I’m hosting Carnival of Mathematics #81. Submit your articles via the form. Please get me your submissions by the end of August for a September 2nd edition.
I've gotten zero submissions so far. If I don't get any (or enough) submissions I'll find math posts on the blogosphere I like and promote those.
Google celebrated Fermat's 410th birthday with this Google Doodle:
The Telegraph has a nice little story on the event.
Mike Croucher has posted Carnival of Mathematics #80 at Walking Randomly.
I'm hosting #81. Submit your articles via the form. Please get me your submissions by the end of August for a September 2nd edition.
[ Editor's note: The following is an opinion piece by Mr. Frederick Koh at www.whitegroupmaths.com. ]
The “Made in Singapore” tag literally applies to me-born here, bred here, educated here. To a certain extent, I was blessed to have studied mathematics in this little country, as its curriculum was exceptionally rigorous and thorough. That said, is Singapore maths really that awesome and perfect? Absolutely not .In fact its pretty flawed. Being someone who “survived” this journey (which was generally manageable, but not quite pleasant at times), perhaps I might be in a better position to put things into perspective.
Mention Singapore Maths to educators around the world, and thoughts normally conjured up would be those of novel primary school textbooks and bar model solving methodologies unique to the Singaporean context. Or the impeccable Cambridge ‘O’ and ‘A’ level examination standards imported from the UK a long time ago. Marvelled from the outside, it is an incredible system which enables the learner to cultivate a high level of mathematical competency through various stages of carefully structured teaching programs. But there within resides serious problems. The extremely competitive nature of academic education here places a strong premium on getting stellar report cards and grades, so much so that a kid goes to school merely to learn how to excel in tests and advance to the next level, rather than learning to better oneself.
Charming Proofs: A Journey Into Elegant Mathematics is a delightful book, published by the Mathematical Association of America (MAA), that lives up to its name.
Given my joyful experiences of exploring challenging problems in middle school and in high school I have a soft spot for elegant problems that are accessible to motivated students who don't have any background in advanced mathematics. And, I have a soft spot for MAA books because they were among the first math books I devoured, specifically their MAA contest prep books.
Here's a brief description, from the publisher's page, of the structure of the book.
Charming Proofs is organized as follows. Following a short introduction about proofs and the process of creating proofs, the authors present, in twelve chapters, a wide and varied selection of proofs they consider charming, Topics include the integers, selected real numbers, points in the plane, triangles, squares, and other polygons, curves, inequalities, plane tilings, origami, colorful proofs, three-dimensional geometry, etc. At the end of each chapter are some challenges that will draw the reader into the process of creating charming proofs. There are over 130 such challenges.
Math Dictionary for Kids: The Essential Guide to Math Terms, Strategies, and Tables is a great reference book that I think should be on every kid's bookshelf. (Disclosure: The publisher sent me a review copy.) New copies are available via Amazon for as low as $7.64 plus shipping in the U.S. making this book an inexpensive back to school gift for 4th to 9th graders.
When I was doing lots of computer programming I would always have reference books available (or online equivalents) to look up how to solve some particular kind of problem in some particular programming language or environment. "Math Dictionary for Kids" is that kind of book for kids who need to review (or learn) some mathematical concept and it's filled with tons of how-to's just like those good programming reference books.
I do think that "dictionary" is a misnomer. I typically use a dictionary to look up the meaning of a word (or the spelling, before spell-checkers were everywhere). This book is much more comprehensive than your typical dictionary.
I'm sure that publishing this quote from "The Four Pillars Upon Which the Failure of Math Education Rests (and what to do about them)", by Matthew Brenner, page 55, won't be appreciated by some readers. I'm not a math educator but Brenner's comparison of how kids learn math (not sure if he is referring only to the U.S. or not) struck me as so funny, so tragic, and so true all at the same time.
Kids are taught math as pets are taught tricks. A dog has no idea why its master wants it to perform. With careful training many dogs can be taught to perform complex sequences of actions in response to various commands and cues. When a dog is taught to perform a trick it has no need or use for any “understanding” beyond which sequence of movements its trainer desires. The dog is taught a sequence of simple physical movements in a specific order to create an overall effect. In the same way, we teach children to perform a sequence of simple computations in a specific order to achieve an overall effect. The dog uses its feet to move about a space and manipulate objects; the student uses a pencil to move about a page and manipulate numbers. In most cases, the student doesn't know any more than the dog about the effect he creates. Neither has any intrinsic motivation to perform nor any idea why the performance is demanded. Practice, practice, practice, and eventually the dog can perform reliably on command. This is exactly how kids are trained to perform math: do a hundred meaningless practice problems, and then try to do the same trick on the test.
[ Editor's note: This is a guest article by Lucas Allen at Tech Powered Math. ]
I talk about graphing calculators a lot, in the classroom, on my blog, on Youtube, Twitter, and recently at the National Council of Mathematics Teachers national meeting. One of the most common questions I get in these venues is: “Why do we still need these things? Why doesn’t Texas Instruments just make an app for the iPad?.”
Before I answer that question, it’s important to understand who the modern graphing calculator is designed for. It’s not the engineer, the programmer, or finance professional. It is the mathematics student. While the majority of professionals have moved on from a standalone calculator to computer software, most students don’t have that option in the classroom. Additionally, from a sales standpoint, there’s a new crop of millions of students entering high school every year for the calculator manufacturers to sell to.
One of the biggest reasons Texas Instruments came out on top in their graphing calculator battle with Casio, Hewlett Packard, and Sharp is because they understood their marketplace was the classroom. As such, they developed relationships with teachers and created workshops and courses to educate teachers on how to use products with students. They made apps and added features on their calculators that were less about number crunching and more about reinforcing mathematical concepts. Before long, they had an army of millions of devoted followers in the education arena.
Jeremy Jones has created an outstanding interactive site, "Stay or Switch," just to help people understand the Monty Hall problem.
I got this email from Jeremy last night and was inspired to check out his site.
I love your blog (got a kick out of the "Fields arranged by Purity" comic). I've also been excited about math since middle school. I love teaching it and I got really interested in teaching/explaining complicated concepts using simple animations. So I picked what I thought was one of the most hard-to-explain problems, the Monty Hall Problem, and made a game simulation and multiple animated explanations. I recently published a website devoted to the problem. It's www.stayorswitch.com. I'd love to know what you think of the site.
All the best,
I was blown away by the effort Jeremy has made to explain a classic but unintuitive problem. The graphics and animation are professional quality, And, the explanation of the problem using 100 goats is the best one I've seen. Awesome job, Jeremy!
Folks, please spread the word and encourage Jeremy to make more of these awesome math animations!
Here's a very cool proof without words by Burkard and Marty.
Can you figure out what this proof without words illustrates?