DragonBox

Browsing blogs last week, I came across this post about math apps. I had not heard of DragonBox before and decided to give it a whirl. At $5.99, it was pricey, but came highly rated.

DragonBox teaches algebra without calling it algebra. The object is to manipulate the two sides of the screen so that the box is isolated on one side. As you progress through the levels, the box eventually becomes an x.

I think the concept and execution are nothing short of brilliant. I worry that the questions I’m going to pose below may highlight a deep pedagogical deficiency on my part, but after working through all the levels, and introducing my 8-year-old daughter to the game, I do have some questions.

Me

At first, I had a really hard time understanding what was going on. I wanted to see the box and cards as variables, coefficients, and constants. They didn’t work exactly the way my algorithmic training wanted them to. I had a hard time separating my prior and totally engrained training from the game. Does the fact that I was taught equation solving in an algorithmic way, and the fact that I practiced those methods over and over again, actually hinder my ability to understand this concept at a deeper level?

My 8 Year Old

She loved this game. She progressed through the first two worlds and enjoyed it, despite the fact that she’s probably not developmentally ready for algebra yet. Her comments were that she didn’t see how this was math, and that she didn’t see what it was that she was supposed to be learning. I took one of the levels she had completed, and translated it into a concrete mathematical equation, and tried to walk her through it. It didn’t work. What’s the bridge between this brilliant app, and the concrete? Is the next step apparent to older children and to better teachers than me? I’m embarrassed to admit that I’m not entirely sure what my next step is, after my students play with this app.

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A Better Calculator

A company called Desmos (that I know nothing about), has launched a free online graphing calculator. What’s beautiful about this one, aside from its ease of use and powerful graphing abilities, is that it uses HTML 5. I know nothing about HTML 5, other than it makes things work on iPads.

This is a screenshot from my iPad.

Their calculator is at www.abettercalculator.com . Try it out. Play around with it.

Making sliders for students to play with is simple. Just type in “a=1” and a slider appears. Now write a function that has “a” in it, and your slider just works.

Here’s one I made with four sliders for a trig function.

Here’s another nice one that Scott Seitz made for a piecewise function.

It doesn’t work on my iPhone (yet?), but the iPad looks great. Manipulating the sliders on the iPad takes a little getting used to, but after that, they work beautifully.

This one is well worth the price.

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Web Tools for Classroom IV

At ISTE 2011, I attended two sessions aimed at showing off as many web tools as possible in 60 minutes. Tammy Worcester showed her Top 20 Favorite Web Tools, giving herself an average of 3 minutes per tool. Brandon Lutz kicked it up a notch, and showed off 60 in 60. He gave us one per minute, for an hour.  In the previous three posts on these sessions, I looked at the tools that I thought would be useful to math teachers or consultants. In this last post, I will look at the tools that I just thought were interesting. Some I use, or will use personally. Some might be of use to teachers of subjects other than math. I just thought these ones were cool.

Tools That Interest Me Personally

Pearltrees – This site seems like a really nice way to collect, organize, archive, and share links. I haven’t tried it yet, but I will. There’s a video on their site explaining what it does.

Puppet Pals is a free iPad or iPhone app that allows children to create, narrate, and animate videos using puppets. I installed this while at ISTE, and my 6-year-old daughter absolutely loves it. The in-app purchases are extra scenes and characters to use. I bought the director’s pass, which gave me access to them all. I could see older students using this in English or Social Studies class to create stories, and with some video editing, they could piece short ones together into a longer movie.

Game Salad is a game creator for iOS devices. No coding is required.  According to Brandon, Angry Birds was created using this program. I’m going to play around with it. If I can stumble upon the next Angry Birds, I’ll be able to retire early and in grand style.

Tools That Might Be Useful to Teachers of Other Subjects.

Free Rice – This organization is a twist on the online rote practice and rewards system. Kids can create accounts, and answer practice questions. For every correct answer that a student gives, rice is donated to hungry nations. The questions seem geared more to elementary students, but I like the idea of this.

Aviary Education is a free online editor for images and audio. I tried the photo editor, and had some trouble getting it to do what I wanted, so it is a bit limited (or else I am).

I don’t use these kinds of things in my sessions or classroom, but many teachers and consultants do. To create back channel chats for classrooms and workshops, two free sites are COVERITLIVE and TodaysMeet.

I’ve tried journaling in the past, and I have never managed to continue beyond a few entries. Oh Life is made for people like me. If you want to journal, but never follow through, then this site is for you. It will send you an email asking about your day. You reply to the email, and your replies are saved for you as a journal. I have no idea who reads your emails, though, so I’d stick to professional journaling.

Storybird allows students to create, collaborate on and share stories. Students start with art, and write a story around it. I can see using this with my daughter.

Google Body – I’m not sure whether or not this is useful to biology teachers, but it sure it cool.

