Sine of the Times

Exploring Conic Sections with Sketchpad

Posted on May 12, 2012 by Daniel Scher

As a student, I didn’t place conic sections on my list of favorite high school topics. The standard textbook treatment of the ellipse, parabola, and hyperbola seemed uninspired. There were messy algebraic equations with multiple square roots. There was lots of terminology. Drawing a conic meant plotting several points on graph paper and connecting them with a wobbly curve.

I gave little thought to conics until I met David Dennis, then a fellow graduate student in mathematics education at Cornell University.

David had a keen interest in the origins of curve-drawing devices. One historical figure in particular intrigued him: Frans van Schooten (1615–1660), a Dutch mathematician whose translation and commentary for Descartes’ landmark treatise, La Géométrie, led to the popularization of Cartesian geometry.

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Posted in Math Software | Tagged Constructions, Dynamic Geometry, Modeling, Sketchpad | Leave a comment

Moral of the Story: Pineapples Don’t Have Sleeves

Posted on May 8, 2012 by Josephine Noah

I intended to start this blog post inspired by this article about “security breaches” of the California Standards Test (CST) standardized test. My thoughts about this article were in two directions: how do you ensure integrity of high-stakes tests in our current era of pervasive cell-phone/camera/internet access; and are kids even taking these tests seriously, and what does that say about their value and meaningfulness?

I started to ponder these topics, then got totally derailed when I came across a reference to “Pineapples Don’t Have Sleeves” in the article’s comments. I was then sucked into a YouTube vortex of videos on the topic of pineapples not having sleeves. In case you don’t have an hour or more to spend on the topic, I’ll provide some highlights. (And if you’re in New York, this may all be old news; apologies.)

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Posted in Assessment | Tagged Standardized Testing | 1 Comment

Some Suggestions for Math Technology Professional Development

Posted on May 4, 2012 by Karen Greenhaus

Demonstrating TinkerPlots at NCTM 2012 I have been really focused on math technology professional development lately, which makes sense of course, since that’s what I do for a living. But after last week’s NCSM and NCTM conferences (see Karen Coe’s recent post), where professional development came up often (see my personal blog), and after responding to numerous email inquiries this week, I decided to share some Key Curriculum Professional Development options and offer my suggestions on how to get the most bang for your buck (luckily, many of these options are free).

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Posted in Professional Development | Tagged Fathom, Modeling, Pedagogy, Sketchpad, Standards for Mathematical Practice, Teacher Collaboration, TinkerPlots, Use Appropriate Tools Strategically, Videos | Leave a comment

Exploring Factor Patterns in an Interactive Array

Posted on May 2, 2012 by Daniel Scher

OK, I admit it: I have factors on the brain.

First, I wrote about When Factoring Gets Personal. I followed that with a post describing what happens When Factors Put on Their Dancing Shoes. So what’s next—When Factors Apply for a Home Equity Loan? Thankfully no, but I do have an update to share.

Last week I had an idea for a new Dynamic Number Sketchpad model that’s easy to describe. A rectangular array of numbers from 1 to n appears on screen. Those numbers that are factors of n are shaded blue. The remaining numbers are shaded orange. By dragging a point in the upper-right corner of the array, you can change its dimensions.

With this concept in mind, I created the sketch. Here are two pictures of the array showing the factors of 24 and the factors of 27. Feel free to download the sketch.

Factor Arrays showing the factors of 24 and 27

What are the mathematical and pedagogical benefits of using this model?

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Posted in Math Software | Tagged Dynamic Number, Problem Solving, Sketchpad | 2 Comments

Behind the Scenes at NCSM and NCTM

Posted on April 30, 2012 by Karen Coe

I thought I’d give you a behind-the-scenes view of last week’s activities in Philadelphia.

