Mark Fantini
• Member for 7 years, 10 months
• Last seen more than a month ago
• Brazil

Making my comment an answer: rationalizing fractions was useful when computers weren't so readily available. Division using integers is way more feasible than dividing by rationals. Even today, if you ...

I suggest you break it down into smaller parts. In fact, don't start on equations. Start on translation of terms: Double of a number, translation: $2x$ Sum of two numbers, translation: $x+y$ The ...

The first two years in the mathematics program in my university in Brazil goes as follows: First semester: Calculus I, comprised of a review of real functions and inequalities (triangle inequality ...

Yes. The idea is not only to give them well thought-out answers and solutions to the problems presented but also (ideally) to show how these were constructed. Enlightening solutions make explicit the ...

I know no better book for reasoning than Thinking Mathematically, by John Mason, Leone Burton and Kaye Stacey. It is superb in inspiring action and instilling methods of reasoning. Quoting from the ...

I would like to complement Speyer's answer with this: encourage their feedback about the course goals, tests and related activities. This is a critical time to take in account what they have to say as ...

For multidimensional real analysis I recommend the two-volume bible by Duistermaat: Multidimensional Real Analysis, Volume 1 - Differentiation, Multidimensional Real Analysis, Volume 2 - Integration....

I enforce Sue's question as for which course is this. I'll assume meanwhile that it is a college one (from calculus to advanced analysis). Examples and computations. Say you are teaching a ...

Researchers Sebastian Rezat, Mathias Hattermann and Andrea Peter-Koop have published a book "Transformation - A Fundamental Idea of Mathematics Education". You can find the link here. This is a ...

Students reaching for real analysis more often than not do not have a firm grasp of calculus as they should. What ends up happening is that they don't understand how most of that was necessary as a ...

The math videos creator 3blue1brown has a webpage and in the FAQ section he goes into detail about how we went about creating his videos. Here's his answer for the question "What do you use to animate ...

Tl;dr: They are all equal and this is a matter of preference. The notations mean the same concept, each with its respective advantages and disadvantages. Newton's notation $\dot{v}$ is commonly used ...

No, they aren't. That said, some subjects are genuinely difficult such that even the clearest writer cannot simplify concepts further. You cannot distinguish your readers in a text. Authors attempt to ...

Generally, is providing a context/big picture helpful or a waste of time when teaching "hard skills"? Disregarding the "added value" of the students knowing the big picture, being able to apply the ...

You may be interested in Zakon's Analysis I and II. It is free for personal use, it is rigorous, it covers the same content as Rudin and Ross. I haven't personally studied it, but it looks good.

Yes, whenever possible. Teaching different proofs or different solutions to the same problem has several benefits: There is less cognitive load because the problem is already known and a solution has ...

The Art of Problem Solving has plenty of problems involving pre-calculus tools, some of them quite challenging. However, the best way forward might not be computationally challenging exercises. You ...