A Teaching-as-Research project exploring conceptual instruction through in-class worksheets in CE 214 Statics
I have been thinking about the balance between conceptual understanding and problem solving for as long as I have been a teaching assistant. There is always a quiet pressure in engineering recitation rooms to move fast, to show students the steps, work through the examples, and get as many problems done as possible before the hour is up. And that pressure exists for a reason: engineering exams are relentless, and students need to be ready for them. But somewhere in that sprint through worked examples, I kept noticing something troubling. Students who could reproduce a solution perfectly, who had clearly memorized every step, would then sit completely frozen in front of a problem that looked even slightly different from what they had practiced. The procedure was there; the understanding was not.
That observation became the seed of this project. What if I deliberately slowed things down? What if, instead of working through yet another homework problem in recitation, I asked students to stop and articulate what a formula actually means, to write it in their own words, to sketch a free body diagram from memory, to fill in a structured worksheet that forced them to engage with the concept before the calculation? Would that feel valuable to them? Would they feel more confident? Would it change how they described their own learning?
This page documents what I set out to do, what I was actually able to execute given the realities of a semester-long teaching context, and most importantly what I found. The findings center not on exam performance, but on something I consider equally important and far less often measured: how students perceive their own learning, how their confidence manifests in language, and whether a structured conceptual review session shifted how they engaged with the material. My TAR question, my data, and my reflection all orbit around that core concern.
This project is situated in the CIRTL framework of Teaching-as-Research (CIRTL, 2024) — the idea that instructors can and should bring systematic inquiry to their own classrooms, using evidence to refine their teaching rather than relying purely on intuition. That framing gave me a vocabulary for what I had always intuitively wanted to do: make my teaching more deliberate, more responsive, and more honest about what I did not yet know.
Before I could design anything, I needed to know who I was teaching, not just their names on a roster, but their backgrounds, their preparation, their anxieties, and their expectations. CE 214 Statics is a compulsory engineering requirement for all undergraduate students in the College of Engineering at the University of Arizona. It is a foundational course: students who struggle here often carry that difficulty forward into more advanced design coursework. The class of approximately 60 students is divided into three TA-led discussion sections of 20–25 students each.
At the start of the semester, I administered a pre-survey (n = 18) to gather demographic information and establish a baseline picture of my students' preparation and confidence. I took inspiration from the situational factors framework described by the Center for Teaching and Learning at Buffalo (CATT, 2024): who are these learners, what are they bringing into the room, and what do I not yet know about them?
What struck me immediately about this demographic picture was its diversity, and not just in the visible sense. Nearly 39% of my students are first-generation college students. They range from freshmen still figuring out what engineering even looks like at the university level, to juniors and seniors who are taking Statics because it appeared as a prerequisite they had not yet cleared. They come from mechanical, civil, aerospace, chemical, biomedical, biosystems, and architectural engineering, each discipline carrying its own relationship to the kinds of forces and equilibria we discuss in CE 214.
Understanding this diversity mattered enormously for how I thought about my intervention. An inclusive instructional approach, as described in the CIRTL Learning-through-Diversity framework, requires attending to the full range of learner backgrounds and not designing only for the student who walked in most prepared (CIRTL, 2024). A structured conceptual worksheet, one that begins with definitions before jumping to problems is, in that sense, a form of access: it does not assume that every student has the same baseline internalization of the material.
What I found particularly meaningful was that not a single student reported completing prior math-intensive courses with a confidence level of 1 (very low), and none reported a 5 (very high). The vast majority sat at 3 or 4, functional, but cautious. They had survived calculus and physics. That tells me a great deal about what the emotional and cognitive starting point looks like for a typical student.
Every instructor has a hunch about where students are struggling. My hunch was specific: I did not think my students lacked the mathematical ability to succeed in Statics. What I suspected was that they had learned to treat mathematical problem-solving as a pattern-matching exercise, find the formula that looks right, plug in the numbers, get an answer. That strategy works well enough on practiced problems. It breaks down, sometimes dramatically, when the problem requires even a slight adaptation.
