As classroom sizes expand, educators increasingly need scalable, targeted feedback mechanisms to support student engagement. πΆπ250, an undergraduate core course in discrete mathematics at UMass Amherst, covers key topics such as logic, elementary number theory, proof by induction, recursion, search algorithms, regular languages, finite state machines, and aspects of computability [1]. These concepts challenge students due to their abstract nature and the logical precision they demand.
To address these challenges, the author developed a Reusable Learning Object (RLO), which refers to "any digital resource that can be reused to support learning" [2]. The RLO incorporates modular, adaptable resources that support specific educational goals. In this context, the RLO focuses on simplifying complex topics in πΆπ250 through interactive and reusable digital content, helping students engage independently with difficult concepts, especially those involving regular expressions.
The RLO includes several key components: a Pythonbased interactive tool for answer verification, structured practice exercises, and integrated feedback mechanisms that guide students through the learning process. Designed to actively support students, the RLO delivers immediate feedback to help them correct errors and strengthen their understanding. During the study, the author assigned a treatment group to use the RLO for regular expression exercises, where students received instant feedback as they practiced. The study also included pre-and post-surveys with the treatment group, capturing changes in understanding and perceptions.
Survey responses indicated that the RLO was primarily used for reinforcing course material and problem-solving skills, with many participants planning to apply these skills directly to their πΆπ250 assignments and exams. Participant #2 noted, "Yes, it was very useful in helping check work, " while Participant #5 highlighted the tool's benefit in understanding regular expressions, stating, "I would recommend it to others because it was helpful in understanding how regex are set up." However, some participants felt the tool's feedback was not sufficiently personalized, as Participant #6 remarked, "It wasn't personalized, but it was useful, " indicating that while beneficial, it did not offer individualized guidance.
A number of participants also suggested improvements to make the tool more user-friendly and accessible. For instance, Participant #3 recommended "more language options" and "text-to-speech" functionality, reflecting a Andre Kenneth Chase Randall CEUR Workshop Proceedings 1-9 desire for inclusive design to meet diverse learning needs. Initial usability challenges were also reported, with Participant #1 mentioning, "I wasn't sure how to use the tool at first, " emphasizing the importance of an intuitive user experience. Participant #15 expressed reluctance to recommend the tool, commenting, "I would not recommend the tool to others; it did not explain very much and took a long time to run, " highlighting areas for improvement in efficiency and instructional depth. While the RLO was seen as helpful for coursework, some participants were uncertain about its long-term applicability, as Participant #12 noted, "I do not plan to use it in my personal life," suggesting that its perceived value was largely limited to immediate academic goals.
Through an iterative design process, the author structured the RLO to enhance student engagement by allowing them to interact with content at their own pace. In this paper, the author uses the terms "Learning Object" and "Reusable Learning Object" interchangeably to describe these modular educational resources [3].
Beyond promoting independent learning, the RLO aims to increase engagement, strengthen problemsolving skills, and improve students' ability to master abstract mathematical concepts. Prior research highlights how learning analytics and feedback within RLOs can enhance learning outcomes, especially in skill-based subjects like those in πΆπ250 [4,5] The next sections address the related works, the study design, development, and testing to ensure the RLO's reusability. Finally, the author outlined a plan for a proof of concept, drawing from the doctoral program insights, related works and testing within real-world educational contexts. Future endeavors, especially in the context of a doctoral program, require continuous refinement and optimization of the initial concept as presented herein to achieve the best outcomes.
As classroom sizes expand, educators face increased challenges in providing scalable, targeted feedback based on student engagement [6]. The application of AI in education addresses these issues through tools like Intelligent Tutoring Systems (ITS), adaptive content creation, and automated administrative tasks [7,8]. AI in education combines multiple fields-learning science, human-computer interaction (HCI), software engineering, natural language processing (NLP), and machine learning (ML) [9]. However, developing effective ITS tools requires seamless integration of advanced algorithms, deep pedagogical knowledge, and user-centered design [10]. Steve Blank's Customer Discovery framework, as outlined in the NSF I-Corps Teaching Handbook, reinforces this interdisciplinary approach by emphasizing iterative development and user feedback, ensuring that adaptive tools like ITS are aligned with real-world educational needs and specific challenges faced by students, instructors, and administrators [11]. This process aligns with AI's objectives in education by fostering adaptable and scalable solutions suitable for diverse learning contexts.
