# Flipping the classroom for deeper student engagement and feedback on learning ![L Mahadevan](/sites/g/files/omnuum12666/files/styles/hwp_1_1__360x360_scale/public/vpl/files/l_mahadevan_final.jpg?itok=MBmri1Ox) **L Mahadevan, Lola England de Valpine Professor of Applied Mathematics in SEAS,** and **Professor of Organismic and Evolutionary Biology, and of Physics in FAS** used a 2017-2018 [SEAS Learning Incubator LInc Faculty Fellowship](https://linc.seas.harvard.edu/linc-faculty-fellowship-overview) to emphasize active learning in his [*Mathematical Modeling*](https://locator.tlt.harvard.edu/course/colgsas-118021/2019/fall/11018) course. He implemented a [flipped classroom](https://projects.iq.harvard.edu/flippingkit/introduction-flipping) approach to enable students to come to class with problems and questions to collaborate on, time to develop their own problems from scratch, and work on modeling with peers. The foundational arc supporting this process has students move from observations through abstraction, analysis and communication, and iteration. ## The benefits Students develop quantitative capabilities for analyzing the world and learn that when they ask questions appropriately, they can answer them quantitatively. “In most courses, we aim to teach tools that students need to answer questions, but we are not so good at teaching them how to think about new questions. The goal in redesigning this course was to move the focus towards enabling students to think from scratch about new problems and be able to determine and apply the right quantitative tools to the problem at hand.” ## The challenges Mahadevan finds that students are not comfortable making mistakes, but says, “I’m happy to be an idiot in front of my students—then work out with them how, where, and why I went wrong and learn to correct the mistakes.” This approach to modeling demonstrates to students that it is perfectly fine to make mistakes while learning and encourages them to feel more comfortable working collaboratively on problems by being constructively critical. ## Takeaways and best practices ### Use the board. As part of their class time, students are divided into teams of three to work through problems on a board. The teaching staff circulates around the room, observing the work and asking questions. “When we ask students to work problems in front of peers, their misconceptions are in plain sight for everyone to be able to critique, but in a constructive way.” This allows students to talk through problems collaboratively to determine how to proceed, while providing a lens for instructors to assess the gaps in both their knowledge and their reasoning. ### Jigsaw sharing. Using past problems and projects, students share critiques about problem formulation, analysis, and conclusions, as well as how to communicate mathematical ideas. This is done in a [jigsaw](https://ablconnect.harvard.edu/jigsaw) so students move from one project to the next. When students are working on their own projects, they have a model for self-assessment as well as for offering constructive criticism and asking questions of their classmates. ### Demonstrate a way of thinking through analogy. Mahadevan divides his course into four modules that highlight mathematical principles across fields using deterministic, stochastic, continuous and discrete ways of thinking: equilibrium and homeostasis, flow and transport, diffusion and reaction, and control and design. These modules move from description to prediction and eventually to design. Each conveys to students that, at a deep level, mathematics is the science of uncovering patterns and discovery using analogy. Demonstrating how the same kinds of methods and tools can transfer to physical and biological sciences or technology is powerful to students’ learning. ### Bottom line Providing students with more class time to actively work on problems and learn from mistakes in real-time helps them develop the skills and confidence to think originally about problems and solutions. ## Related Research [### Ten‐year follow‐up of patient‐centered comprehensive care using case completion curriculum ](https://hollis.harvard.edu/permalink/f/1mdq5o5/TN_cdi_webofscience_primary_000636486400001) The purpose of this study was to evaluate the patient‐based comprehensive model in the student teaching practice at Harvard School of Dental Medicine (HSDM) as a result of the case completion curriculum. T [### Student staff partnership to create an interdisciplinary science skills course in a research intensive university ](https://hollis.harvard.edu/permalink/f/1mdq5o5/TN_cdi_crossref_primary_10_1080_1360144X_2015_1113969) This paper reflects upon the development of a multidisciplinary lesson plan aimed at developing science skills for Physics and Astronomy, Geographical and Earth Sciences, and Chemistry students at a research intensive Scottish university. The lesson plan... [### Students as co-creators of teaching approaches, course design, and curricula: implications for academic developers ](https://hollis.harvard.edu/permalink/f/1mdq5o5/TN_cdi_eric_primary_EJ926191) Within higher education, students' voices are frequently overlooked in the design of teaching approaches, courses and curricula. In this paper we outline the theoretical background to arguments for including students as partners in pedagogical planning... [ More Research arrow\_circle\_right ](/intopracticeresearch) ## Related Resource [### Interested in co-creating curriculum with students? ](https://itali.uq.edu.au/teaching-guidance/curriculum-design-and-review/transforming-curriculum/co-creating-curriculum-students) Check out this guide from the University of Queensland. [### Interested in learning more about the HSDM Curriculum Hackathon? ](https://drive.google.com/file/d/10gMeq3GI2-7dt2GHvBha-GjtuycTGpIq/view?usp=drive_link) Check out the materials that were distributed to participants. [### 2023 HILT Conference, “Teaching in the Age of AI: Nurturing Connections and Empowering Learners”. ](https://hilt.harvard.edu/news-and-events/annual-conference/) Interested in discussing the impact of artificial intelligence on classrooms at Harvard? Be sure to register for the 2023 HILT Conference, “Teaching in the Age of AI: Nurturing Connections and Empowering Learners”. [### Digital Scholarship at Harvard University ](https://dssg.fas.harvard.edu/) Drop in during Digital Scholarship Support Group Office Hours with questions. DSSG members will suggest tools and approaches and connect you with relevant resources, organizations, and researchers. [ More Resources arrow\_circle\_right ](/intopracticeresources) See also:- [ FAS ](/featured-faculty/fas) - [ SEAS ](/featured-faculty/seas) - [ Into Practice Issues ](/practice-categories/practice-issues) - [ active learning ](/activelearning) - [ blended approaches ](/topics/blended) - [ course transformation ](/coursetransformation)