Car Talk Algebra Puzzler

I came across a math puzzle from Click & Clack on NPR's always entertaining Car Talk, see if you can figure it out, it goes like this:

"RAY: Last month, Tommy and I decided that we were going to take a trip north to see the foliage. Tommy drove the first 40 miles. I drove the rest of the way. We looked at the foliage for three or four minutes, then decided to head home.

We took the same route home.

On the way back, Tommy drove the first leg of the trip and I drove the last 50 miles.

I got home and my wife said, "Who did the driving?"

I explained that Tommy drove the first 40 miles, then I drove the rest of the way. On the way back, Tommy drove the first leg of the trip, and I drove the last 50 miles.

She said, "But who did most of the driving?"

I told her, "You can figure it out. In fact, you can even figure out how much more of the driving was done by that person."

And that's the question. Who drove the most -- and how many more miles did that person drive?"

Creating Art Using Only Lines and a Circle

Have you ever used a Spirograph? If you have ever been drawn toward the geometric patterns and colors created by this nostalgic toy, then you should try using some of the techniques described here at MathCraft and here at Jill Britton's website. Both of these wonderful sites teach you how to create intriguing works of art using very simple supplies: just a compass and straight edge, or a needle and thread.


Straight lines can be deceptive, as you can see see in the pictures to the side, believe it or not these pictures are made using nothing but straight lines! Notice the circle in the middle of the top picture is made by the outlines of the inside of 6 different colored pentagrams. The heart-shaped cardioid below has the same kind of outline, getting its curves from the perfectly straight lines composing its border. The same principle can be used by weaving a needle and thread through a piece of paper or fabric, as demonstrated on the Jill Britton site.

Take a look and try it out on your own, at the very least youll have something to doodle in class that actually uses math.

Visualizing Global Population Trends

In the video to the left, NPR explains visually how much the world's population has exploded in recent history. Its interesting to think about, it almost seems like we are in an age of flux, between an old time and a new future. How will our global culture as a species change just within the next hundred years or so? Will individuals naturally decide to have less children as a conscious or subconscious reaction to longer lifespans, better medical services, less food, water, & other resources to divide between an ever growing population? Is there a self-regulating limit that nature silently exerts on all of us, like an inflating balloon aware of the pop?

The Garden of Cosmic Speculation

I found this awesome mathematically-designed garden at reckon.posterous.com, check it out!

Technology & the Classroom

In this article by Ian Jukes of The 21st Century Fluency Project, he discusses the role of technology in the classroom. The phrase that stuck out at me was: "Because the most powerful technology in the classroom was, is and will remain...a classroom teacher. But not just any classroom teacher - it has to be a classroom teacher with a love of learning, an appreciation of the aesthetic, the esoteric, the ethical, and the moral - a teacher who understands Bloom and Gardner."

I have had discussions with people and read articles saying that we need to switch to a educational system based around ideas such as the Kahn Academy, in which learning is a very individualized, self-motivated, "high-tech" path, all but getting rid of physical classrooms, if not teachers.

I agree to a certain extent, and I love sites like the Kahn Academy, but the problem is that the only students that will really benefit from this method are those who are self-motivated, genuinely curious learners in the first place, the rest would not suddenly start to care about, say, Algebra just because its now on a computer screen.

So I agree with this article to a certain extent in the same manner; yes, I think that the younger generations do have a certain intuitive link with computers, the internet, and technology, and yes I agree that not only should schools be trying to utilize these tools to their advantage, but that it is inevitable that schools will naturally have to change technologically in this direction just like every other industry on the planet. We should absolutely be educating our students to be technologically savvy to be able to lead the way in the ever globally connected world. On the other hand, I sometimes think that articles like this one can sound a bit exaggerated in that I dont know that technology will suddenly make a higher % of students more interested in learning, because this problem of lack of self-motivation and caring about school has existed long before 20 or so years ago. This % of students, I would have to guess, wont be a drastically different % in a classroom loaded to the brim with technology - though I do believe technology implementation definitely does have a positive effect, if any, I think its more than anything the quality of teacher that matters more at inspiring students.

I do not necessarily think that children in America, on average, seem to be declining in motivation, inspiration, creativity, intelligence, or curiosity relative to the general American populace of any age, nor that they are so ADD or electronically "rewired" that they need to be surrounded by the stuff in order to learn. I do, however, see this trend becoming a growing problem in our society in general, not just in children who are growing up with it. This problem is more complex than I care to go into.

What has seemed fascinating to me is putting our education system into historical relevance, and I havent heard too many people doing that. Correct me if Im wrong, but the last century or two have been a significant historical aberration in regard to to % of educated populace. Before that, it was only a very small % that were fortunate enough to have an education as we know it available to them, and now its not only available, but mandatory, in our country! This is a great thing, but we forget how new this experiment is. I imagine (though just guessing) that those who did receive an education more than a couple centuries ago, would be comparable to our modern classroom's most self-motivated, interested learners.

So now we are faced with the challenge of educating the entire populace - and in an exponentially ever-changing technological world. Keeping up with all the tech is absolutely positive and unavoidable, but it doesnt erase more complex underlying social problems, and it doesnt trump what I believe to be the 2 greatest factors: an inspirational, creative, understanding, intelligent teacher and as small class sizes as possible.

So for SASIC, I think we are doing a great job with infusing technology, and we have some really awesome teachers, and have an atmosphere of creativity and room for the students to become inspired, and stretch their legs out, so to speak. So I think we should keep up the great work, and try to keep in mind that inspiring the students to want to learn throughout their lives, be constantly curious, and express their creativity constructively are the best gifts we can give to them and to our society, species.