After I read Merrill’s First Principles, it reminded me of a lot of things I learned before. When I was learning Math 204 Calculus IV in UVic, I was confused about how can I understand so many complicated math terminologies like complex numbers when I was young. I didn’t think deeply at the beginning and attribute the reason to the great learning ability of the young human brain. Roughly two years ago, I had an opportunity to get the digital version of my primary school math textbook. I was surprised by the knowledge organization and content examples inside.
In the Chinese national math textbook, the entire math digits learning process can be analyzed by a simple question “Why numbers are not enough for using?” For example, some fifth-grade primary school students are going to learn negative numbers. The textbook first uses real-life examples, such the temperature, to build a common sense that negative numbers are necessary and reasonable. Then it links the graphical basics that the existing negative numbers are the other side of the natural numbers which are familiar with before. After this process, the textbook applies many examples with illustrations to enhance the learning process. Once this part becomes stable, when the students are in grade six, a new textbook will ask the same question “Why numbers are not enough for using again?” and introduce fractions to them. And then followed by decimals numbers, irrational numbers and complex numbers with the same process in high school.
There are many fun things I want to tell in this “number learning process.” First, the example they choose to introduce negative numbers is a smart choice. In Chinese society, most family parents have a habit of watching national and international news on a big TV screen during dinner time. This TV program is always followed by the weather report program and repeated every single day. When I was at that age, I can easily recite all of the city names in order even though I had zero geographical knowledge. And I can easily understand that some cities are followed by “negative XX Celsius” even if I had no idea about the meaning. Here we find the common sense to link the new knowledge to the existing fields.
This is a learning process infographic. It shows learning inspirations for students to get familiar with the math number system. I don’t have more space to illustrate the insight ideas here. Maybe in the future blog, I can show more about the details.
ahen 19 February 2023
Hey, Jasper great post I really enjoyed reading it. Seeing a contrast of learning compared to how I learned in my schooling made it a compelling read. The illustrations were effectively used here and made it interesting to show how they could be used for many different courses. The infographic is very well put keeping it simple and completely understandable. I enjoyed your discussion of Merill principles in one of your classes at the university . Thank you for the post Jasper seeing your real-life comparison for the stuff we’ve been learning.