I resonated with Shulman’s statement of how a knowledgeable teacher that knows general pedagogical strategies can not be a good teacher (1986). Think back to the content I learned in middle schools, and I merely recalled lectures and pure theories in science and math classrooms. Every single scientific theory I remember is directly related to a piece of memory of a specific experiment in labs, or a project in collaboration. Although my math teachers along the way are always passionate about teaching and easy-approaching for after-class consultations, there is a lack of memory of math classes compared to the vivid memory of science labs. I was able to stand out in learning math, but there was a lack of understanding of the relationship between math and reality back to high school. As I proceeded to the undergrad studies of applied math classes, I finally build the connection between numbers, equations, theories, models, and the real world by one after one project. And in most cases, our projects were conducted through technologies such as using analytical software to build mathematical models, where coding skill was necessary throughout the process.
PCK and TPACK could be the trickiest issue for secondary school math teachers. Unlike the tons of scientific simulation experiments with and without technologies, there is a lack of entertaining or comprehensive programs designed for secondary math classrooms. Students who are less confident with math learning could be further discouraged by the complexity of setting up technology tools as we have witnessed in the case studies in week 2. The TPACK strategies in this particular education section should emphasize the user-friendly interface to encourage all students’ participation instead of employing cutting-edge tools to attract math minds. Gaming on math concepts is always my personal choice. I was so into Sudoku when I was a child, and now, there are many more options on the field. Pinterest.com is my to-go place to check new updates on educational games since it has straightforward user interface displays.
While the discussions around TPACK strategies is in trend, PCK strategies in high school math learning still attract my attention due to their reasonable costs and ease of convenience. Drawing dots by different columns and rows on the blackboard to explain why 4 times 7 is equivalent to 7 times 4 by results is still an effective method nowadays (my classmates raised this question in the Grade 10 math classroom). Here is an article I found online that introduces 17 innovative mathematics projects that inspire students:
https://medium.com/however-mathematics/17-innovative-mathematics-projects-that-inspire-students-c652005cc627
You may know some of these simple experiments with minimal use of digital technologies. Still, they provide hands-on experience for students to construct meaningful and artistic artifacts and help them understand some abstract terms in math. Among these 17 projects, I love the activity of drawing harmonographs the most. Some creations like below demos could help students witness the beauty of math and increase their internal motivation in learning. Also, this is something students can share with friends and family to “show off” and receive recognitions. 🙂
 
References:
Shulman, L.S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4 -14. Text available on Connect.
17 Innovative Mathematics Projects that Inspire Students. (2021, Feb). https://medium.com/however-mathematics/17-innovative-mathematics-projects-that-inspire-students-c652005cc627