The pre-survey data confirmed this suspicion with striking clarity. When I asked students how they typically approached a new problem, and why they thought they got problems wrong, the answers painted a very consistent picture.
Student Self-Reported Confidence Across Five Dimensions (Pre-Survey, n=18)
Confidence in attempting new, unfamiliar problems had the lowest mean at approximately 2.57 out of 5 the only category where a meaningful share of students rated themselves at 1. By contrast, performing calculations accurately had a mean of about 3.22. This gap is important: students feel okay about the mechanics once they know what to do, but they feel genuinely unsure the moment the problem is unfamiliar. That is precisely the transfer gap I wanted to address.
The pre-survey also revealed something subtle about error attribution: 33.3% attributed their wrong answers to not recognizing which method to use, another 33.3% said calculation mistakes, and 22.2% said conceptual misunderstanding. The fact that students split almost evenly across three very different types of errors suggests they do not yet have a clear framework for diagnosing their own mistakes, a metacognitive gap that the diagnostic rubric component of my project was designed to address.
The Core Finding of the Pre-Survey
Two out of three students in my section (66.7%) entered the semester already self-aware enough to say: "I do well on practiced problems, but I struggle when the problem is unfamiliar." This is not just a learning challenge, it is a transfer problem. Students are not building mental models that generalize. They are building scripts that work in narrow contexts. The goal of my intervention was to begin interrupting that pattern by centering concepts before calculations.
One of the most validating parts of designing this TAR project was discovering that what I had been noticing intuitively in my section is a well-documented, deeply studied phenomenon in engineering education research. The patterns I was seeing, students applying formulas without understanding them, freezing on unfamiliar problems, conflating procedural fluency with conceptual mastery, have been described, analyzed, and theorized for decades.
Engineering mathematics is frequently taught in a traditional, didactic manner that encourages students to learn by repetition, memorizing the steps taken by instructors to solve highly theoretical problems (Ooi, 2007, as cited in Charalambides et al., 2023). As a result, students often view mathematics as a collection of symbols and rules rather than a tool for practical application (Charalambides et al., 2023). This "formalistic perspective," as Charalambides and colleagues term it, is exactly what I see when a student can execute a friction force problem step-by-step from a textbook example but cannot set up the free body diagram from scratch.
Progressive educators have noted for over a century that teaching mathematics without reference to engineering practice leads to students who merely know how to "juggle with quantities" to produce results, but lack the ability to adapt this knowledge to real-world engineering problems (Nyamapfene, 2015). That phrase, "juggling with quantities", has stuck with me since I first read it, because it captures so precisely what I was watching in my section every week.
Students struggle to apply math in engineering contexts, even when they perform well on traditional problem sets. When mathematics is taught "out of context" as an isolated subject, students fail to recognize the underlying engineering physics or the practical relevance of the equations they are solving (Nyamapfene, 2015). This "out-of-context" problem is particularly acute in a course like CE 214 Statics, where the equations are few but the conceptual reasoning required to apply them correctly is extensive. A student who cannot articulate why static friction reaches a maximum before kinetic friction begins will be unable to correctly identify which phase of friction applies to a given scenario, even if they can reproduce both friction force formulas from memory.
A significant number of students are admitted to engineering programs without sufficient mathematical backgrounds, and they are often unaware of how mathematically demanding their education will be (Charalambides et al., 2023). Furthermore, students' self-efficacy beliefs, their confidence in their ability to understand and solve difficult mathematical concepts, are significantly correlated with their academic performance and mathematical identity. Low-performing students often hold strong beliefs that success in mathematics depends on innate talent rather than hard work, which functions as a barrier to engagement (Charalambides et al., 2023). This finding is particularly relevant in a classroom where nearly 40% of students are first-generation college students, who may not have had access to the kinds of academic support structures that build mathematical confidence early.
