As classroom sizes expand, formal education faces increased challenges in providing scalable, targeted feedback based on student engagement. 250, an undergraduate core course in discrete mathematics, covers topics such as logic, elementary number theory, proof by induction, recursion on trees, search algorithms, regular languages, finite state machines, and computability. These concepts often present challenges due to their abstract nature and the precision required in logical reasoning. Primarily enrolling computer science and related majors, the course benefits from reusable learning objects (RLOs) designed to support concept mastery. In this context, the author proposed a new discussion material on mathematical foundations, specifically targeting regular language expression. He tested a Python tool that allowed students to check their answers' correctness while mastering regular language expressions. Students completed the Python tool and a survey, which confirmed the tool's usefulness and provided valuable feedback for iterative design. This paper aims to contribute to the existing body of knowledge on AI in education by shedding light on student perspectives with RLOs. In future iterations, we plan to recruit a more diverse range of educators, including female educators from all-women colleges, to broaden our perspective on instructional efectiveness. Moving forward, we seek to explore the balance between technological and human interventions required for efective course delivery. Although these findings are preliminary, continued research and richer data may reveal organic, inductive themes as this iterative process unfolds.
based interactive tool for answer verification, structured
As classroom sizes expand, educators increasingly need practice exercises, and integrated feedback mechanisms
scalable, targeted feedback mechanisms to support stu- that guide students through the learning process.
Dedent engagement. 250, an undergraduate core course signed to actively support students, the RLO delivers
in discrete mathematics at UMass Amherst, covers key immediate feedback to help them correct errors and
topics such as logic, elementary number theory, proof strengthen their understanding. During the study, the
by induction, recursion, search algorithms, regular lan- author assigned a treatment group to use the RLO for
guages, finite state machines, and aspects of computabil- regular expression exercises, where students received
ity [
To address these challenges, the author developed a capturing changes in understanding and perceptions.
Reusable Learning Object (RLO), which refers to “any Survey responses indicated that the RLO was primarily
digital resource that can be reused to support learning” used for reinforcing course material and problem-solving
[
Through an iterative design process, the author struc- needs of educational stakeholders [
Beyond promoting independent learning, the RLO contexts [
The next sections address the related works, the study design, development, and testing to ensure the RLO’s The study design happened as an iterative process. First reusability. Finally, the author outlined a plan for a proof the authored created a pilot project as a proof of concept. of concept, drawing from the doctoral program insights, Thereafter, the author became the entrepreneurial lead related works and testing within real-world educational for Team Intelligent Tutoring Systems R Us. Team Incontexts. Future endeavors, especially in the context of telligent Tutoring Systems R Us obtained U. S. National a doctoral program, require continuous refinement and Science Foundation’s Innovation Corps (I - Corps™) Cusoptimization of the initial concept as presented herein to tomer Discovery Project funding. achieve the best outcomes.
2. Related Works As part of teaching assistant preparation course, the
author and classmates conducted a pilot study without
InAs classroom sizes expand, educators face increased chal- stitution Review Board (IRB) approval. The pilot study
lenges in providing scalable, targeted feedback based on ended with 147 participants in March-May 2022.
student engagement [
Steve Blank’s Customer Discovery framework, as out- The survey responses varied significantly. Over 31.3% lined in the NSF I-Corps Teaching Handbook, reinforces of participants reported “no challenges,” indicating a this interdisciplinary approach by emphasizing iterative smooth experience with the Python script. In contrast, under 15.6% of participants expressed dificulties, 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 to- 3.2.2. I-Corps Study Methods wards 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 efectiveness 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).
4. Administrators aim to boost institutional ranking through future-generation technologies while addressing academic integrity, accessibility, and privacy concerns. 1. Customer Segmentation: The team focused on understanding the mental models of STEM students, professors, and administrators, exploring their behaviors, characteristics, and needs. 2. Customer Discovery Interviews: Using a hybrid approach of virtual and in-person interviews, the team engaged participants to uncover educational pain points and evaluate the RLO’s commercial viability. 3. Data Collection and Analysis: With over 90 contacts from 15 colleges and universities, the team conducted 35 detailed interviews with students, instructors, and administrative professionals in instructional roles. • Phase 1: Literature Review and Case Studies. The ifrst 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. • 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.
program provides an intensive seven-week
entrepreneurship training course with mentorship and funding for 3.2.3. I-Corps Conclusion
customer discovery. As part of this program, the author The team initially accepted the null hypothesis but
discovled Team Intelligent Tutoring Systems R Us as the en- ered a strategic pivot by broadening customer
segmentatrepreneurial lead, receiving a travel grant supported by tion beyond the host institution. This pivot enabled the
Cornell Tech and the National GEM Consortium to ex- development of a more dynamic business model,
continplore market potential for the Reusable Learning Object uously revised through customer insights. Aligning with
(RLO) project [
The I-Corps program guided the team in conducting creating intelligent tutoring systems, real-world
simua hybrid field study to test initial hypotheses and make lation environments, and natural language processing
adaptive pivots. Insights from customer discovery in- capabilities to enhance adaptive learning [
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’ problem
solving 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?
