Permutation Group; and Numbers in French
It is Sunday, February 23, 2025. And as night falls and the daytime hours of February 23, 2025, slide into eternity, I can't let the joy of some mathematics learning experience go unnoticed. Today was a beautiful day for mathematical reflection. As a teacher on the educational side of mathematics, I have a dose of respect for mathematicians. My healthy respect has led me to try to grasp (1/100)%, yes 0.0001, or 10^(-4) part of some parts of mathematics. This time, it is the permutation group concept. When I took introductory abstract algebra, the concept presentation was rushed. I didn't get it. Yet, many years later today, I picked up a Modern Algebra textbook, and what seemed like a foreign language to me just suddenly opened my eyes in less than 30 minutes. It was like God was saying, You waited long enough. I would like you to take a look at this.
Speaking of foreign languages, other languages have an advantage over English for elementary school students learning mathematics. My eight-year-old told me today, "Daddy, do you know that there is no word for seventy in French?" And like that, I immediately researched, and she and I had a great discussion about numbers in French. Here are a few notable numerical ideas that came up, at least in my mind.
So, from the above, French elementary or kindergarten students know that 70 = 60 + 10 from the onset of counting. For 70, it is given as 60 + 10 in name. Without being stressed, students are already experiencing whole numbers as magma (see?https://tinyurl.com/3abx98nd?).
2. French elementary school students see that composite numbers can be represented nontrivially as products of other whole numbers from the outset.
Here, we can see that 80 is spelled 80 = 4 x 20 in French.
Mathematics is a fascinating subject.
See you next time for another episode of Thinking Overheard.