The literature is equally consistent about what helps. Integrating practical, real-world engineering applications into foundational courses improves engagement, increases motivation, and fosters critical problem-solving skills (López-Díaz & Peña, 2021). Active learning strategies, including guided peer teaching, self-assessment, and structured recall, have a highly positive effect on students' cognitive behavior, persistence, and academic performance (Charalambides et al., 2023; López-Díaz & Peña, 2021). Perhaps most relevant to my specific design, writing-to-learn approaches, where students articulate concepts in their own words as part of structured activities, are consistently associated with deeper processing and stronger conceptual retention (Teaching Tools, 2024).
Critically, however, the literature also warns that instructional reform is slow and uneven. Despite clear evidence supporting curriculum redesign and contextualized teaching, changes frequently fail to take root due to lack of institutional capacity, insufficient pedagogical training, and a cultural reluctance among academics to move away from traditional monologue teaching practices (Nyamapfene, 2015; Charalambides et al., 2023). This is why a small, evidence-gathering intervention at the TA level, precisely what Teaching-as-Research enables, feels so important. I do not need to redesign the course to test whether conceptual review helps. I just need to systematically observe what happens when I offer it.
With the challenge identified and the literature mapped, my formal TAR question crystallized into this:
To assess these outcomes, I planned a combination of formative and summative approaches: pre- and post-course surveys with confidence rating scales, mini-surveys after each teaching intervention to capture immediate student perception, and comparative exam performance data across TA sections. This mix was designed to produce both quantitative and qualitative evidence about student learning (CIRTL, 2024).
The project originally proposed four instructional activities, each aligned to one or more learning outcomes and timed to occur before midterm and final assessments.
I want to be honest about the gap between what I planned and what I was able to implement. The semester moved faster than any proposal can account for. The guided peer teaching session did not materialise in a structured enough way to gather clean data. The pre-finals session was abandoned because attendance had dropped to a very small number of students, making it neither pedagogically fair nor data-rich enough to include. The diagnostic rubric, while shared informally, was not deployed as a formal data collection instrument.
What I was able to do twice before two different midterm exams was the in-class worksheet. And that turned out to be more than enough to generate genuine insight and was more impactful than I ever expected.
One of the most important lessons I am taking away from this TAR experience is that a project's value is not diminished by the distance between the proposal and the reality. The semester I planned for on paper in January 2026 was not the semester that unfolded. Students got busier as exams stacked up. Class attendance at the end of the semester became unpredictable. And the perfect moment for every planned activity rarely arrived with the clean timing the timeline diagram suggested.
But here is what I did do: I ran the in-class conceptual worksheet twice, once in mid-March, before Midterm 2, and once on April 29, before Midterm 3. The first session was attended by 8 students, and the next session witnessed a surge in the number of students to 17. This showcased, the effectiveness and the importance of the first session which led to increase in students showing up in the second session. Both sessions were followed by short mini-surveys. I administered a pre-survey at the start of the semester and a post-survey at the very end. The post-survey had only three respondents, too small to draw any general conclusions, but the qualitative signals it offered were very meaningful.
I want to describe the worksheet itself, because the form of the activity is central to why I believe it worked as well as it did. It was not a problem set. It was not a quiz. It was a 7-page structured document that I designed specifically to require students to retrieve and articulate concepts from memory before doing anything computational. Students were asked to write the formula for static friction force — just the formula, not a solved problem. They were asked to sketch a free body diagram. They were asked to complete the sentence "About the x-axis, the element considered is _____ to _____ axis." These prompts sound simple. But in a room full of students who had been doing weekly homework by searching for similar solved examples, they were genuinely challenging and genuinely productive.
This design philosophy was partially inspired by what I think of as the "kindergarten model" of learning: young children do not take self-notes during instruction; they fill out guided worksheets (in the form of letter books or half drawn doodles) that ask them to demonstrate understanding in the moment. The worksheet transferred that idea to an undergraduate engineering context. And I made it explicitly non-graded, which turned out to matter a great deal for how students engaged with it, there was no performance anxiety, only learning.
Eight students completed the mini-survey following the March worksheet session. The quantitative results were unambiguous: every single respondent rated the activity's relevance to the course as a 5 out of 5. Every student said they would want to do this again.