Implementing a SWOT (Strengths, Weaknesses, Opportunities, Threats) analysis further aids in evaluating the feasibility of adaptive learning technologies, identifying strengths like personalized learning pathways and addressing limitations such as data privacy concerns [? ]. Together, Steve Blank's framework and SWOT analysis underscore the importance of developing adaptive educational tools that effectively respond to the evolving needs of educational stakeholders [8].
Moreover, adaptive algorithms similar to those employed in fields like gaming-where neural networks, enhanced by genetic algorithms, refine responses based on real-time performance feedback-illustrate how iterative adaptation could similarly benefit educational contexts [12]. Such an approach could allow educational AI systems to adjust dynamically to varying learner progressions, supporting engagement and promoting personalized learning paths across diverse skill levels.
The study design happened as an iterative process. First the authored created a pilot project as a proof of concept. Thereafter, the author became the entrepreneurial lead for Team Intelligent Tutoring Systems R Us. Team Intelligent Tutoring Systems R Us obtained U. S. National Science Foundation's Innovation Corps (I -Corpsβ’) Customer Discovery Project funding.
As part of teaching assistant preparation course, the author and classmates conducted a pilot study without Institution Review Board (IRB) approval. The pilot study ended with 147 participants in March-May 2022.
In pilot study, they introduced a python script and sought to probe students' reactions to its usefulness as a RLO.
They designed the RLO to enhance the students' understanding of a regular expressions. During the pilot study, they gave participants the Python script along with instructional materials for completing a series of tasks. The study concluded with a survey featuring open-ended questions to collect qualitative data on the students' experiences and feedback.
The survey responses varied significantly. Over 31.3% of participants reported "no challenges," indicating a smooth experience with the Python script. In contrast, under 15.6% of participants expressed difficulties, with comments such as "I found the instructions hard to follow and get the code running. " These responses highlighted areas for instructional materials improvements.
Additionally, 24.7% of participants, particularly those majoring in computer science, showed motivation towards the concept of using programming in their coursework. These students appreciated the practical application of programming skills and expressed interest in further integrating such tools into their studies.
Overall, the pilot study provided valuable insights into the effectiveness of the RLO and the Python script. The feedback collected not only show improved student learning experience but also aided the instructional materials refinement as part of an IRB protocol (See Figure#1).
The National Science Foundation (NSF) I-Corps Teams program provides an intensive seven-week entrepreneurship training course with mentorship and funding for customer discovery. As part of this program, the author led Team Intelligent Tutoring Systems R Us as the entrepreneurial lead, receiving a travel grant supported by Cornell Tech and the National GEM Consortium to explore market potential for the Reusable Learning Object (RLO) project [13].
The I-Corps program guided the team in conducting a hybrid field study to test initial hypotheses and make adaptive pivots. Insights from customer discovery interviews were essential in refining the RLO's interface and feedback mechanisms. This process identified key challenges, value propositions, and market opportunities, structured within a business model framework as illustrated in the SWOT analysis (See Figure 2). Future work includes developing a comprehensive Strengths, Weaknesses, Opportunities, and Threats (SWOT) analysis as preparation for a national I-Corps application and further expanding the study's scope.
The team initially accepted the null hypothesis but discovered a strategic pivot by broadening customer segmentation beyond the host institution. This pivot enabled the development of a more dynamic business model, continuously revised through customer insights. Aligning with Woolf et al.'s AI Grand Challenges, future goals include creating intelligent tutoring systems, real-world simulation environments, and natural language processing capabilities to enhance adaptive learning [8,7].
This study employed a mixed-methods research design, consisting of both quantitative and qualitative data collection and analysis. The author conducted three phases:
β’ Phase 1: Literature Review and Case Studies. The first phase of the study involved another comprehensive review of the literature on the use of AI in Education. This phase helped to identify best practices and potential challenges associated with using AI in Education. During this phase, the author worked with an undergraduate student to complete an Honors Thesis Project, where the author served as a committee member. β’ Phase 2: Surveys and Interviews. The second phase of the study involved the administration of surveys and interviews to educators, teaching assistants, and students. The surveys and interviews assess perceptions of RLOs and its potential impact and other considerations. β’ Phase 3: Analysis and Synthesis. The third phase of the study involved the analysis and synthesis of the data collected in phases 1 and 2. Quantitative data analyzed using descriptive and inferential statistics, while qualitative data analyzed using content analysis. The results of the analysis synthesized to identify best practices and potential recommendations for future research and practice.
After beginning Phase 1, the author collaborated with an undergraduate student on the Honors Thesis Project committee to explore educators' mental models and perspectives on how RLOs impact learning. Key research questions included:
1. How does the RLO compare with traditional methods in understanding regular expressions? 2. How does the RLO shape students' problemsolving skills? 3. Does RLO use deepen understanding of automata principles? 4. What is the connection between RLO engagement and CS250 performance? 5. How do demographics correlate with learning outcomes?
