Scenes from a Dynamic Math Classroom

Here we go again

2012-01-11T06:14:00.000-08:00

Latest "NCTM Summing Up" posts the inevitable. More study needed. What a surprise. As if we haven't done enough studies already! It's business as usual. The major players in the math ed community want to have fun telling us what we should be doing with our students using scare tactics to get the nervous public to go along with their latest hype. We're still a "Nation at Risk" and will continue to be as long as the "hafta-do" curriculum rules in most schools. Kids need to be heard more and college professors less because the current paradigm is not making any substantial improvements in teaching school math.

Google's latest math trick

2011-12-06T07:44:00.000-08:00

(Click on image to go to blog entry.)

Compare the Google result with WolframAlpha. Since we search all the time it's convenient to have this feature inside of Google. But we've had WolframAlpha for while. So it's good to have choices. Right? Well, most of the time. With vulnerable math students using the same graphing software can be a plus. Think of it as a bicycle with training wheels. Once the training is successfully over switching bicycles can indeed be fun. But most math students have struggled with staying on the bicycle even with training wheels moving from one software app to another until they collide head on with their fragile knowledge of math and give up. (Refer to my "Ok, if you say so." story in Mathematical Encounters.)

Google

WolframAlpha

Noon Day project measurements begin this week- September 19, 2011

2011-09-20T18:03:00.000-07:00

Carl Sagan tells the story (6.5min)

The Goal of the Noon Day Project is to have students measure the circumference of the earth using a method that was first used by Eratosthenes over 2000 years ago. Students at various sites around the world will measure shadows cast by a meter stick and compare their results. From this data students will be able to calculate the circumference of the earth.

Doing the measurements

Follow me on Twitter (Hashtag #noondaymeasure) as I recreate the experiment that Eratosthenes did. I hope to do my measurements on September 22 weather permitting.
There is some good background material on the measurement at the Noon Day project site hosted by the CIESE (Center for Innovation in Engineering & Science Education) - Stevens Institute of Technology in Hoboken, NJ.

Brother, can you spare a quarter (or something like that?)

2011-09-15T06:21:00.000-07:00

Misconceptions revisited...

How much do the pencils cost?

Two different versions of the same thing?

2011-09-10T08:40:00.000-07:00

Example from mathatube.org (2:19)

Video makes it more interesting. Right? Wrong.. It's still boring....

Those #?%& Supermarkets: They're Out to Catch You

2011-08-14T17:19:00.000-07:00

Nothing like the word Free to make you take notice at a supermarket. But of course there is always a catch since I have to buy at least one 16 oz. package for $3.99. So what I'm really paying for my free box of strawberries is $2.00! Now if I'm in the market for more than one package I might consider paying $2.00 per package. But since for me they go bad pretty quickly and I'll never finish the second box before it does goes bad, that really means I'm paying $3.99 for the box I actually eat! Wouldn't it be just plain old easier and more honest to leave the word "free" out if the sign read:

Get your students to find examples of this and to write the manager of a store that pulls this nonsense and see how the company tries to justify this deception.

Why the Chelsea Spike in the early 1990s?

2011-08-10T10:13:00.000-07:00

In the early days of summer nature has a way of entertaining us with magical views of flowers in full bloom. A kind of neat phenomena that makes everyone who is not too busy take notice. A camera can capture such a scene in its full glory. Mathematical photos such as graphs can also reveal some interesting neat phenomena that can bring about similar rewards. At least it did for me when Kelvin Misco of Wolfram Research at their booth at the NCTM conference in April showed me what happens when you type the name Chelsea at the Wolfram Alpha website. You can do additional baby name investigations at this cool website. Type a name and see what happens. Students really like this one and will explore it in interesting ways without much help. I'm curious if any math teachers have used this. If you try it with kids let me know how it went.

