19 votes
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Co-curricular lessons between geometry and chemistry?

One angle you could look at is molecular geometry. Not really my subject area but a couple of examples: Organic molecules can have different chiralities. That means that while one is the mirror image ...
Nate Bade's user avatar
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10 votes
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Scientific results on the usefulness of physical units in secondary education?

This is not exactly what you seek, but at least you can find educational research articles under the key phrase dimensional analysis. Below [1] says it's useful, [2] questions that usefulness. [1] ...
Joseph O'Rourke's user avatar
9 votes

Examples of real-life vector fields for vector calculus

Air speed/direction on a weather map) is a very intuitive one. There's also other fluid velocity (and flux) vector fields in various chemE, mechE, and nukeE applications. I personally think the air ...
guest's user avatar
  • 304
7 votes

How to explain that we live in a three-dimensional world?

Flatland. W. Abbott, 1884 Here's the Project Gutenberg link to read or download in your preferred e-version: https://www.gutenberg.org/ebooks/97 As an advanced student in elem school, my engineer ...
Deporodh's user avatar
6 votes

A Question about Theodore Frankel's "The Geometry of Physics"

I've owned the revised first edition of Frankel's The Geometry of Physics: an Introduction at least since I was a graduate student. The texts I suggest in this answer are largely based on my personal ...
James S. Cook's user avatar
6 votes

Co-curricular lessons between geometry and chemistry?

Pick your battles. Don't expect to have synergy in every place. But where you do have synergy, exploit that, call it a win, and move on. Concentrate on the partial fullness of the glass, not the ...
guest's user avatar
  • 61
6 votes
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Elementary physics course for pure math student

While I did not attend any elementary physics courses by mathematicians for mathematicians, I did attend a curriculum of courses called "Mathematical Physics" held by mathematicians for mathematicians ...
Roland's user avatar
  • 1,801
6 votes

Does education research support the idea that answer keys are bad?

In the paper Research on teaching and learning Mathematics at the Tertiary level, by Biza, Victor-Giraldo, Hochmuth, Khakbaz, Rasmussen, recently published by Springer (ICME 13 Topical Surveys) you ...
Nicola Ciccoli's user avatar
5 votes

Activities for calc based physics

I am going to assume that you are teaching a calculus "helper" versus the entire physics class. Your initial statements don't match that. But then all your content described is math, not physics. ...
guest's user avatar
  • 51
4 votes

Co-curricular lessons between geometry and chemistry?

This is perhaps more molecular biology than it is chemistry. There are some accessible planar geometric questions suggested by the H-P (hydrophobic-hydrophilic) model of protein (amino acid) folding,...
Joseph O'Rourke's user avatar
4 votes
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How can I visualize differential equations and Integration in real life?

You have asked two very different questions. I'll leave the differential equations for someone else. There is one particular application of integration which is my favorite last problem to do in Calc ...
Sue VanHattum's user avatar
  • 20.2k
3 votes

Examples of real-life vector fields for vector calculus

The oscillation of species' populations due to predation. The convergence of machine learning models using gradient descent - this is a special vector field that's tuned by uniformly multiplying the ...
Still.Tony's user avatar
3 votes

Elementary physics course for pure math student

You might be interested in Brian C. Hall's book Quantum Theory for Mathematicians. The author writes on his webpage about the book: This book aspires to be a self-contained and reasonably ...
J W's user avatar
  • 4,635
2 votes

Best way to memorize the conversion between m/s and km/h

You should calculate with magnitudes: m/s = (1/1000)km/(1/3600)h = 3.6 km/h My experience is that math teachers detest calculations with magnitudes. They left them to physicists. Their problem is ...
Zvonimir Sikic's user avatar
2 votes

Elementary physics course for pure math student

See Michael Spivak's "Physics for Mathematicians" See also the notes that the book came from
David Steinberg's user avatar
2 votes

Elementary physics course for pure math student

From a comment by Michael Joyce: The notes are by Igor Dolgachev and can be accessed here: http://math.lsa.umich.edu/~idolga/lecturenotes.html
Tommi's user avatar
  • 7,019
2 votes

What science books would you recommend a curious middle school student to read at home?

You could just go ask what the previous books used were, or look at what some gifted schools use for texts in 7th, 8th grade science. I'm not sure how fun/useful such a text is, especially if ...
guest's user avatar
  • 164
2 votes

Does education research support the idea that answer keys are bad?

I would be shocked if there were any research on this, either supporting the practice or against it. It does not seem like the kind of research question people study -- simultaneously too narrow to ...
mweiss's user avatar
  • 17.3k
2 votes

Structure of math textbooks

(Comment) I'm not really sure that your predicate is as you've described. I took down a copy of my Calc book (Thomas Finney 1980) and my college chemistry book (MSS fifth edition) and both are ...
guest's user avatar
  • 234
2 votes

Examples of real-life vector fields for vector calculus

The Hairy Ball Theorem:        wikiwand link: "there is no nonvanishing continuous tangent vector field on even-dimensional $n$-spheres."
Joseph O'Rourke's user avatar
2 votes

How to use Calculus to give an explanation for a video by Lewin

To understand rolling without slipping we need to understand the kinetic energy falls into two modes; linear kinetic energy and rotational kinetic energy. For a rigid body if the velocity of the ...
James S. Cook's user avatar
2 votes

How to teach integrals motivated by the work done in moving an object?

The best way to illustrate the sense of $W=|F||AB|\cos(\alpha)$ is to show that it makes sense that each of the factors is proportional to the work done. If you double the amount of force to an ...
Matthew Daly's user avatar
  • 5,599
1 vote

Co-curricular lessons between geometry and chemistry?

Are proofs still part of the geometry curriculum? (Some of my math colleagues have mentioned they've been downplayed over the last decade or so.) A good Chemistry answer looks an awful lot like a ...
Van's user avatar
  • 111
1 vote

Integrated math curriculum in different countries

If by high school you mean lukio/gymnasium, the Finnish info is available in Finnish and Sápmi https://www.oph.fi/saadokset_ja_ohjeet/opetussuunnitelmien_ja_tutkintojen_perusteet/lukiokoulutus and in ...
Tommi's user avatar
  • 7,019
1 vote

Structure of math textbooks

I think the short answer, particularly for graduate texts but to some extent for undergraduate texts in the style you describe, is that the textbooks are written that way because that is the way ...
Jessica B's user avatar
  • 5,772
1 vote

Analogies or explanations for duality, at the college sophomore level

The symmetry between vectors and co-vectors in your example (i.e. the possibility to identify a vector with a co-vector) exists only since you have a scalar/hermitian product on the vector space $V.$ ...
Michael Bächtold's user avatar
1 vote

What science books would you recommend a curious middle school student to read at home?

Not mathy, but I loved T Rex and the Crater of Doom, by Walter Alvarez (a scientist), about why the dinosaurs went extinct. His explanation of the history of the question gives some great insight into ...
Sue VanHattum's user avatar
  • 20.2k
1 vote

What science books would you recommend a curious middle school student to read at home?

I found this book a delightful mix of geometry, history, and engineering. Your daughter might have to skim of sections that employ trigonometry, but skimming in this book would not lose her the ...
Joseph O'Rourke's user avatar

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