“Is There Any Good Reason To Make Students Rationalize The Denominator? I’ve Never Seen The Point.”. 2022. Quora. https://www.quora.com/Is-there-any-good-reason-to-make-students-rationalize-the-denominator-Ive-never-seen-the-point/answer/Roman-Andronov.
The only point that I am trying to get across here is that, especially early on in mathematical education, it is way more beneficial to show the kids why this or that action may be undertaken (or not) and what can be achieved with it.
Mr. Andronov then presents a potpourri of tactical examples which hopefully show – why bother what can be achieved.
I. Rationalizing the denominator as an answer to a genuine mathematical concern – two (or more) distinct solutions or one unique?
II. Rationalizing the denominator as a problem-solving tool
III. Rationalizing the denominator as a source of approximations of irrational numbers
“The Connection Between Mathematics And Empirical Sciences”. 2022. Medium. https://mathladyhazel.medium.com/the-connection-between-mathematics-and-empirical-sciences-588b55d41c91.
The mathematics of thought interests me very much in my research. How does mathematics shape our conceptualization of reality? That is the basic question that I always ask myself. You might have a trivial answer to this question because mathematical methods are everywhere, especially in the empirical sciences such as physics.
Physical theories cannot be formulated without using mathematics. In biology, we use mathematical models to study the behavior of specific patterns of organisms, and in sociology, we use mathematics to analyze social networks. In that sense, mathematical methods are everywhere in empirical science because empirical science has shaped the way we see reality. Naturally, mathematics has a part in that as an indispensable scientific tool.
“What Does It Feel Like To Be A Math Student In College?” 2021. Medium. https://mathladyhazel.medium.com/what-does-it-feel-like-to-be-a-math-student-in-college-d121ba0bea40.
Of course, professors are brilliant people, but during the lecture, their job is just writing down stuff that they’ve already written for other students in the past. They don’t bother themselves to update their notes. The lectures are abstract or theoretical rather than actual numbers, and they take a lot of work to understand each lecture. Unfortunately, there’s no time in lectures to grasp the main idea because you need to keep writing the lecture notes on the board. Otherwise, you’re not going to have lecture notes. That means there needs to be a lot of independent study time to understand what’s going on.