On April 24, 2024, Class 401 held a math public lesson. Warm-up activity before class: Light switch game (created by Meng Baoxing). Teacher: What "magic" is there in the game? Today, we are going to decode the magic. There are 10 switches (checkboxes) numbered from 0 to 9 and a total of 50 lights numbered from 0 to 49. The children observe, guess, verify, and express the relationship between the switch numbers and the light numbers. They attempt to represent the "circuit diagram" using alphanumeric expressions. Through the process of discovering the magical secrets, they gain insights into mathematical concepts such as "representing quantitative relationships," "one-to-one correspondence," and "range of values."
After class, Director Zhou Xiang, the curriculum supervisor, commented: The design of thinking training activities should be procedural, visual, and standardized, especially the design of teacher's introductory remarks, aiming for precision, clear logic, and step-by-step progression. Director Zhou proposed: Students can be encouraged to try designing formulas to light up any light bulb (the following teaching design is based on this suggestion).
After class, the elementary school math team prepared for the lesson again. The teachers unanimously agreed that regarding creating scenarios, they should be bolder, more thorough, and more precise. Children should naturally gain insights during the process of completing project works (such as "domain" and "range" knowledge that cannot be mentioned temporarily) and foster creativity through creation.
Specifically, taking the scenario of a large-scale urban audiovisual light show, Geogebra courseware presents a small-scale light show. "Deciphering the magic" means decrypting the programming of the light show (exploring new knowledge), and students work in groups to design and showcase their own light shows.
The math teachers unanimously agree that the powerful animation and interactive features of Geogebra should be utilized. For a small-scale light show, two sliders are sufficient. Students directly input formulas (using letters to represent numbers) in the Geogebra software, and the corresponding light settings are completed. The number of switches, light bulb numbers, playback speed, playback order, and other settings are all available. Audio can also be inserted into the courseware (and sound can be edited and generated). For example, to light up all the diagonals, only one formula "9n" needs to be entered. In this way, students naturally understand concepts like "domain" and "range" that teachers may have difficulty explaining (different light shows require different switches to light up different lights), and they understand them deeply and thoroughly. This is the "real outcome" that makes students excited because it's their own work. In this process, students naturally feel the necessity of using letters to represent numbers; without letters, the project cannot be completed.
Special thanks to Director Zhou Xiang for her meticulous guidance and patient support. Indeed, Project-Based Learning (PBL) is easier said than done, and it's challenging. Achieving authentic scenarios, real problems, genuine inquiry, and real outcomes requires teachers to diligently seek and create situations before class. Moreover, teachers need to "disappear" during class; the more thorough the preparation, the easier the teaching process. A good "project" will inevitably inspire student creativity.