The entire process adhered to ethical guidelines outlined in the IRB protocols #5139 "Team Chase Undergraduate Research Volunteers (URV)" and #5358 "AI in Education and Automata Theory: Synthesis Proposal".
Before conducting interviews with educators, participants were required to provide informed consent. The consent form outlined the purpose of the semi-structured interview, which aimed to contribute to an honors thesis exploring adaptive learning tools for future-generation technologies within the realm of AI in educational Reusable Learning Objects (RLOs). The research study was designed to unpack the mental models surrounding AI in education. Eligible participants for the study included instructors and teaching assistants specializing in areas such as proofs, induction, reason, number theory, automata theory, regular expressions, finite state machines, and related courses. We informed participants that the interview lasted approximately 20 minutes and primarily focused on soliciting their opinions and views regarding their experience with curriculum development and AI in Education, as well as related research topics. The interview posed minimal risks such as potential fatigue or boredom. We disclosed risks and encouraged to adhere to the 20-20-20 rule for eyestrain and to maintain hydration throughout the interview. The 20-20-20 rule advises taking a 20-second break from looking at screens every 20 minutes. During this break, focus on something at least 20 feet away. This practice helps prevent eye strain and fatigue caused by prolonged screen use. The consent form also covered data privacy, assuring participants that personal information would be handled confidentially with the IRB protocols. Data collection will be conducted anonymously with transcribed interviews in the study's codebook. Communication on any concerns was encouraged throughout the interview as well. The consent form process and interview protocol were carefully designed to uphold ethical standards, ensure participant confidentiality and comfort, and facilitate valuable insights into participants' mental models surrounding AI in education.
We designed the questions to explore educators' mental models regarding their teaching experiences and perspectives on adaptive learning tools. Some questions were adapted from the I-Corps customer discovery project to ensure depth in understanding both practical and attitudinal dimensions of their insights. The specific questions Educators provide thoughts on adaptive learning tools. 12. Open Feedback: Educators can add any other relevant thoughts.
From interview with instructors and teaching assistants, we gain insight into teaching experiences, adaptive learning perspectives, and practical integration strategies. Generally, interviewees highlighted several common themes:
Challenge in Differentiating Instruction: Educators often noted difficulty in addressing the varying levels within a single classroom and expressed interest in tools to support personalized pacing.
Positive Reception for Adaptive Tools: Many valued adaptive tools for their potential in enhancing concept retention and student engagement, specifically when tailored to individual learning trajectories.
Implementation Considerations: Practical constraints, including time, ease of integration with current learning management systems, and reliance on teaching assistants, were often mentioned as significant factors influencing tool adoption.
This feedback forms a basis for refining adaptive learning tools to meet real-world teaching demands.
One of the most notable advantages of AI in education is its ability to personalize learning, tailoring educational experiences to meet the diverse needs, preferences, and learning styles of students [15]. Using an RLO as the foundation for intelligent tutoring systems could enhance the educational landscape by providing customized learning paths and tailored feedback [9]. Participant feedback in this study highlighted the RLO's potential for supporting course material and fostering problem-solving skills, with Participant #2 noting, "Yes, it was very useful in helping check work." Participant #5 also recommended the tool, sharing that "it was helpful in understanding how regex are set up. " Despite these benefits, participants expressed a desire for more personalized feedback. As Participant #6 remarked, "It wasn't personalized, but it was useful, " underscoring the need for individualized support within such tools. Suggestions for improvement, including "more language options" and "text-to-speech" functionality (Participant #3), point to the importance of accessibility and adaptability in future RLO iterations. Additionally, feedback from Participant #1, who stated, "I wasn't sure how to use the tool at first," indicates that enhancing user guidance could improve ease of use. Comments from Participant #15, who noted, "I would not recommend the tool to others; it did not explain very much and took a long time to run, " suggest areas for improving efficiency and instructional depth.
Future work on this RLO aligns with the AI Grand Challenges for Education outlined by Woolf et al., particularly the goals of providing "mentors for every learner" and "lifelong and life-wide learning" [8]. In line with AI's strengths, weaknesses, opportunities, and threats in education, as explored by Randall in recent discussions with HBCU faculty [? ], future RLO development will focus on designing adaptable tools to support students from varied backgrounds, ensuring inclusivity, accessibility, and effectiveness. Planned enhancements include:
β’ Adaptive Assessment and Skill Tracking: Implementing a system that tracks student performance to provide tailored difficulty levels and additional exercises based on individual progress. These enhancements aim to make the RLO a more flexible, accessible, and impactful educational tool that supports a broad range of learners. By focusing on personalization and adapting to diverse learning needs, this RLO aligns with AI's grand challenge to democratize educational resources and extend individualized learning opportunities beyond traditional settings.
