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The document proposes a project-based learning activity to teach students about Fermat's problem for Torricelli. Students will form groups and use dynamic geometry software to investigate Viviani's theorem. They will then perform an experiment involving drilling holes in acrylic boards and attaching strings to masses to measure angles. Finally, students will research the Fermat point online and present their findings to the class. The teacher's role is to facilitate learning through questioning rather than simply providing answers. ICT tools like dynamic geometry software and videos are used to enhance collaboration and make the activities more interactive.
Uiit ai1
- 1. Project-Based Learning Proposal<br />ITC3001 Upper Intermediate IT Competency In Education<br />Wong Hang Chi 09451331<br />Objectives<br />This Project-Based Learning (PBL) activity is aimed to enhance the problem-solving strategies and collaboration skills of the participants through investigating a classical extreme problem, the Fermat's Problem for Torricelli. It is designed for the senior secondary students. The required subjects are Mathematics and Physics.<br />Activities<br />Introduction<br />At the beginning, the teacher introduces Fermat's Problem for Torricelli to the students.<br />Given a triangle ∆ABC, find a point P in the plane such that the sum PA + PB + PC is the smallest. The point P is called the Fermat point.<br />To motivate the students, the teacher may tell a fictional story like the following one. <br />Three students, Peter, Paul and Mary live in three different places A, B and C. Once they decide to have dinner together. What place P should they go in order to minimize the sum of the distances they need to travel?<br />The students are required to form into groups with three or four persons in each group. During the activities, the teacher encourages them to share their ideas that they may come up with and to help one another among the group.<br />Viviani's Theorem <br />Before coping with the Fermat's Problem for Torricelli, the teacher may first let the student get used to the Viviani's Theorem.<br />Given an equilateral triangle ∆XYZ, and an arbitrary point P in the interior of the ∆XYZ, the sum of the distances from P to the three sides is a constant.<br />We may use dynamic geometry software, such as Geogebra, to investigate the theorem.<br />Experiments<br />The students are required to perform an experiment about the Fermat point. A piece of acrylic board is given to each group and the students are asked to drill three holes in the board. Then, attach three pieces of string to three equal masses. Finally, measure the angle made between the three pieces of strings. <br />After the experiment, the teacher asks the students to find information about the Fermat point in the Internet by using search engine such as Google and Yahoo.<br />The Teacher as a Facilitator<br />In the activities, it is not desirable to tell the students directly the answer. In order to help the students to find it out by themselves, the teacher may use some questioning techniques. For example, “What is the unknown of the problem?”, “Can we use our previous results?”, etc. <br />The Importance of ICT<br />ICT is virtually indispensable in some of the activities. For example, using Geogebra to investigate the Viviani's Theorem makes it much more interactive and convenience. It would be a nightmare if the students are asked to construct the equilateral triangle and the three perpendiculars by using merely a pair of compasses and a straight edge. <br />In the experiment part, taking videos and sharing them in the Internet would enhance the collaboration among the students. For the students could see the results of the other groups more easily. <br />Assessment<br />(30%) Each group of students are required write a report about their findings, in which they should<br />state their observations in the Geogebra activity;<br />write down the numerical results obtained in the experiment; <br />(optional) give a formal proof of the assertion they might have.<br />(40%) They also need to take a video of the experiment and upload it to the Internet. <br />(30%) In order to ensure that the students could understand the information obtained from the Internet, each group should present their findings to the other students using PowerPoint.<br />