The Ultimate Equation*

2011-08-10T09:40:00.000-07:00

Source: New York Times

Talk about our country slip-sliding into global economic oblivion. Here's one that could set education back to 1984 and Big Brother. I'd love to see how this formula correlates with human judgement of teacher skills. Watson beat the best jeopardy players, but would you spring him on your kids without human intervention?

*Originally posted on March 6, 2011 but not published.

What can you do with this* sign?

2011-08-04T16:28:00.000-07:00

Wrap your brain around this one. Makes perfect sense. Doesn't it? I just checked on my calculator and the total is right. Even in Gold Hill over a 150 years ago they would have gotten an "A" for addition. But making sense out of things wasn't one of their strong points.

This sign - well actually one similar to this - gave me an idea for what I (or you) can do with this.

Here is what I did with it in a 6th grade math class. (Click here.)
* See #WCYDWT on twitter.

ISTE 2011 Reflections - My presentation

2011-07-01T09:24:00.000-07:00

In case you missed it, the title of my presentation at ISTE was Math 2.0: Scenes from the Dynamic Math Classroom. (My soon to be revised agenda page's link is here.) Besides promoting my vision of Math 2.0 and sharing some scenarios from potential dynamic classrooms, my personal goal for the session was to kick off my plan to write a "dynamic book" that is tentatively titled the same as my presentation "Math 2.0: Scenes from a Dynamic Classroom". It will include the five activities (stories) I mentioned in my talk:

Average traveler
Stock Market Game Jr.
Shopping Spree Adventures*
Measuring the Circumference of the Earth (In the spirit of Eratosthenes)
The Great Green Globs challenge

The first story I'm putting together is the Eratosthenes measurement activity/project which BTW is considered one of the greatest achievements of all time. (If you missed the video of Carl Sagan telling the Eratosthenes story before my session started you can see it at the Noon Day project** page here.)

I will be chronicling my adventures in writing this book in this blog. If you would like to be informed when I've updated this blog, please let me know by sending me an email: ihor@dmcpress.org

Also if you would like to be on my emailing list please sign in at the agenda page for my session.

*See what Dan Meyer did at a grocery store that led to a great problem solving scenario. Link

**You can sign up your students for the Fall Noon Day project starting on September 1st. Let me know if you are interested and I can help you with more details.

Crowdsourcing Jr. Classroom Activity

2011-03-05T15:44:00.000-08:00

Here's a great idea for students
going out and collecting data!

I read this article "Smart phones foster dumb habits among pedestrians" today and realized that students could do a similar investigation to the the author of this article did.

"One too many times stepping around a shuffling pedestrian immersed in e-mail led me to conduct a social experiment. I decided to count the number of people I saw distracted by their electronic devices during my 25-minute morning walk to work from New York's Grand Central Terminal to the far west side." -David Bauder

It doesn't have to be exactly the same thing if your location doesn't lend itself to observing people on cell phones. But I think you get the idea of what I'm after: kids doing research/data collecting in order to answer a question that interests them.

Here's another example that might not be as interesting to kids, but is on the right track:
Brian Lehrer a PBS host of a call-in radio show started (according to him) an informal, unofficial, thoroughly unscientific crowd sourcing experiment to determine the price of milk in NYC. The blurb for the radio/pod broadcast segment was:

"Our next "crowdsourcing" project sets out to look at how the prices of a pre-determined basket of goods differ throughout the New York area. We plan to ask listeners to investigate the prices in their local stores, or stores in any other neighborhood, to get a snapshot of prices. We're still trying to select the three goods, and we're inviting listeners to collaborate with us at this early stage. What are the most representative products? Milk, eggs, flour, breakfast cereal? Let us know on the air and in the comments section."

I've been a long time fan & practitioner of trying to find interesting things from the media to motivate my math lessons and sometimes I'm even successful.

It can be a perfect vehicle for the "do now" panacea that Everyday Math and other current textbooks have popularized and taken to new level by Dan Meyer and company which you can follow at the hashtag #wcydwt on Twitter.