Karen Greenhaus, Andres Marti, Elizabeth DeCarli, and I were assigned to the first event, NCSM. We were up bright and early on Monday morning to set up our booth, even although it was 4:00 am in our heads, having just flown in from California (Karen from Texas). Our booth was to be delivered at 8:00 am and set up by the opening of the show at 11:00 am. We waited and waited… and waited.

Finally I called Lainie Johnson, our Marketing Manager in California (I apologize for the VERY early call, Lainie) who gave me the shipping company’s information and the case of the missing booth was opened. I got my first real glimpse of the massive behind-the-scenes logistics of the NCSM and NCTM events after multiple calls between the main hall and the loading dock yielded no results. I asked if I could go down to the loading dock and was told “you don’t want to go down there, it’s dangerous.” So I went anyway…

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Posted in Conferences | Tagged Fathom, Ignite, IMP, Interactive Whiteboards, NCTM, Sketchpad, TinkerPlots | 1 Comment

Philadelphia Freedom

Posted on April 23, 2012 by Andres Marti

If you’re around my age, you clearly remember the famous Elton John song. I can’t help but think of “Philadelphia Freedom” whenever someone mentions Philadelphia. It’s an involuntary response that shoots straight out of my unconscious. And since today is the first day of the NCSM conference in Philly, that song has been percolating in my head ever since I arrived in town a couple of days ago.

Elizabeth DeCarli tinkering with her plots at NCSM.

It turns out that since I joined Key, I’ve met many people from Philly, including Scott Steketee, who works for KCP Technologies. Scott is one of the most thoughtful, intelligent, and kind-hearted people I’ve ever met, and he’ll be one of our Ignite speakers this Wednesday. (For those of you fortunate to be here this week, Scott has a Sketchpad-based surprise waiting for you!)

Philly is also the home of Drexel University, which houses the Math Forum, the world’s largest online math community. As seems appropriate in this historic city of freedom, the Math Forum is completely free, and has been a source of support for math students seeking help for two decades now. They are currently set up next to us in the exhibit hall, which is great because we love Annie Fetter, Steve Weimar, Max Ray, and the rest of the gang, who will also be presenting talks at the Ignite. In fact, there’s a long history between the Math Forum and Key, as the Math Forum and Sketchpad both evolved out of the Visual Geometry Project in the late 1980′s.

Anyway, teachers really seem to love free stuff, so we’ve got some free technology gifts to give away. First of all, you can download all three of our software products, Sketchpad, Fathom, and TinkerPlots, for free. Granted, they are in preview mode which prevents saving and printing, but it does allow you to play with the tools and explore the ample free sample activities that come with them. Then we have Sketchpad Explorer, which is a Sketchpad player for the iPad, which you can download for free from the Apple App Store. And finally we have our Technology User Group on Thursday evening, which includes free activities, appetizers, and drinks.

So if you’re in Philly, stop by and visit our booth or come to our Ignite on Wednesday, or join our User Group on Thursday. We’d love to see you! And if not, take a look at our technology tools, and watch some videos of previous Ignite speakers while you’re there.

Posted in Conferences | Tagged Fathom, Ignite, Interactive Whiteboards, NCTM, Sketchpad, Teacher Collaboration, TinkerPlots | Leave a comment

NCSM 2012 Ignite – It’s Fast, It’s Fun, It’s Math!

Posted on April 20, 2012 by Karen Greenhaus

The big annual math conferences are next week in Philadelphia. First up, the National Council of Supervisors of Mathematics (NCSM) conference, April 23–25, followed by the National Council of Teachers of Mathematics (NCTM) conference, April 25–28. Naturally, those of us at Key have been gearing up to meet thousands of math teachers and leaders and “bring math to life” (to borrow from our new motto!) with all our software and resources. One of the big events we are sponsoring is our Ignite! presentation at NCSM, where we bring together math leaders and thinkers to share their thoughts on math education.