The April session produced equally strong results. This session saw a surge in students because this time students were informed before hand about the sessions and students from different sessions attended. 8 out of 17 students responded to the mini survey. Six of eight gave the activity a relevance score of 5/5; two gave a 4/5, yielding an average of 4.75/5. Every student said the activity was helpful, and every student said they would do it again.
Aggregated Mini-Survey Outcomes Across Both Sessions
Across 16 total responses (8 per session), the activity consistently received maximum positive ratings on all binary measures.
Post-Survey Confidence Ratings (n=3 Exploratory Only)
The post-survey administered at the end of the semester yielded only three responses, one student who had not attended any revision sessions, and two who had attended exactly one session each. This sample is too small to generalize from, and I want to be clear that I am not attempting to draw quantitative conclusions from it. What I can say is that both students who had attended a session reported that the revision activities helped improve their confidence, and their qualitative comment ("thank you for the pretest practice") is consistent with the mini-survey feedback from both sessions.
One pattern in the post-survey that I found genuinely interesting: all three post-survey respondents, regardless of whether they had attended sessions, reported "Identify relevant formulas immediately" as their first step when approaching a problem. This contrasts with the pre-survey, where 50% of students said they try to understand the physical or mathematical meaning first. I am cautious about over-interpreting this given the tiny sample, but it does raise a question worth pursuing in future iterations: does exam-season pressure push students back toward more mechanical, formula-first approaches, even if they have experienced conceptual instruction? That would be an important finding if confirmed with more data.
Numbers tell part of the story. But what I find most compelling, most genuinely illuminating, about this project is what students wrote in their own words. The mini-survey included one open-ended prompt: "Was this activity helpful in any way? I'd really appreciate your feedback, both on what worked well and what could be improved." The responses I received were not the polite non-committal answers I might have feared. They were specific, reflective, and in several cases, deeply honest about what the experience meant to them.
Reading these responses carefully, several themes emerge that I believe deserve individual attention in the analysis.
The comparison to traditional homework-based recitation is striking. One student wrote explicitly that they "got more out of this single discussion than any of the others I have attended so far" and contrasted the worksheet with "only working on 1 and half problems from the homework." This is not a mild preference; it is a substantive comparison of learning experiences by a student who has been attending discussions all semester. That student is telling me something important about what the typical session feels like versus what the worksheet session felt like.
The physicality of the worksheet was mentioned explicitly: "I enjoyed the step by step and a physical worksheet to fill out for reference rather than the normal just difficult problems as practice." This resonates with the "writing to learn" literature, there is something about the act of writing concepts by hand, filling in blanks, that creates a different cognitive relationship with the material than watching someone else write it on a whiteboard (Teaching Tools, 2024).
The most consistent feedback across both sessions: students wanted more time. The worksheet was designed to cover significant conceptual territory in a 50-minute recitation slot, and in both sessions, students reported feeling that the pace was ambitious. This is both a limitation and a design signal for future iterations. The fact that they wanted more time, not less, suggests the activity was genuinely engaging rather than something students were waiting to finish.
The comments about participation dynamics in Session 2, the student who appreciated that I "tried to get us to participate but would also move on if no one was responding", reflects a sophistication in the student-instructor relationship that I value deeply. They noticed that I was balancing two competing goods: drawing out participation and not letting awkward silence derail the learning flow. The March comment about "the silence of waiting for someone to answer" becoming awkward is something I had already tried to address by April, and the April feedback suggests that adjustment was noticed.
Stepping back from the specific data points and looking at the shape of the findings as a whole, I think this project demonstrates something that I will be carrying into every classroom I inhabit for the rest of my teaching career: students are hungry for conceptual structure. Not more problems, but structure. Not faster coverage, but clarity. The worksheet did not give students new information they did not already have access to. It gave them a format for accessing the information they already had, in a way that made the underlying logic visible rather than implicit.