The author thanks the study participants for their valuable insights and time. Besides the study participants, the author extends appreciation to several entities who contributed to the development of this paper and its findings. Research professor Beverly P. Woolf serves as his research advisor. Professor Woolf specializes generally in educational computer science research and more specifically in intelligent tutoring systems. Professor David A. Mix Barrington, the authors teaching assistant supervisor and synthesis reader, focuses on computational complexity, Boolean circuits, automata, and logic. The combined expertise of both professors bridges diverse fields, offering a comprehensive perspective on the project.
Samuel Osebe and Sabrina Zaman Ishita assisted in RLO prototype development as part of a course team project. They both helped in crafting a proof of concept for the pilot project.
Under the UMass Human Protect Office (Internal Review Board Protocol #5139: Team Chase Undergraduate Research Volunteers), Jasmine Ngo assisted the deployment of the semi structured interviews and the survey instruments as part of an undergraduate Computer Science Department Honors Thesis Project.
Shravan Janga, served as part of Team Intelligent Tutoring Systems R Us. He provided invaluable back up support during the customery discovery phase.
The author acknowledges partial funding from the National GEM Consortium, the Intel Scholars Program, the NSF I-Corps Hub for Interior Northeast led by Cornell Tech, Manning College of Information and Computer Science along with the Spaulding-Smith Fellowship awarded by the UMass Graduate School.
Every week for the length of the course, students met for a 50 minutes discussion group to cover the following topics:
1. "What is a Proof?"
β’ Objective: To foster an understanding of mathematical proof in real-world scenarios and to practice constructing proofs based on definitions, highlighting the role of preconditions, postconditions, and loop invariants in validating code.
β’ Objective: To develop deductive reasoning skills using propositional logic, demonstrating the process of narrowing down possibilities based on given clues, and applying rules of propositional logic to deduce conclusions efficiently.
β’ Objective: To enhance proficiency in applying proof methods to statements about functions and relations, emphasizing predicate proof rules and the significance of properties of functions and relations.
β’ Objective: To apply proof techniques and congruence principles to establish and understand facts about prime numbers, specifically the infinitude of primes.
β’ Objective: To cultivate a strong foundation in mathematical induction, focusing on the structure of induction proofs including base cases, inductive hypotheses, and inductive steps.
β’ Objective: To reinforce and expand students' skills in mathematical induction, challenging them with diverse problems that require careful proof construction.
β’ Objective: To familiarize students with Java-based boolean expressions, emphasizing the differences between common programming languages and the structure of tree representations in code.
β’ Objective: To gather feedback on the course content, pedagogy, and overall learning experience, aiding in future improvements and refinements.
β’ Objective: To master the art of constructing accurate regular expressions for specified languages, promoting a systematic approach to capture all desired strings while excluding undesired ones.
β’ Objective: To comprehend the principles behind the Myhill-Nerode Theorem, and to acquire hands-on experience in minimizing DFAs by leveraging the equivalence classes of the relation on strings.
β’ Objective: To understand the foundational role of deterministic finite automata in the lexical analysis phase of compilers, underscoring the transition from highlevel programming languages to machineunderstandable code.
Writing Exercise: Construct a regular expression for the set EE ("eveneven") of strings in {π, π} that have both an even number of π β² π and an even number of π β² π . Justify your answer carefully -explain why your expression generates only even-even strings and why it generates all even-even strings.
Note that all even-even strings have even length, so you may think of the whole string as being broken up into two-letter blocks.
Here are some more hints. You are not required to use them to solve the main problem, but they will probably be useful. Define the language πΈπΈπ ("even-even-primitive") of nonempty strings that are in πΈπΈ and have no proper prefix in πΈπΈ. (That is, if π€ β πΈπΈπ and π€ = π’π£ with both π’ and π£ β πΈπΈ, then either u = or v = .) It turns out that while πΈπΈπ is harder than πΈπΈ to describe in English, it has a simpler regular expression.
β’ Explain why πΈπΈ = (πΈπΈπ )
β’ Which strings of up to six letters are in πΈπΈπ ?
β’ Construct a regular expression for πΈπΈπ , and explain why this solves the main problem.