams, fifty percent of Black women ‘somewhat disagreed’ that the CPs prepared them for exams, while black men were equally’ neutral’ or ‘somewhat agreed’. CONCLUSIONS Peer educators can effectively develop and implement contextualized math problems as part of their workshops. Overall, CPs increased understanding, introduced career and social relevance (particularly for women students), and for many students were enjoyable and challenging. In peer-supported disciplinary learning workshop models, where consistently underrepresented engineering students are enrolled at higher relative percentages, peer-led learning spaces are a clear opportunity to impact the quality of education experienced by students. Key considerations in the overall success of implementing CP’s are 1) training peer educators to scaffold the ‘surface learning’ of concepts before the CP is implemented so that deeper or transfer learning can occur, and, 2) interrogating and mitigating important gender and ethnicity differences in the perception of the value of the problems to improve benefits for all participants in these workshops. Linking previous research on the value of peer-led collaborative workshops for confidence and belonging of participants, with careful scaffolding of the inclusion of CPs, will improve the efficacy and support the systematic inclusion of CPs into these workshops to make engineering math more relevant and enjoyable, and to develop deeper content understanding. Table 3.Statistically significant gender response differences (table probability, P value, Fishers Exact test) by ethnicity (self-identified) compared to the overall comparison of male and female participants as whole (final column). Note sample size for Ethnicities are smaller than sample size for gender because these student demographics had sample sizes large enough to evaluate. Survey Question Responses Across Gender, Within Ethnicity Group Overall Responses Asian White Black/Hispanic By Gender Female Male Female Male Female Male Female Male n=16 n=15 n=16 n=32 n=12 n=12 n= 64 n= 64 Working on this contextualized problem was _________ enjoyable than a typical noncontextualized question of the same topic 0.019, p= 0.17 0.06, p= 0.78 0.124, p= 1.00 0.002, p= 0.06 This contextualized problem helped me understand the topic better 0.002, p= 0.02 0.01, p= 0.74 0.02, p= 0.52 0.002, p= 0.91 The contextualized problem helped me see the relevance of the topic to my education, life, or career 0.001, p= 0.14 0.000, p< 0.001 0.133, p= 1.00 0.0005, p= 0.57 Working on the contextualized question helped me see something new about the social value of engineering in general 0.006, p= 0.53 0.0003, p= 0.06 0.05, p= 0.45 0.0000, p= 0.02 Working on the contextualized question helped me feel more prepared for the course exam 0.022, p= 0.82 0.009, p= 0.66 0.002, p= 0.02 0.0017, p= 0.88