The iTunes count up to 10 billion downloads counter quits early

2011-01-22T08:28:00.000-08:00

I was disappointed to discover that the count up counter for iTunes quit early. So one can only guess when exactly the 10 billionth download occurred. Watch the 24 second clip to see what happened.
I did my last estimated guess for when the counter would reach its goal just before I went to bed at 2:30am. Since ETA was 5:30am and I wasn't willing to stay up or get up early to watch it live, I sort of TiVoed it using a screen capture video app.

Untitled from ihor charischak on Vimeo.

Why did it quit early? Was the count up counter not really accurate? Or was it just simply human error? I wonder if Milo's grandson who works for iTunes can find out for us.

Also, I'll have a detailed description of my effort in predicting this outcome posted soon.

iTunes downloads approaching 10 billion

2011-01-20T09:21:00.000-08:00

The number of iTunes downloads continue to grow. Watch it live by clicking here.

Can you predict when this counter will hit 10 billion?

Have your students figure it out and post their predictions (below) before the end of school on Friday. We'll acknowledge the student(s) who comes closest.

Who knows they may even win the prize for downloading the 10,000,000,000th app!

Supermarkets marketing strategies 101: How to pull the wool over the shopper's eyes

2010-12-08T09:16:00.000-08:00

Notice Dial's effort to conceal the

decrease in the amount by using a
taller, thinner container.

Another gem from Dan Meyer's repertoire of great lesson ideas. Here's what this particular "lesson" offers.

The context for the lesson makes for a great story. Your supermarket is out to hoodwink you!

The math is intrinsic to the context of the problem. The only way to understand the supermarket's strategy trickery is to do the math. Kids will actually want to understand how unit pricing works. This is what I mean by learning the math from the "inside out." That is, the math is embedded in a context that encourages real, non-scripted learning.

Dan does not offer you a specific plan of action, but rather helpful guidelines. He gives you resources to work with and makes them accessible via download.

The ideas for the lesson are developed collaboratively online with other math teachers.

Dan credits his sources.

Dan ships* his product.

*An expression coined by Seth Godin that mean you get your idea/project out there so that others can take of advantage of it.
Shipping is fraught with risk and danger. - Seth Godin

Deceiving graphs

2010-11-22T08:20:00.000-08:00

I was surprised find someone on the TED talk circuit use a classic example of graph distortion that advertisers like to use to make the growth of sales look bigger than it actually is. Here's how they do it. (I'm using Sketchpad to demonstrate it.)

Circle C is almost 16 times
bigger than circle A.

Since the money total in 2000 is double that of 1990 it makes sense to show visually this doubling effect. If you want to enhance it and make it more than just mere doubling then use a circle graph where doubling the diameter actually produces an area that is 4 times larger as I did in this Sketchpad sketch I made.

In the actual diagram used in the TED talk, the diagram was definitely not done to scale. The area of the largest coin is 7 times bigger than the smallest coin though the amount is only 5 times bigger. Not outrageous but still misleading.

Be less helpful? It Depends

2010-11-19T10:16:00.000-08:00

Dan Meyer writes about teachers being less helpful in the classroom. For me that depends on the situation. Knowing when to step back and let a student "flounder" a bit can be useful, but sometimes it can do more harm than good. A swimming analogy may not be appropriate, but it comes to mind. Here's what someone wrote about learning to swim: "Contrary to popular belief never throw your child in the water to help them learn to swim." Apparently in China parents aren't worried about this; it's very commonplace. Now learning math is not as life threatening as possible drowning might be but for many of our students who are not intrinsically motivated to learn math it could be a problem to be less helpful. I'm sure Dan doesn't have in mind to let kids flounder. His concern is that there is too much hand-holding and dependence of students on teachers to tell them what to do most of the time. What we want is to have students become independent learners so they don't rely on the teachers to have to crack the whip all the time. A blend of both (nudges and standing back) by the teacher applied appropriately yields the best results.