The pattern I documented in CE 214 students who can execute practiced procedures but freeze on novel problems is a known and documented challenge across STEM education. It is present in linear algebra, thermodynamics, circuit analysis, organic chemistry, and every other course where procedural fluency is mistaken for conceptual understanding. The specific worksheet I designed is Statics-specific, but the format is transferable. Any instructor in any mathematically intensive course could:
Design a short, structured pre-exam conceptual worksheet that asks students to write definitions, explain formulas in plain language, draw relevant diagrams from memory, and complete prompted sentences about physical meaning. Make it non-graded, explicitly positioning it as a learning tool rather than an assessment. Facilitate it actively, not as a passive exercise students complete alone, but as a structured class conversation that the worksheet anchors. Collect brief post-activity feedback to understand how students are experiencing it.
This is a low-cost, high-signal instructional intervention that does not require curriculum redesign, course restructuring, or institutional support. It requires only a TA or instructor willing to give up one recitation's worth of problem-solving time in exchange for an hour of conceptual consolidation. The fact that students in both sessions asked for this format to become a regular part of their learning experience is, I think, one of the most practically actionable findings of this project.
The Finding That Moves Me Most
One student wrote that they "got more out of this single discussion than any of the others [they had] attended so far." That student had been coming to recitation all semester. They were comparing this session, a worksheet, a piece of paper with blanks to fill in, to a full semester of traditional TA-led problem-solving sessions. I am not claiming the worksheet is categorically superior to all other instructional formats. But I am claiming that for this student, in this moment, being asked to slow down and explain rather than calculate opened something up. That is worth taking seriously.
Time management. Both sessions produced feedback about feeling rushed, and I take that seriously. The worksheet was ambitious in scope, it covered three full chapters, and the 50-minute recitation slot was not quite large enough to do it justice without some students feeling like they were sprinting. In future iterations, I would either (a) reduce the scope of the worksheet to cover two chapters instead of three, or (b) coordinate with the instructor to borrow additional time. The ambition of the content is a feature, not a bug, but the pacing needs to respect that processing conceptual material takes time.
I would like to explore the post-survey finding about formula-first approaches more systematically. If exam-season pressure genuinely pushes students back toward mechanical, formula-first reasoning even after they have experienced conceptual instruction, that has implications for when and how often interventions like this should occur. Perhaps one session per exam cycle is not enough. Perhaps the workshop needs to be embedded earlier in the exam-preparation timeline, giving students more opportunity to consolidate the conceptual scaffolding before the exam stress intensifies.
I want to end this, not with a tidy conclusion but with a genuine reflection on what this project has changed in me as a teacher and an educator.
Before this project, I had an intuition that conceptual instruction mattered. I had watched students freeze on unfamiliar problems enough times to feel certain that something was missing in the standard approach. But an intuition is not evidence, and I have learned through this TAR experience that there is a profound difference between knowing something intuitively and having evidence for it. The evidence changes how I speak about my teaching, how I justify my choices to colleagues and to myself, and how I design future sessions with specificity rather than vague good intentions.
The student who wrote that they "got more out of this single discussion than any of the others they had attended so far", I think about that comment often. Not because it is flattering (though I will not pretend it is not), but because it contains a challenge. If a single structured conceptual session can generate that response, what are we doing in all the other sessions? What is the baseline do we compare to? That question makes me uncomfortable in exactly the way good research questions should.
Going forward, I am committed to three things. First, I will design at least one structured conceptual review session before every major assessment in any course I teach, and I will make it an explicit, visible, named part of the course structure rather than a one-off addition. Second, I will treat student feedback, including mid-semester feedback, not just end-of-semester evaluations, as evidence to act on in real time, not simply as data to report. The adjustment I made between Session 1 and Session 2 based on feedback about participation dynamics is the model I want to scale. Third, I want to share this with every graduate student and early career educator to think about this research and what role it can play in their own teaching pedagogy. The Chronicle of Higher Education's guidance on inclusive teaching argues that sharing effective practices across instructors is itself a form of equity work (Chronicle, 2020). I believe that.
The answer to my TAR question, based on the evidence I collected, is this: concept-focused instruction, even in a single, non-graded, 50-minute session using a structured worksheet, consistently produced strong positive learning perception among students in CE 214 Statics. Students found it relevant, helpful, and worthy of repetition. They described it as a qualitatively different experience from the standard problem-based recitation format. They asked for more of it. That is not a controlled experiment. But it is evidence, gathered systematically, by a teacher who started with a question and ended with clearer sight.
