Kids are taught math as pets are taught tricks
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.
Your thoughts?
Why the graphing calculator still matters in an ipad world
[ 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.
Great Monty Hall problem site
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.
Dear Sol,
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,
Jeremy
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!
A nice proof without words
Here's a very cool proof without words by Burkard and Marty.

Can you figure out what this proof without words illustrates?
Math Pickle live and interactive talk 7/27
There's a live talk tonight by Gordon Hamilton of Math Pickle, which is one of my very favorite Math sites.
Math Pickle: Million-dollar problems with grades 7 to 12.
During the event, Gordon Hamilton will talk about solving real million-dollar problems with middle and high school students.
The recording will be at
http://mathfuture.wikispaces.com/MathPickleGrades7to12
All events in the Math 2.0 weekly series:
http://mathfuture.wikispaces.com/events
The perfect formula for toast
From the BBC:
Food scientists at the UK's University of Leeds have developed a formula for making the perfect piece of toast.
The equation - which details butter and toast temperature - took three months and cost £10,000 to develop.
Researchers' found that people think the perfect piece of toast should have partly melted butter patches on it, improving its taste and texture.
For this to work, the butter should be applied at fridge temperature of five degrees Celsius, the equation shows.
The formula was developed following research commissioned by the butter brand Lurpak made by Leeds-based Arla Foods. More.
Conrad Wolfram on teaching Math
Here's a recent interview in Madrid with Conrad Wolfram titled: The right way to teach math.
What do you think?
Wolfram founded ComputerBasedMath.org to change how Math is taught:
How do we fix math education? The importance of math to jobs, society, and thinking has exploded over the last few decades. Meanwhile, math education has gotten stuck or has even slipped backward. Why has this chasm opened up? It's all about computers: when they do the calculating, people can work on harder questions, try more concepts, and play with a multitude of new ideas.
computerbasedmath.org is a project to build a completely new math curriculum with computer-based computation at its heart—alongside a campaign to refocus math education away from historical hand-calculating techniques and toward relevant and conceptually interesting topics.
Conrad Wolfram also presented a TED Global 2010 talk.
Engaging summer Math activities at CTK Insights
Alexander Bogomolny has a number of outstanding "Cut-the-knot" sites that educate and inspire Math teacher and students. One of his sites, CTK Insights, has a great twelve part series of engaging Math activities for the summer break.
Here are the introductory paragraphs for the first three activities. To find the other nine just go to the day 3 activity and follow the link at the bottom of that article to get to day 4, follow the day 4 forward link to day 5 and so on.
Day 1
Mathematics is certainly not (only) about counting, graphing and solving equations. I do not believe that every child can reach beyond those. I do not believe that a child who does not show an inclination to dig deeper into math mysteries lacks in intellect or creativity. I do think that it is worth trying to find out. I child who gets excited on a discovery of uncommon patterns will have enriched his/her life experiences. [ Full article ]
Day 2
An engaging activity has been described by Martin Gardner in his Mathematical Games column in Scientific American, v 201, No 6, Dec 1959 and later included in one of his collections, New Mathematical Diversions. Rather recently, an upgraded variant has emerged as the Japanese ladders game. Amazingly, neither Gardner has mentioned the Japanese sources in 1959, nor half a century later his article has been referred to in the latest development. [ Full article ]
Day 3
Counting a group of objects can be done in many different ways. The most fundamental idea is that counting is at all possible in the sense that, regardless of the manner in which it is performed, the result is always the same. For example, place random numbers in a rectangular array and then compute separately the column and row sums. Then adding the column sums gives the same total as adding up the row sums. For little children the array and the numbers inside should be small. Letting all the numbers be 0 or 1 not only makes the activity more accessible to younger children but also adds a twist with a mathematical flavor. [ Full article ]
Review: The Best Writing on Mathematics 2010
Imagine for a moment that you had a friend who was a voracious reader of Math journals and periodicals. And, imagine that this friend had a knack for finding articles that were of interest to mathematicians and non-mathematicians alike by well-known writers and by new talent. Would you be interested in reading a few dozen of these articles? Mircea Pitici, editor of The Best Writing on Mathematics 2010 is such a friend, even if you've never met him.
Publisher Princeton University Press has an interview with Pitici at their blog where he answers the question of how many articles he read to select the ones that got into the book.
It’s difficult to give an estimate, but let me try. I see several thousand articles in one year but obviously I discard most of them quickly (as far as this particular book series is concerned). Not necessarily because they are not worthy of my attention or do not deserve reading; I just know by reading the first paragraph or by a cursory look at the prose and the exposition that they wouldn’t fit in the book I envision. Perhaps I gave serious attention and read thoroughly in direct connection with this volume about four-five times more texts than I finally chose—which means 150 or so. That is a rough approximation.
The end result is 35 interesting and varied articles in six areas: Mathematica Alive, Mathematicians and the Practice of Mathematics, Mathematics and Its Applications, Mathematics Education, History and Philosophy of Mathematics, and Mathematics in the media. The contents are here.
Find me on LinkedIn
I'm about to make a big change in my life to have my work be aligned with my deep love of Math. Part of that change is going to be about having richer connections with other people who love Math. If you and I have made a nice connection through this blog and if you are a Math person, especially someone who is working to popularize Math, I'd love to be connected with you on LinkedIn. Just click on this link and request that I add you to my network. You can use the email sol dot lederman at gmail dot com. I find LinkedIn to be a great way to connect with people even when they move or change jobs so it's a great way to make connections and to keep them.
Oh, and I'm not closing down this blog.
Food scientists at the UK's University of Leeds have developed a formula for making the perfect piece of toast.