Innovative mathematical modelling resources for real-world applications
The project team exchanges ideas on how to use real-life examples to help students understand abstract mathematical concepts. From left to right: Ms Huang Xiaowei, Dr Lo Chung-kwan (project team leader), Dr Manpreet Singh, Dr Leung King-shun and Ms Xu Simin.
Advancing mathematics pedagogy has been a key mission of the Department of Mathematics and Information Technology (MIT). To help learners connect abstract mathematical concepts with tangible real-life applications, Dr Lo Chung-kwan led a project team in developing three learning and teaching resource packages based on mathematical modelling. The Education Bureau (EDB), which funded the project, organised a dissemination seminar on 20 January 2025 where Dr Lo shared how to use the packages with an audience of around 100 panel heads and subject teachers from local secondary schools.
Mathematical modelling involves solving real-world problems using mathematical expressions and concepts. “By incorporating mathematical models into the resource packages to analyse real-life problems, make calculations and predictions, students realise that mathematics is relevant to their everyday experiences. The packages also help students become familiar with data analysis, a vital skill in STEAM education and today's data-driven world,” Dr Lo, the project team leader and an Assistant Professor from the department, explained. Other team members include Dr Leung King-shun, Dr Singh Manpreet, Ms Huang Xiaowei, and Ms Xu Simin.
The three learning and teaching resource packages include: creating 3D virtual models of buildings, finding optimal locations for company headquarters and warehouses, and setting a price for a property.
One question of the worksheet of the “setting a price for a property” resource package uses many real-life examples of property prices to teach students how the price of a property varies with its size.
Titled “Developing Learning and Teaching Resource Packages for Conducting Mathematical Modelling through Inquiry and Investigation”, the EDB-funded project contains three learning and teaching resource packages: setting a price for a property, creating 3D virtual models of buildings, and finding optimal locations for company headquarters and warehouses. Each package includes supporting materials such as lesson plans, worksheets, and presentation slides.
We used many real-life scenarios to stimulate students’ interest in learning the packages. For example, we gathered extensive real property price data when developing the package on setting a property price. In this package, students uncover factors affecting property prices, such as size, location, condition, facilities, and types. They also learn how to use simultaneous linear equations involving two variables to formulate a model predicting property prices based on factors such as size and age,” Dr Lo explained.
The Education Bureau granted a HK$598,000 fund for MIT’s knowledge-transfer project, which ran from August 2023 to October 2024. Once the initial versions of the three sets of teaching and learning materials were prepared, the project team invited teachers from three secondary schools to test these materials in their mathematics lessons or STEAM learning days. “I have to express my sincere thanks to the three participating schools—Confucian Tai Shing Ho Kwok Pui Chun College, TWGHs Chang Ming Thien College and Salesians Of Don Bosco Ng Siu Mui Secondary School—for testing the pilot packages. Their feedback has tremendously helped us in perfecting the packages,” Dr Lo remarked.
On 20 January 2025, the Education Bureau (EDB) organised the dissemination seminar for the “Developing Learning and Teaching Resource Packages for Conducting Mathematical Modelling through Inquiry and Investigation” project. In the group photo taken at the seminar, Dr Lo Chung-kwan from MIT is fifth from left, while Mr Stanley Lee, the then EDB Senior Curriculum Development Officer, is fifth from right. Also present are teachers from the participating secondary schools.
Members of the MIT project team, from left to right: Ms Xu Simin, a PhD student at MIT, Dr Lo Chung-kwan, leader of the project team, and Ms Huang Xiaowei, a research assistant at MIT.
To enable more teachers to understand the content and application of the resource packages, Education Bureau (EDB) hosted a dissemination seminar on 20 January 2025. At the seminar, Dr Lo’s team presented background of mathematical modelling, as well as the initial thoughts of the project, and development process of the three resource packages. He also gave a few highlights on how to use the packages. “Mathematics works in an idealised world where all the required conditions allowing the calculations are met. In real-world problems, however, we make a lot of assumptions to reduce complexity and simplify the calculations. To maximise the learning outcome, teachers need to guide students to think about what assumptions are being made and how valid these assumptions are,” Dr Lo elaborated.
Students from Confucian Tai Shing Ho Kwok Pui Chun College estimate heights of school buildings, aiming at “creating 3D virtual models of buildings”.
A teacher at the Salesians of Don Bosco Ng Siu Mui Secondary School teaches his students using the resource package of “finding the optimal location for company headquarters and warehouses.”
In addition to Dr Lo’s presentation, the three participating schools shared their user experiences at the dissemination seminar. Teachers from Salesians of Don Bosco Ng Siu Mui Secondary School noted that their students’ overall reaction to the mathematical-modelling-based learning materials was positive. “Most students proactively participated in class activities about learning the packages. Under the guidance of teachers, students could also make reasonable assumptions behind the calculations. We found that even students who were usually inattentive in class participated willingly during the try-out activity. When teaching the package about property prices, students with weaker learning abilities were able to use it for price estimation,” a teacher from the school said.
The Education Bureau (EDB) is very appreciative of MIT’s efforts in the project. Following the success of the first project, the EDB approved a funding of HK$598,000 and appointed Dr Lo’s team in November 2024 to start working on the second phase of the project. “Incorporating new ideas, we will develop another set of learning and teaching resource packages. We will fully consider experiences learnt from the first project so that resource packages from the second phase will be even more stimulating and effective for conducting mathematical modelling. We aim to complete it by November 2025,” Dr Lo said
