UCI Feature
ALOHA: Inside a UCI Mathematics Professor’s Effort to Maximize Hybrid Learning
By combining an online course with an in-person active learning sessions model, UCI Mathematics faculty developed a winning formula for boosting student performance.
It was an unassuming early-December afternoon. Tucked away from Ring Road’s usual hubbub of club-run booths and clusters of students was the Anteater Learning Pavillion (ALP), a spacious and modern dedicated active-learning space divided into intimate, tech-equipped classrooms and open study areas. In Room 1600, we joined as UCI Mathematics faculty Rachel Lehman along with graduate teaching assistants and undergraduate peer mentors, guided a room full of students through a carefully curated set of math problems at the final precalculus discussion session ahead of their final exam.
Around the classroom were tables fitted with monitors displaying that week’s math problems, which were surrounded by groups of students diligently working away on notebooks and iPads. The graduate teaching assistants and peer mentors assisted the faculty, rotating between tables, facilitating lively group discussions and encouraging collaboration among the students. Buzzing with energy, the atmosphere contained in that classroom was anything but standard fare. In place of Q&A-based discussion hours where students bear most of the responsibility of coming to class with questions about specific concepts, Lehman’s discussion sessions take a more dynamic and interactive approach by offering students a thorough review of the week’s materials through hands-on problem-solving and instructor-led group discussion. These sessions, dubbed ALOHA, which stands for Active Learning Office Hours & Assignments, utilize math exercises and group learning to actively engage students. Students are encouraged to discuss, explore, practice and experiment with lecture concepts, a process known as active learning. This in turn motivates students to formulate new questions, learn rather than memorize, and gives students an in-person outlet to apply concepts they’ve not yet practiced. Observing the effectiveness of active learning in precalculus courses since 2018 and documenting its implementation at UCI, Lehman collaborated with Kameryn Denaro (Research Scientist, Division of Teaching Excellence and Innovation) and Alessandra Pantano (Professor of Teaching, Department of Mathematics) to publish their findings.
Currently hosted every Wednesday, these sessions were created by Lehman in response to a need for students to interact with one another and the instructor. The in-person sessions accompany the large, lecture-based online math courses, which traditionally limit faculty-student guidance, peer-to-peer interaction and decrease motivation for many students. Each week, students work together to complete a set of math problems by the end of the hour and peer mentors can be spotted zigzagging from table to table to assist students and promote a positive learning environment. The undergraduate peer mentors have previously excelled in Precalculus or Calculus and are trained through the UCI Certified Learning Assistants Program (CLAP), contributing to the effectiveness of the active learning environment. Speaking to how these discussion sessions remedy the shortcomings of online learning, UCI Ph.D. Computer Science ‘25 and B.S. Computer Science ‘19 student Andrew Chio, who served as an peer mentor in Fall 2018 and Winter 2019, stated that most students were receptive to having mentors as a resource and noted that “a key challenge for students in [precalculus] was the largely online nature of instruction.” Chio said, “This made [learning] for students quite rigid, as online explanations are unable to cater to the more nuanced misunderstandings that a student may have. Being a mentor and having the opportunity to more thoroughly gauge a student’s grasp of a concept was very effective in this regard.”
Through the addition of ALOHA’s in-person active learning model, students get to develop proficiency with the techniques they’ve learned from online lectures and are able to form a deeper level of conceptual understanding of course topics. Sahil Habibi, a B.A. Political Science and B.A. Quantitative Economics ‘25 student who served as a peer mentor for the Fall 2023 and Winter 2024 quarters, wanted to encourage a learning environment where students felt comfortable enough to ask questions about any concept and to engage with peers in the class for mutual learning. Fostering a positive learning environment for students to excel was also personal for Habibi, who identified himself as “not [having] a math background,” stating, “My biggest goal was to make sure that there was never a ‘stupid question,’ and that he feels “very fulfilled when [a student] truly learns and understands a concept, as opposed to memorizing a formula.”
With UCI’s precalculus courses being moved online in 2012, over 1200 students take their first math course online each year. Faculty and students alike realized that there were limited opportunities for student-instructor and student-to-student interactions, which negatively affected student performance in not only precalculus, but the following calculus courses as well. Finding that incorporating active learning has outpaced traditional learning in improving outcomes in STEM courses (Denaro, et al. 1), Lehman created the ALOHA active learning discussions in 2018 to complement the online asynchronous lectures, making them mandatory the following year.
Lehman and Pantano from the Math department partnered with Denaro from the Division of Teaching Excellence and Innovation to research the impact of implementing the ALOHA discussion program in an online course. Noting that online courses have been found to exacerbate learning gaps between White and underrepresented racial/ethnic minority students, and that previous literature has found active learning to benefit all students but particularly improve outcomes for underrepresented groups and those who may not thrive in online learning environments (Denaro, et al. 1), the trio set out to uncover the effects that ALOHA attendance had on students’ performance in the online precalculus and subsequent in-person calculus courses.
Comparing historical student data from Winter 2018 and Winter 2019, before and after ALOHA attendance was made mandatory, respectively, what they found was that there was a marked improvement in overall grades outcomes for students who attended the ALOHA sessions (they had an average score of 2.79 GPA points, roughly equal to a B-minus) compared to those who did not (they scored 2.46, or a C-plus). Furthermore, ALOHA-attending students who went on to attempt the subsequent calculus course also performed better on average (they had an average score of 1.79, a C-minus) than those unexposed to ALOHA (they scored 1.65, which is a D-plus [1.7 is a passing grade for most students]), showing a positive carryover effect correlated with ALOHA attendance (Denaro, et al. 16-17).
Although these results support the effectiveness of implementing active learning in precalculus courses, the trio note that the continued high failure rate of the subsequent calculus courses and the sub-2.0 (a C grade) average student performance suggests that there is still room to improve student outcomes and reduce learning gaps (Denaro, et al. 16-17). As such, Denaro, Lehman, and Pantano conclude their study with a plea for more interventions to be considered and a promise to iteratively tweak the ALOHA discussion section as needed. Denaro elaborated on these sentiments a year later, echoing that the format of ALOHA is now more-or-less situated, but reaffirmed that the goal of improving student performance in these math courses is still very-much a priority, with additional learning strategies pending research and development. In the meantime, Denaro, Lehman and Pantano are committed to reducing barriers to student performance and promoting active learning as an effective companion to traditional online and in-person math instruction, with Denaro stating that UC Irvine has the robust infrastructure and procedures necessary to embrace active learning and become a leader in realizing equitable student academic performance.