Learning mathematics the fun way with MIT's GeoGebra!
The MIT project team develops over 80 GeoGebra-based teaching materials and ten online training lessons to teach mainland teachers how to use GeoGebra for interactive mathematics instruction. Posing in the photo are Dr Lo Chung-kwan, principal investigator of the project, and one of the team members Miss Huang Xiaowei.
Students often find mathematical learning a nightmare due to the traditional mathematics curriculum’s emphasis on abstract reasoning and the symbolic presentation of mathematical concepts. With the funding support from the Tin Ka Ping Foundation, a group of academics from the Department of Mathematics and Information Technology (MIT) devised a programme to teach mainland mathematics teachers how to use GeoGebra-based teaching materials in their instruction. Around 40 teachers participated in the programme and responded positively about the usefulness of the GeoGebra-based learning materials in helping students learn mathematics. Approximately 4,000 mainland students have been directly benefited from the project.
The knowledge-transfer project titled “Online interactive educational resources for junior secondary school mathematics: Research and development with teacher training” was aimed to train mainland teachers to use GeoGebra-based interactive mathematics learning materials and equip them with basic knowledge about GeoGebra. GeoGebra is an interactive mathematics software that combines geometry, algebra, statistics, and calculus. As one of the most popular open access software, it is widely used in education to help students understand mathematical concepts through interactive learning.
“Our project started in July 2023 and completed in June 2024. It has achieved all the five pre-set goals. First, we developed a set of free GeoGebra-based teaching materials designed for mainland’s students at seventh to ninth grade. Second, we constructed a website that contains all interactive teaching materials. We then created a WeChat platform for participating teachers to ask questions and share learning experiences,” Dr Lo Chung-kwan, an assistant professor from MIT who headed the project, said.
The project team created a WeChat platform to faciliate learning, where participating teachers ask questions related to the use of GeoGebra teaching materials.
A screenshot of the video demonstrating how a mainland teacher creates GeoGebra teaching materials to teach mathematics. The teacher submitted this video for the teaching competition.
Dr Lo added that the project team has also organised ten online training lessons to teach teachers basic techniques for using GeoGebra so they can produce their own teaching materials. A set of teaching manuals related to the training was also produced. Finally, the team held a teaching competition to assess how well participants can apply their knowledge about GeoGebra in their mathematics teaching.
Mathematical formulas and concepts are usually too abstract for students to comprehend. By using pictorial, numerical and symbolic representations to explain mathematics, the GeoGebra-based teaching materials developed by the MIT team reduce the hurdles of learning. With the use of interactive teaching materials, students not only engage their minds, but also use their hands and eyes to learn.
One of the GeoGebra-based teaching materials focuses on the concept “The sum of two sides of a triangle is greater than the third side”.
Another GeoGebra-based teaching material illustrates how the three medians of a triangle meet at a point called the centroid.
“GeoGebra helps students grasp complex concepts through visual representation. For example, in the teaching material about the concept ‘The sum of two sides of a triangle is greater than the third side’, users can manipulate the lengths of AB and AC, two sides of the triangle, to observe real-time changes in the visual representation of the triangle. In another teaching material, learners can simply follow steps to draw medians of a triangle and observe that the three medians meet at the centroid of the triangle,” Dr Lo elaborated.
Through the ten online lessons, around 40 teachers from eight participating schools on the mainland learnt how to create GeoGebra-based teaching materials to enhance their teaching practices. One of the teachers was Mr He Jiaju (何家駒) from Guangzhou Nansha Dongchong Middle School (廣州市南沙東涌中學). As a member of the project team, Mr He adapted and further developed the ten training lessons into a set of online courses. He posted the online courses onto the ‘Guangzhou Primary and Secondary School Teachers Continuing Education Network (廣州市中小學教師繼續教育網)’.
“Through these online courses, our programme has reached 200 teachers from Guangzhou. This brings the total number of teachers who have received training, either directly through our programme or via online courses on the Guangzhou Continuing Education Network, to 240. Given that each teacher typically instructs two classes with approximately 100 students annually, the MIT GeoGebra project has the potential to benefit over 20,000 mainland students,” Dr Lo stated. He also mentioned that Mr He is currently pursuing a Doctor of Education (EdD) degree at EdUHK under MIT.
As a result, students showed more interest in the subject and gained a deeper understanding of mathematical concepts. The GeoGebra teaching materials has raised my teaching efficacy.
Participating teachers responded positively about the programme. They expressed that through the ten well-designed online lessons, they learnt how to incorporate GeoGebra teaching materials into their lesson plans. “By using GeoGebra teaching materials, mathematics lessons became more stimulating and interactive. As a result, students showed more interest in the subject and gained a deeper understanding of mathematical concepts. The GeoGebra teaching materials has raised my teaching efficacy,” one participating teacher said.
This paper explores the use of GeoGebra and scaffolding strategies to develop OER (Open Educational Resources) for secondary school mathematics teaching, as well as formative evaluation techniques to enhance the quality of the OER.
Based on the insights behind the project and participating teachers’ experiences in using the GeoGebra materials, the team authored an academic article titled “Scaffolding-informed design of open educational resources in Chinese secondary school mathematics: insights from multi-cycle formative evaluation. The article was published in October 2024 by Smart Learning Environment, a high-impact journal in the Education and Educational Research fields. The publication allowed more mainland teachers to learn about MIT GeoGebra project’s results and expanded the project’s social impact beyond primary and secondary school teachers.
The idea for the MIT GeoGebra project originated from a policy document issued by the Ministry of Education about strengthening online teaching resources for primary and secondary schools on the mainland*. “The Tin Ka Ping Foundation has supported numerous educational projects that improve education quality in mainland schools. We thank them for their generous funding of HK$494,000 for this project. As an open access software, GeoGebra is available in over 30 languages and has been continuously improved since its inception two decades ago. The software provides a dynamic and interactive learning approach to motivate students to explore and learn through direct engagement with mathematics objects. We believe our project improved learning quality and promoted equity in education on the mainland,” Dr Lo concluded.
While Dr Lo Chung-kwan is the principal investigator of the knowledge-transfer project, its team members included Miss Huang Xiaowei and Mr Mau Yuk-lun from MIT, and mainland teacher Mr He Jiaju. Professor Philip Yu Leung-ho, Dr Alpha Ling Man-ho, Dr Zhang Qiaoping, Dr Cheung Ka-luen and Dr Tony Yee Tat-leung, all from MIT, served as advisors to the project.
