Mark Fantini
  • Member for 7 years, 10 months
  • Last seen more than a month ago
  • Brazil
How to justify teaching students to rationalize denominators?
13 votes

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 ...

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Difficulty with word problem interpretation
10 votes

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 ...

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Mathematical education by country
8 votes

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 ...

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Is it good to have solutions of homework published?
7 votes

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 ...

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Book request: teaching proving and reasoning at an American university
6 votes

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 ...

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Should tests given after the drop date be made less difficult in order to help the remaining students raise their grades?
6 votes

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 ...

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Resources for teaching Riemann integration in higher dimensions and on submanifolds, with view toward Stokes' theorem?
6 votes

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

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How to balance higher order thinking and drill/practice
6 votes

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 ...

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Fundamental Ideas in Mathematics
5 votes

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 ...

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How should one tutor a student in undergraduate real analysis?
5 votes

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 ...

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Math 3d animation software
Accepted answer
4 votes

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 ...

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Is this example of Leibniz notation sloppy?
Accepted answer
4 votes

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 ...

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Do teachers and books target more apt students?
4 votes

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 ...

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"Feynman effect" in teaching mathematics
2 votes

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 ...

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Open source lecture notes textbook in "introductory real analysis"
2 votes

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.

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Do you teach different proofs or calculations of same question?
1 votes

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 ...

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Resources for improving computational skills at the high school/university transition
1 votes

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 ...

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Looking for an online mathematics practice resource
Accepted answer
1 votes

I believe Khan Academy is what you're looking for. As far as introductory mathematics university courses go, it has plenty of resources. Certainly it covers Trigonometry, Geometry and Calculus well ...

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Writing mathematics in real time for lectures using Latex
0 votes

I was using Overleaf for my classes, and switched over to Notion (for other reasons as well). One of Notion's amazing abilities is to render LaTeX in real-time, both in-line or as a block equation (...

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