A historical note:
Logo the programming, learning software environment that Seymour Papert championed in the 1980s and got such a splash from the media lost some its sparkle when too many teachers expected Logo to work its magic all by itself and were "less helpful." Guidebooks were written to try to help with that, but that didn't allay the public perception that Logo doesn't work. Withholding help in a teaching sense is a skill that needs to be carefully applied.

Are page numbers becoming obsolete? Check out how a Kindle app handles them

2010-10-15T07:37:00.000-07:00

Add caption

Since I don't mind and actually kind of like to read (as well as listen to) books on my iPod Touch and I'm not going to spring for a Kindle (though the "experience of reading*" might be better) anytime soon, I discovered I can use an app for my Touch that will let me read books I buy on Amazon.com intended for a a Kindle Reader. At the moment I'm enjoying reading "The Science of Liberty" by Timothy Ferris. One problem I have is knowing what page I'm on. You see eBooks for Kindle do not keep track of location by page numbers but rather according to units dependent on bytes (1 unit = 16 bytes or 16 characters.) It really didn't matter that much as long as everything worked properly, but since electronic devices have a habit of causing trouble, so when I had to reinstall my operating system on the Touch I lost my location in the eBook. I knew what chapter I was in (because I printed out the TOC of the physical book from the Amazon website) so I searched for the title and found my location that way. But what if I didn't know the name of the chapter or remember any key words on the page** that I was last reading?

This is a 4 unit location.
The final unit is at 8486.

I scratched my head and figured I could set up a function relating the number of units in the eBook with the total pages in the real book which is what I did. The accuracy was not great. Anyone one out there want to do another example and check the accuracy? Download any free Kindle book. Check out how many units long it is. Comapre that with the number of pages the physical book has. Let me know what you come up with. (I'm being purposely "less helpful" here to honor Dan Meyer who has coined the phrase in a teaching math context.)

*Positive attributes of reading on a handheld: All the usual suspects including: easier to carry and manipulate device; you can carry more books and articles than you probably can read in a life time etc. But also the most important one for me: I don't need a lamp to read at night since my wife can't sleep if there is any ambient light on. And so far the back lighting of the ipod touch doesn't bother her.

**Chronological pages on the screen depend on factors such as font size and the size of the screen. So the units used for the numbering system is based on the number of alphanumeric characters used in the book. So 1 unit in a Kindle eBook is 128 bytes or 16 characters (which include spaces and other punctuation.) My Science of Liberty ebook has 8486 units which means 8486 * 16 = 135,776 characters.

The Monty Hall problem revisited

2010-09-17T09:20:00.000-07:00

This is one of my favorite problems because it always baffles me why its so hard to get to "know" the solution. Every time I come across and read it, it's like I'm seeing it for the first time. Holding an intuitive notion of the solution always seems to elude me.

I came across it again today. This time on video explained by Keith Devlin who is a wonderful explainer.

http://www.stanford.edu/~kdevlin/Movies/MontyHall.mov

More about Keith, Monty Hall and why some math needs to be learned "top down" - at least according to Keith - coming soon.

Phantom Traffic Formula

2010-06-19T06:44:00.000-07:00

Phantom Snarl?

Ever wonder why traffic snarls for no particular reason? Here's a mathematical explanation. (Formula below.)

Another math app added to the Apple Apps store

2010-05-06T08:03:00.000-07:00

The Apple Apps store is starting to fill up with this kind of skills practice software. Since the only thing of interest for the kids is the game itself, there's not much learning going on here math-wise, unless you want kids to practice math facts they already know. But then, again, it's only a buck ninety-nine.

Tax Day Math

2010-04-15T07:02:00.000-07:00

Doing homework 2.0

2010-04-12T05:58:00.000-07:00

Link to story

Different...