I would like to extend my sincere gratitude to Dr. Kristen Winet for providing me with the opportunity, mentorship, and guidance necessary to conceptualize, plan, and implement this project. Her support throughout this journey has significantly shaped my growth as an educator and researcher. I am also deeply thankful to Dr. Emily Jo Schwaller for her mentorship through the teaching writing course, which introduced me to the concept of “writing-to-learn” pedagogies. The knowledge, feedback, and practice I gained in her class inspired the design of the conceptual worksheets used in this project.
My sincere thanks also go to Dr. Tribikram Kundu for supporting the implementation of this project within the discussion sections of CE 214 Statics and for alway encouraging me in my endevours. Finally, I would like to thank the Department of Civil and Architectural Engineering and Mechanics at the University of Arizona for providing me with teaching assistant opportunities during Spring 2025 and Fall 2025 . Those experiences not only strengthened my confidence, but also instilled in me a genuine love for teaching, mentoring, and supporting student learning.
Shruti Singh is a PhD candidate in Civil and Architectural Engineering and Mechanics at the College of Engineering, University of Arizona, where she studies sustainable construction materials and structural health monitoring using non-destructive testing techniques. Originally from Gorakhpur, Uttar Pradesh, India, Shruti completed her bachelor’s degree at IIT Roorkee in 2024 before moving across the world to Arizona, driven, as she likes to say, “by a love for concrete.” She later earned her MS from the University of Arizona in 2025.
Her research sits at the intersection of materials, mechanics, and sustainability, with a focus on understanding how innovative construction materials can be made smarter, stronger, and more resilient for the future. Deeply passionate about both research and education, Shruti hopes to one day lead her own research lab as a professor, mentoring and teaching the next generation of engineers, researchers, and problem-solvers.
Beyond the lab and classroom, Shruti enjoys hiking through the trails of the Sonoran Desert, experimenting with new recipes in the kitchen, and staying connected with family and friends nearly 8,000 miles away. She is also an enthusiastic traveller who loves exploring new places whenever she can carve out time between research deadlines and concrete mixes.
At the heart of her work is a simple belief: engineering is not just about calculations and equations, but about building systems, communities, and ideas that make life better.
For comments, questions, collaborations, or general inquiries, feel free to contact her at shrutis@arizona.edu
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Kuzmar, A. S. (2024). Mathematicians and scientists teaching engineering courses: Practices, advantages, and concerns. Proceedings of the American Society for Engineering Education (ASEE) Annual Conference.
López-Díaz, M. T., & Peña, M. (2021). Mathematics training in engineering degrees: An intervention from teaching staff to students. Mathematics, 9(13), 1475. https://doi.org/10.3390/math9131475
Nyamapfene, A. (2015, August 8; updated 2020, December 19). Reforming engineering mathematics teaching: A century-old debate. Engineering Learning & Teaching. https://engineeringedu.press/2015/08/08/18/
Ooi, A. (2007). An analysis of the teaching of mathematics in undergraduate engineering courses. Proceedings of the Australasian Association for Engineering Education (AAEE) Conference, Melbourne, Australia.
Teaching Tools. (2024). Active learning activities. https://teaching.tools/activities
Weimer, M. (2020, November 18). How to make your teaching more inclusive. The Chronicle of Higher Education. https://www.chronicle.com/article/how-to-make-your-teaching-more-inclusive/
Perplexity was utilized to assist with the literature review process and to identify relevant scholarly resources related to engineering education and concept-based learning. NotebookLM was used to help generate portions of the worksheet structure based on teaching slides and instructional materials created for the CE 214 discussion sessions. Grammarly was used to edit and rephrase parts of this webpage. The written analysis, interpretation, project design, implementation, reflections, survey analysis, and conclusions were developed by the author. All research data collected, instructional activities conducted, and findings presented in this project are original work carried out by the author.