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1

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 good proof; same sort of logic flow. (As does a good programming solution, if you're looking for another connection.) It might be a bit simple, but you could ...


5

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 partial emptyness. For that matter, you don't have time to totally redesign each course from the ground up in a way new to man. Nor do you want to screw up the ...


4

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, which could be explored with simple manipulatives (such as K'nex). For example, which proteins in this model have a unique minimum energy folding?   &...


18

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 of another you cant rotate one molecule to the other. The reasons for this are pretty deep mathematically, but chemically give rise to interesting things as ...


4

Secondary math is a pretty broad subject for something as individualized as manipulatives, but this is a list of things I'd love to have if I were teaching every subject in the same year for some reason. A two-pan balance scale and a bunch of clearly-labeled weights (Algebra I) - I feel that it can be really evocative how an equation like $3x+4=16$ can lead ...


2

I might think about some iconic objects of the past that excite interest, perhaps mainly in geometry. Drafting table (probably $500 for a professional one, but you can check second hand). French curve as Rust mentioned. Slide rules. Parallel rulers and 10 point dividers (good for poking people when bored...I would know). Sextant. Abacus. Towers of ...


1

As a no-cost option that gives you so many capabilities besides the conventional black/white-board, I always use geogebra. Not only as a demonstration tool, but also as a functionality for the students to investigate almost anything in precalculus or algebra. By simply adding, e.g. some moving graphics you can easily explain why, say, $e^x\approx\left(1+\...


4

I don't know if this is the right dollar amount, but I think getting access to a 3d printer and making some useful manipulatives of your choice with it would be cool. That is, if you are in a large district and have enough time to invest in trying them out - I don't think it's a one-off process! As an example, Henry Segerman's website has some absolutely ...


7

This is not an answer, but an assertion that what you are experiencing is not something new. Here are some quotes from a 1993 article of a Russian (actually, native Estonian) math prof, who moved to the U.S. in the early 1990s, so the problem is at least thirty years old. Some say that the commoditization of universities started from the Reagan times. This ...


1

I ... find myself troubled by lacking proper examples of why a sophisticated theory can actually turn out to be beneficial ... I agree this is troubling. "I feel your pain," as the saying goes. I would like to suggest that computer graphics can serve as a source for a subset of the examples you seek: to motivate polynomials, and motivate finding roots of ...


1

Parabolas in a fountain at Parque das Águas, Cuiabá, Brazil.


5

Well, there is a recent and excellent book about this question: Why Students Resist Learning: A Practical Model for Understanding and Helping Students by Anton O. Tolman, Janine Kremling and Anton O. Toman. The authors say resistance in learning may be a joint consequence of several factors, including resistance from teachers and schools. Here is a ...


1

My advice is to accept 3/4 of a loaf. Tailor your instruction to cover exactly this: "solution to problems that are known to be on their school's exams, and prefer step-by-step instructions free from any context/theory/mathematical properties." This is really still useful content to cover and better than nothing. Also, I wouldn't kill yourself in terms ...


3

This is how most students perceive math tests. Whether it's fair or not, this is the perception and it is the normal response to a broken math education system. Imagine you are a teenager and your driving test for your full license is in a week. The Department of Motor Vehicles is massively understaffed, so if you fail, you can't book another test for a ...


11

If you are a private tutor, hired by an undergrad or adult student, or hired by the parents of a student in 6-12 (middle school/high-school), then I'd suggest that when you meet with a "client" as a potential tutor, that you develop a contract with the student and/or parents to make clear your expectations: what is the minimum level of participation/effort ...


3

Ever notice the $5$-point star at the base of a pumpkin stem? This one's pentagonal symmetry is especially evident:                     Two views of the same pumpkin.


1

Although (as with several other answers) this one is more about persistence, I think it's relevant enough ("depressingly slowly" sure implies intermittent failure to me) to post. This is a poem by Piet Hein. T.T.T. Put up in a place where it's easy to see the cryptic admonishment T.T.T. When you feel how depressingly slowly you climb, it's well to ...


3

There are plenty of quotes here... But if you're trying to increase willingness to make and learn mistakes, I doubt that quotes will change a lot of minds, because a quote will be a tiny trickle of words pushing in the direction you want versus a raging river pushing the other way. Even Michael Jordan's quote about being cut from his high school basketball ...


5

I prefer A. It essentially says these 25 questions represent the whole course. Knowing them, you know it all. The 8 selected will be broad, but by nescessity (time constraint) won't cover whole course. So if you only give B, yuu're basically leaving too much of the course as untested. (In that people won't prepare to know anything other than what is on ...


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