4.2.1. Consent Form
pants 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. 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 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.
included are as follows:
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 [
thoughts on adaptive learning tools. Future work on this RLO aligns with the AI Grand
12. Open Feedback: Educators can add any other Challenges for Education outlined by Woolf et al.,
particrelevant thoughts. ularly the goals of providing "mentors for every learner"
and "lifelong and life-wide learning" [
tants, we gain insight into teaching experiences, adaptive learning perspectives, and practical integration strategies. Generally, interviewees highlighted several common themes:
Challenge in Diferentiating Instruction: Educators often noted dificulty 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 • Immediate Corrective Feedback: Ofering for- Research Volunteers), Jasmine Ngo assisted the deploymative feedback that is specific to the type of ment of the semi structured interviews and the survey error made, enabling students to correct misun- instruments as part of an undergraduate Computer Sciderstandings promptly. ence Department Honors Thesis Project. • Personalized Learning Pathways: Creating Shravan Janga, served as part of Team Intelligent Tucustomized learning pathways based on initial as- toring Systems R Us. He provided invaluable back up sessments or adaptive quizzes, allowing students support during the customery discovery phase. to focus on areas that require reinforcement. The author acknowledges partial funding from the • Progress and Performance Dashboards: De- National GEM Consortium, the Intel Scholars Program, veloping dashboards that give students personal- the NSF I-Corps Hub for Interior Northeast led by Corized insights into their strengths and areas need- nell Tech, Manning College of Information and Coming improvement, supporting self-directed learn- puter Science along with the Spaulding- Smith Fellowing. ship awarded by the UMass Graduate School. • Natural Language Processing (NLP) for Open
Ended Responses: Using NLP to analyze open- 7. Appendices ended responses and provide customized feedback based on the semantics of students’ answers. • Gamification and Motivational Feedback : In- 7.1. Appendix A: Automata Theory corporating gamified elements that reward indi- Discussion Objectives vidual achievements and keep students motivated Every week for the length of the course, students met throughout their learning journey. for a 50 minutes discussion group to cover the following • Student Profile Customization : Enabling stu- topics: dents to set preferences or learning goals within the RLO, allowing it to customize feedback based on their unique needs and learning styles.
lfexible, 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, ofering 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 Ofice (Internal Review Board Protocol #5139: Team Chase Undergraduate 1. “What is a Proof?” • 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. 2. "A Murder Mystery” • 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 eficiently. 3. “Practicing Proofs” • 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. 4. “Infinitely Many Primes” • Objective: To apply proof techniques and congruence principles to establish and understand facts about prime numbers, specifically the infinitude of primes. 5. “Practicing Induction Proofs” • Objective: To cultivate a strong foundation in mathematical induction, focusing on the structure of induction proofs including base cases, inductive hypotheses, and inductive steps. 6. “More Induction Problems” 7. “Boolean Expressions” • Objective: To reinforce and expand students’ skills in mathematical induction, challenging them with diverse problems that require careful proof construction. • Objective: To familiarize students with
Java-based boolean expressions, emphasizing the diferences between common programming languages and the structure of tree representations in code. 8. “Course Evaluation Essay Questions” • Objective: To gather feedback on the course content, pedagogy, and overall learning experience, aiding in future improvements and refinements. 9. “Designing Regular Expressions” • Objective: To master the art of constructing accurate regular expressions for speciifed languages, promoting a systematic approach to capture all desired strings while excluding undesired ones. 10. “Minimizing a DFA” • 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. • 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.
11. “Applications in Compilers”
Construct a regular expression for the set EE ("eveneven") of strings in {, } that have both an even number of ′ and an even number of ′. 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.
nonempty strings that are in and have no proper prefix in . (That is, if ∈ and = with both and ∈ , then either u = or v = .) It turns out that while is harder than to describe in English, it has a simpler regular expression.
• Explain why = ( ) • Which strings of up to six letters are in ? • Construct a regular expression for , and explain why this solves the main problem.