2010-04-09T08:44:00.000-07:00

Marketing Done Different
Friday, April 09, 2010
Consumer marketing expert and Harvard Business School professor Youngme Moon talks about how companies can stand out in a saturated market and how she's practicing what she preaches in selling her new book: Different: Escaping the Competitive Herd.

Source: Brian Lehrer Show 4/9/10

Math 2.0? I don't think so...

2010-04-06T17:09:00.000-07:00

According to the students at Lincoln Middle School the Mathtrain.TV video (below) demonstrates Math 2.0 in action. Watch the video and see if you can tell me what my problem with it is.

Hint: This is Math 1.0 using Web 2.0 tools. What's missing? (See What is Math 2.0?)
Tweet me at @climeguy with your comment.

Noon Day Project - My measurement - part 2

2010-03-27T07:44:00.000-07:00

Here's how I measured the sun angle for the Noon Day project.

I set up a meter stick perpendicular to the ground with the help of a metal bookend.
I checked the Internet for the approximate time of local noon (when the sun is highest in the sky). Sunrise was at 7:00am and sunset at 7:06pm. I found the midpoint between those times which was 1:03pm.
I set up my station at about 12:45 and then watched and recorded the lengths of the shadow every 5 minutes using a piece of chalk as the time approached local noon. (The length was getting shorter and the shadow was moving west to east.)
After I put down my mark I also took a photo of the shadow and stick from as close to ground as I could.
I continued till 1:15 when I noticed that the shadow was now getting slighter longer and more easterly in direction.
I used the photo where the shadow appeared to be at its shortest which was 1:03 EDT and copied an pasted it in Geometer's Sketchpad.
The Sketchpad tools allowed me to make the sketch with the details that you see in the picture including the sun angle which is formed by the sun's ray and the meter stick. (The image size of the meter stick was 6.7 cm.)
Next I'm going to post this summary on the CIESE Noon project page. (My School Name is: CLIME)

This is part 2. See previous post for part 1.

Windy News

2010-03-16T22:37:00.001-07:00

The Big Tree Take Down

The wind brought it down to its present position. How would you bring it to the ground without further damage?

Here's what the experts did.

I do wonder why the chain saw guy stopped cutting it and was told to saw it elsewhere. I was too busy filming and didn’t think to ask.

I was looking for math in their solution to the problem. But what I learned is that if you have the right tools and the know how to use them properly the job becomes a “no brainer.”

There obviously is a lot of science here. Any suggestions as to how the science might inform the math?

Noon Day project begins this week - March 8, 2010

2010-03-12T08:27:00.000-08:00

Watch as Carl Sagan describes some of the background surrounding Eratosthenes' experiment in this 6 1/2 minute video.

Follow me on Twitter (Hashtag #noonday) As I recreate the experiment that Eratosthenes did. I hope to my measurements on March 17 weather permitting.
There is some good background material on the measurement at the Noon Day project site hosted by the CIESE (Center for Innovation in Engineering & Science Education) - Stevens Institute of Technology in Hoboken, NJ.

Get real "Do Nows" to kick start your math class

2010-03-01T06:25:00.000-08:00

"Do Now" classroom openers are all the rage these days (i.e. Everday Math). Why not reach out of the box and do one that's timely for the day you do them? Today is the day (3/1/10) after the Olympics closed and by the latest count the USA, Germany and Canada were the biggest winners.

What if we wanted to give a gold medal to the country that "won" the Olympics how would you decide? One way might be to assign 3 points for each gold medal won, 2 for the silver and 1 for the bronze. (This is similar to how they determine standings in the National Hockey League.) Who would be the winner? Would Canada's 14 gold medals compensate for their lower total of medals than the USA? (See a Google Spreadsheet with the results.) Feel free to edit it! Help me turn this "do now" into an activity worth exploring.

WCYDWT defined?