If you have never been to an Ignite! event, it’s really quite a fun, unique, and enlightening experience. Each speaker gets 20 PowerPoint slides to make their point. The slides auto-advance every 15 seconds, so the total talk is five minutes. Not a lot of time, so the challenge is to use visuals and key words to make your point quickly and succinctly. I speak from personal experience when I say planning a five-minute talk is significantly harder than planning for an hour talk or even a day-long workshop—especially when the clock is ticking!

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Posted in Conferences | Tagged CMC, Ignite, NCTM, Teacher Collaboration, Videos | 4 Comments

The Dynamic Number Project Comes to NCTM Philadelphia

Posted on April 18, 2012 by Daniel Scher

It’s time for the NCTM Annual Meeting!

For the past two and a half years, my colleague Scott Steketee and I have been collaborating with elementary teachers in New York and Philadelphia as they field test curriculum materials for the Dynamic Number project. We’ll be showcasing our work at three sessions during the upcoming NCTM conference in Philadelphia.

Image courtesy of the National Council of Teachers of Mathematics

I’ll be presenting with Janice Manning, Matt Silverman, and Sonal Malpani from the School of Discovery and Exploration in Brooklyn, NY. Our talk focuses on students’ understanding of fractions and the impact of using a variety of Sketchpad fraction models. We’ll be bringing classroom videos with us to give the audience an up-close look at students’ conceptual understanding.

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Posted in Conferences | Tagged Dynamic Geometry, Dynamic Number, Fathom, NCTM, Sketchpad, TinkerPlots | Leave a comment

Branding isn’t about math. Are you sure about that?

Posted on April 16, 2012 by Karen Coe

At around Pi-hour on Friday afternoon we successfully launched our new website. The night before (the night of the big storm for Bay Area folks), Andres and I were out with a dear former colleague and I mentioned I was going to blog about our new branding, new website, and new name. She said, “You can’t do that, it’s a math blog, nobody is interested in branding!” To which I replied, “What other company do you know used their own software to create their logo? Our branding is math.” We then had another drink.

Let me explain. We were working with a very talented designer and trying to communicate we wanted a logo that expressed math in motion to match our new tag line of “bringing math to life.” He came back with some wonderful designs but none of them felt quite right to us. Our favorite was a design that had eight colored petals but it didn’t deeply resonate. I was talking to Milan, our CFO, about it and as he wandered over to the local coffee shop for his “Milan special” he sent me an email that simply read, “Not fewer petals, more petals, 22 to be exact.” I knew exactly what he meant. The day before he and I were in a business development meeting with Steve Rasmussen, where Steve constructed the “pi-petal rose” by way of introducing construction in Sketchpad. People are always delighted to see a visual representation of Pi for the first time–something very familiar seen in a new way. With a little finessing by the designer we’ve adopted the pi-petal rose as our new logo.

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Posted in Math Software | Tagged Constructions, Dynamic Geometry, Modeling, Sketchpad, Use Appropriate Tools Strategically, Videos | Leave a comment

Who survived the Titanic?

Posted on April 14, 2012 by Andres Marti

Exactly a century ago, the RMS Titanic struck an iceberg and sank on its maiden voyage. Most people know the story better than me, or at least the Hollywood version of it, as I’ve never seen the movie. (On the other hand, my daughter just saw it again in 3D and “cried the whole time.”)

One of my favorite data sets to demonstrate on TinkerPlots is a record of the people who were on that tragic journey. There are very few attributes, but precisely those that are the most interesting: gender, class (or crew), adult or child (here numeric age would have been even more interesting), and whether that person survived.

So for this special Saturday blog edition, I’m going to share a short silent movie (seems era-appropriate) of me visually exploring the main question in my head: Was survival correlated to other variables such class or gender? Take a look and see what you think.

I was really surprised by the size of the crew given the number of the passengers…and they certainly took a heavy toll that day. If you want to learn more about the people on the Titanic, I recently read this interesting collection of communications from the before and after the tragedy. And if you want to see more dynamic data animations, see what we’ve done at our website to show TinkerPlots in action!