Sharing the impressions of a person who earned 2 IMO bronze medals in his youth, but whose dreams of a successful research career were never truly fulfilled :-)
Mathematics is, indeed, not only about problem solving, but it isn't only about building theory either. Individual mathematicians may place themselves near one of the end points of this "...
I would love to get an answer by a teacher who is trying to teach prime numbers to elementary school students about what's happening with their attempt to teach them prime numbers. I would like them to tell me what teaching style they're using.
This may not be exactly what you're looking for but just the other day I introduced prime numbers to my first ...
Here's one that students always enjoy.
A bottle and a cork cost 1 dollar and ten cents. The bottle costs $1.00 more than the
cork. How much does each cost?
Student often think that it is one dollar for the bottle and 10 cents for the cork. That's incorrect because \$1.00 isn't \$1.00 more than 10 cents but the answer is easily discovered with algebra.
What is the medium of the content?
If they are videos, then YouTube would probably be first option but if they are, say, pdfs, then you might have to make a blog and then upload to that there. It still might feel like an island at first but it will gain traffic from your students and then other people who find it in search results. There are also problem-...
Algebra is a like a hammer that always works unlike arithmetics that may require inventive tricks, different for each problem. You may want to read a pertinent short story Tutor by Anton Chekhov. The problem posed in the story can be solved arithmetically, algebraically and arithmetically with tools like abacus.
Do you do word problems with your students? ...
My goal is not only for my students to recognize that there are multiple methods for solving a problem, but more importantly, for them to be able to identify the appropriate method(s) for solving each problem.
To me, once a proof of a particular method is learned, it becomes a tool that can be used.
Specific to differentiation, the reason why I would use ...
I relate prime numbers to prime factorizations of big numbers and usually ask the students, "which is easier to work with? Large numbers all at once, or small numbers one at a time?"
If it's elementary school, I'd think of arithmetic of fractions.
Do operations with highly composite numbers in two ways: one without prime factorization, and one with. I ...
razivio, look at Joseph Edwards Treatise on Integral Calculus froim 1920 (can find pdf on the web). Full of challenge problems from Cambridge Tripos exams. (Warning, stay in the earlier part of the text as that is calc 2. But he also has calc 3 and really complex analysis in there also.)
One of the most interesting word problems of all time, which broadened the human intellect in many ways, is the Archimedes cattle problem. There are many excellent books and articles about this--start with the wikipedia page. Also look for "The Sand Reckoner."
Archimedes is trying to explain that "infinity" is (conceptually) much more ...
Another common problem often used in school algebra classes are of the form, similar to the following:
Maria and Juan are siblings. The sum of their ages now is 16. In four years, Maria will be twice as old as her brother Juan.
What are Maria's and Juan's ages now?
Algebraically, we'd have the system of equations, with $j$ representing Juan's current age, ...
Here's a problem that's so practical, I solved it on a piece of scrap wood in the middle of building a gate for my wooden picket fence. I used it in my intermediate algebra class and it went over really well.
I have a section of pre-built picket fence that is irregularly sized (I had to cut an 8 foot panel in half to fit it in my hatchback). It is ...
Here's an interesting attempt in both text and
interactive images. Not a hierarchy but rather a "map."
The Map of Mathematics.
A project by Quanta Magazine. Text by Kevin Hartnett.
Design and visualizations by Kim Albrecht and Jonas Parnow.
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 already been found;
You strengthen students' schemas by creating a connection between existing domains, possibly unconnected until then;
You exhibit an ...