2010-02-13T07:39:00.001-08:00

Blog entry - 2/13/10 updated 3/1/10

Two Excellent Entries For The WCYDWT Course Catalog

February 9th, 2010 by Dan Meyer

Kate Nowak:

Here’s what basically has to happen to make a successful WCYDWT lesson:

Lighting strikes (you observe something).
You recognize that lightning has struck (you say “holy *&^%”).
You investigate by building layers of abstraction on your observation.
You realize that that particular abstraction fits in your curriculum.
You strip away all those layers to a core question interesting to a 15 year old, who (I’m sorry and draw whatever conclusions you will about me or my school system) are the least interested people on the planet.
You rebuild the abstraction in a way that will support the questions you successfully predict they will ask.
You make attractive keynote slides out of it.
You extend your original abstraction to questions that they will want to pursue to enhance their understanding.

This is a pioneer profile of a WCYDWT activity. The education world will never be the same once this becomes mainstream. Why? Because it encourages teachers to break out of the mold and be creative in "lesson planning" whether its in the box (brick & mortar school) or out in the virtual world probably a combination of both.

In one of Amazon's user reviews of Seth Godin's latest book "Linchpin: Are you Indispensible?" the reviewer writes:

Linchpin is a most unusual, well-organized, concise book about what it takes to become indispensable in the workplace - whether you work for someone else (at any level) or are self-employed. It's about how business has rapidly changed and how treating employees like factory workers (or doing your job like one) doesn't work any longer. We must make choices and take action to "chart our own paths" and add value that others do not. We cannot wait for a boss or a job description to tell us what to do, rather we must just take the initiative ourselves. Only then can we become indispensable "linchpins," rather than replaceable "cogs."

(This is a key to educators becoming "life long learners".)

Get ready, get set, go Educon 2.2 with a math spin (I hope)

2010-01-29T17:10:00.001-08:00

So here I am ready to do Educon 2.2. Since the event is in Philly and I'm at home I got my tweetdeck set up to view tweets that I follow along with tweets that contain #educon and #noneducon in their message. Let the circus begin....

I'm back from my first go at it. Lasted about 45 minutes. What did I make of it so far? I'm reminded of what computers were said to do most of the time: GIGO - garbage in, garbage out. It wasn't really that bad. A #educon tweet told me about an interview the writer did with Seth Godin and that transcripted in her blog. His views on education. Interesting. I followed my mind drift and clicked on an intervew Seth gave on his quidoo.com website as I was being bombarded by a cacophony of tweet flashes every few seconds or so it seemed. There's something fun about this blitz of info. Nothing about math. but then retrieving relevant stuff is like catching the proverbial needle in the haystack. There has got to be a better way. The show begins tomorrow. This time I will be ready for Math!

PS - I missed the virtual feed of the panel discussion at Franklin Institute. I wonder if it actually happened.

Was Belicheck's math right when he said: "I thought it was our best chance to win."

2009-11-17T05:40:00.000-08:00

Was Bellichick's math right when he said "it was our best chance to win." I agree with him. Kick or pass: Which was a higher probability? Anyone want to offer an analysis?

Here's mine.

Probability of Patriots getting a first down on 4th and 2? I say 90%. It's only a guess but given the Patriots football prowess along with the element of surprise, I say they would have made it on average 9 out of every 10 times they tried it. On the other hand, punting to the Manning machine is a shaky 50-50 proposition at best. Also, what are the chances the receiver would bobble the ball? Video of play.

What do you think?

WCYDWT (What can you do with this): How Big is the Gorilla?

2009-10-24T08:26:00.000-07:00

Here's a good slide to show to start a conversation about decimals with your class. The first question that comes to my mind is: So, really, how big is this gorilla? What are some of the questions that come to your mind?

Most textbookish review sections for decimals are pretty boring. How might this help? Putting a common idea in a interesting, surprising way will get the kids attention. Now how do achieve your math objective with that?

Source: Wired Magazine (Nov. 2009) p. 45. I had to scan it; couldn't find it on the Web.)

