Abstract:
For most students, Mathematics is an abstract and difficult subject to learn. Quite often, they find it hard to understand abstract mathematical concepts (e.g. sets, functions, limits, etc.), or difficult to prove mathematics results in a rigorous manner. This project developed exploratory pedagogy to facilitate the students to learn Mathematics more effectively. With a set of well-designed exploratory learning materials on hand, students were able to explore the related mathematical concepts first, via numerical examples, real-life cases, diagrams, games or concrete objects, etc., before being introduced to the formal mathematical definitions or concepts. Consequently, under the guidance of the lecturers, students were led to develop the ability to work out proofs deductively, using proper mathematical language. To this end, the project team worked closely with the module lecturers concerned to identify the mathematical concepts or topics that were often found difficult for students to learn; and then designed and developed the related teaching and learning materials for use in several Mathematics modules. The project products would contribute to enhancing the quality of teaching and learning of Mathematics via an exploratory pedagogy in the Institute. Furthermore, they served as exemplified examples for in-serve teachers on how to improve students’ Mathematics learning, and also as a reference for future designs of Mathematics modules in the 3-3-5 curriculum or new programmes offered by the HKIEd.
Code:
T0067
Principal Project Supervisors:
Subjects:
Start Date:
01 Jan 2010
End Date:
30 Jun 2011
Status:
Completed
Result:
For the analysis course, the designed interactive applet can serve as a good visualization tools for learning the concept of limit of a sequence. According to students’ interview, the use of information technology could help students master and understand the concept of limit via the epsilon-delta approach. However, it was realized that more careful design or choice of computer tools was needed. For instance, a revised applet based on the feedback from students and colleagues was designed and used for teaching the same topic in the semester I of 2011-2012.
For the calculus course, guided-exploratory activities were developed for exploration of the limit of trigonometric functions. Analysis of students’ performance in the activities was conducted. Based on the common errors detected or misconceptions identified, an interactive GeoGebra applet was designed for online exploration and assessment for teaching of this topic. Besides, another GeoGebra applet was also implemented for helping students to conceptualize the concept of improper integrals. The results found that allowing students to do some explorations before formal lectures would help them to understand the related concepts better. Relevant experiences and discussion was prepared in a journal paper.
For the essential mathematical concepts course, the common misconceptions of the students were identified and analyzed via pre-test. An online courseware was developed to help students to master the concepts of mathematical logic and set theory. Some exploratory worksheets were designed to assist students to conceptualize the principle of mathematical induction, and quiz was conducted to assess students’ performance in doing proofs by using such a principle. It was found that more than 80% students demonstrated significant improvement in the paper use of the principle of mathematical induction and its application in doing proof. Feedback from the students’ questionnaires also confirmed that the consolidation exercises did help them to understand their misconceptions and the ways to avoid them. A departmental seminar was held by the team members concerned to share the experiences and findings to our colleagues and students.
Impact:
The project designed different exploratory learning activities and conducted try-outs in class. The data collected was analyzed and the overall results were positive and promising for adopting an exploratory approach in teaching and learning mathematics. It provided a valuable experience for the team to understanding more about how to learn mathematics effectively from the students’ perspective, as well as the ideas for further development of pedagogy for learning and teaching of mathematics via integration of IT components and proper use of online learning resources and materials.
Deliverables:
Cheng, K., Ho, A., & Leung, A. (2011, June). Teaching the rigorous concept of Limit. Paper presented at the Hong Kong Mathematics Education Conferences, Hong Kong. https://repository.eduhk.hk/en/publications/e71f03d7-9268-4c76-8b5f-e323...
梁景信、張家麟 (2011.06)：數學歸納法的教與學，香港，香港數學教育會議。https://repository.eduhk.hk/en/publications/592680ce-ebb7-407a-b662-d390...
A departmental seminar on "Techno-pedagogic task design in a technology-rich mathematics classroom" by Dr Allen Leung held on 3 November 2010. (No. of Participants: Around 10-12)https://repository.eduhk.hk/en/publications/4d886f6f-80a5-4aff-bb36-2b72...
A departmental seminar on "Teaching and learning of Mathematical Induction" by Dr K. L. Cheung and Dr K. S. Leung held on 11 May 2011. (No. of Participants: Around 40-50)https://repository.eduhk.hk/en/publications/88f2ab1c-603a-4524-9243-59c7...
An exploratory tool for learning the concept of limit of a sequencehttps://repository.eduhk.hk/en/publications/1580a08e-3e4c-420d-ae18-5f13...
Financial Year:
2009-10
Type:
TDG