WCYDWT (What can you do with this): Rolling boxcars

2009-10-13T07:30:00.000-07:00

DYBT?*

You can win one million dollars if a celebrity rolls a pair of sixes on the Tonight... (Woops sorry) the Jay Leno Show. See daily dice roll clip.

What are YOUR chances of winning? 1/36? Read the fine print to find out... if you can stand it.

http://playatMcD.com

Use the Menu to avoid all the animation. Check out the "helpful" registration process video.

*Do you believe this?

What would you do with this sign?

2009-09-30T20:52:00.000-07:00

I've tried it with many 6th grade classes. Have gotten some interesting results.

See my comments about it.

Measuring Circles: Good idea, bad pedagogy?

2009-09-17T09:25:00.000-07:00

From the WCYDWT files:
Watch this video and tell me: Would you show this to kids as is? Anything missing here? If so, is the missing thing necessary?

To see video click here.
(2:42 min)

What's Wrong with this Picture?

2009-05-07T16:22:00.001-07:00

Hint: It appeared as an ad in the program book for the NCTM conference where the theme was EQUITY. Hello? Anybody home?

Activities website for the New DMC workshop is up.

2009-01-20T15:04:00.000-08:00

Here it is. Link. See you in Philly.
-Ihor

The NEW Dynamic Classroom. What happened to the old one?

2009-01-19T08:26:00.000-08:00

It's still good... just a bit dated. Here are a couple of articles that will help you to get ready for my workshop this Thursday.

A Look at Technology's Role in Professional Development of Mathematics Teachers at the Middle School Level” (School Science & Mathematics November, 2000)
Link: http://mathforum.org/clime/ssm.html

The Dynamic Classroom: What is it?
Link: http://web.mac.com/ihor12/home/Articles/dmc.pdf

Workshop Activity page link - later today.

Description of my session:

The New Dynamic Classroom: Teaching & Learning Math with Technology and Web 2.0 (Ihor Charischak)
Come and experience a series of unique & compelling activities that incorporate significant software environments (Spreadsheets, MicroWorlds, and Sketchpad) that will help a teacher to engage their students in gaining a deeper understanding of powerful mathematical ideas. For more information see http://DMCpress.org

-Ihor

The Average Traveler Activity

2009-01-18T12:30:00.000-08:00

At the AMTNJ Conference last Thursday I did the average traveler activity with the 26 math educators who attended my session "Back to the Future: Teaching & Learning Math with Technology (3.0)"
Based on the distances that each attendee traveled to get to this conference, I asked who in this room would represent the average distance traveled? Guesses ranged from 20 to 50 miles. Since we didn’t have access to computers to do this in real time, I used the distance from each attendee’s school (or administrative office) to the Holiday Inn in Somerset, NJ (where this session took place) to figure this out. I added placemarks at each school's location using Google Maps and used the distances provided by the software. Which school’s placemark do you think is closest to the average distance that the participants traveled to this conference? The yellow marker is the site of the conference.

I used Geometer’s Sketchpad to draw a circle with the location of the session at the center and the radius of the circle gives an estimate of the distance to the various schools represented. By changing the radius of the circle I could approximate what the average was. The radius of the circle in the image is 49 miles. Note there are several schools that are candidates for being closest to the average distance. Take a look at Google Maps and identify your location. The sites are open for you to make corrections and updates.
Here is a Google spreadsheet of the relevant data.

Check out the links provided and see if all this makes sense to you. Let me know by sending me a comment below.

Oh, I almost forgot. The Average travelers were from Wayne Valley High School. The average distance was 46.42 miles and Google Maps reported that Wayne was 46.6 miles away. It was almost a bull's eye. I owe you a prize!

original posting: 11/30/08

DMC Press Blog continued

2008-07-18T16:05:00.000-07:00

Due to unforseen problems with iWeb's blogging component during the switch from dot mac to mobile me, I decided to move my blog to this current site: http://dynamicmathclassroom.blogspot.com

You can still see the previous blog at dmcpress.org

-Ihor