PHET has lots of online science simulations.

SideVibe allows teachers to support students with their webquesting by providing a sidebar companion with questions and directions superimposed on a website. It would help students remember what to look for.

Tagxedo turns words into art, sort of like Wordle, but with the words arranged into pictures. Here’s a Tagxedo of my recent twitter feed. I’m a little concerned about my love for Terry Kaminski.

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Web Tools for Classroom III

At ISTE 2011, I attended two sessions aimed at showing off as many web tools as possible in 60 minutes. Tammy Worcester showed her Top 20 Favorite Web Tools, giving herself an average of 3 minutes per tool. Brandon Lutz kicked it up a notch, and showed off 60 in 60. He gave us one per minute, for an hour. There was some overlap.  I made a Venn Diagram because I’m a math geek. In this third post about those sessions, I will look at the tools from Brandon’s presentation that I think are useful for math teachers and consultants.

I will write one more post about the tools that interested me personally, but may not be applicable to math classrooms or consultants.

Tools That Were Unique to Brandon’s Presentation

Drop it to me – This is a service that works with Dropbox. It lets people upload files directly to your dropbox account, so students could submit work directly to a dropbox folder. The benefit of receiving student work this way, is that it is easier to manage than having them email files to you. With emailed files, you have to save them to a folder. This process puts them directly in a folder. There is a demo of the service here.

Ge.tt – Ge.tt is a file sharing site. It seems to be similar to box.net and scribd. I can see using this to share session handouts and notes for participants in my workshops. I think the files are only available for 90 days, though, so it it not a permanent storage and sharing site.

Brandon shared two ways to import video from YouTube and other sites. I always pull videos off the internet before I use them in sessions. I do this because I don’t want to put myself in the position to have to rely on an internet connection, and some schools I work in block YouTube. I have used both of the services Brandon shared extensively.  Zamzar is an easy to use online file conversion utility. You can download videos directly from YouTube and other sites, and save them in whatever format you like. He also shared Video Download Helper which is a FireFox Add-on. I find this one incredibly easy to use, and it is my preferred way to download internet videos. Other sites I have used to bring in video are Bender Converter and KeepVid.

Blog from anywhere, even on your mobile phone using Posterous.

Write a project proposal for a classroom project, and receive funding through Donors Choose. Your students must write thank you notes, and include photos showing their learning. I’m not sure this project extends to Canada, but those of you in the USA should take advantage of this gift.

There is a nice set of classroom applets at Triptico. These applets include timers, random group selectors, and more.

Jaycut is a free online video editor. I have been editing more and more videos as I work on presenting math problems. I do all the editing on my Mac at home because I have no software on my work PC to edit. This may be my solution. I haven’t tried it yet, though.

MultiURL is another tool that lets presenters or teachers collect a list of websites to share with students or session participants. I like this one better than fur.ly, which was mentioned in part I of this series. Here is a sample that I set up in MultiURL. This one lets you set up a free account, and the lists you create are editable. I will use this one. I might like it better than urli.st, which I use extensively.

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Web Tools for Classroom II

At ISTE 2011, I attended two sessions aimed at showing off as many web tools as possible in 60 minutes. Tammy Worcester showed her Top 20 Favorite Web Tools, giving herself an average of 3 minutes per tool. Brandon Lutz kicked it up a notch, and showed off 60 in 60. He gave us one per minute, for an hour. There was some overlap.  I made a Venn Diagram because I’m a math geek. In this second post on those sessions, I will look at the 14 tools that were unique to Tammy’s presentation.

Not all of the 14 tools are of interest to math teachers. If you want to see them all, click the link above. I am going to discuss only those which I think are of use to consultants or math teachers.

Tools That Were Unique to Tammy’s Presentation

Screen Capture and Screencast Tools – Jing (Mac and PC) and Skitch (Mac).  I have been using Jing for a year now to create screencasts to share “how to” videos with colleagues. I have not tried Skitch, but apparently it does the same thing on a Mac. I see tools like these being useful for explaining to people how to do something on a computer, because you can narrate a walk-through of the process.

Random Name Picker at ClassTools.net. I was not familiar with this site, but it has all kinds of tools you could use in a classroom setting.  There is a random name picker to randomly select students to respond. There is a timer, a Venn Diagram creator, a plagiarism checker, and others.

Fur.ly – This is a way to shorten multiple URL’s into one link.  I have been sharing multiple links with people who attend my presentations using urli.st, which creates one short link that brings up a list of all the websites I mention in the session. Fur.ly presents the same thing in a better way. Rather than having a list, it opens the first site in a frame, and participants can visit the other sites listed by using a simple drop down menu. You can see what it would look like by clicking on this one that I set up. http://fur.ly/5ujg The one major drawback I see with fur.ly, though is that it doesn’t seem to be editable. Once I create a list, I can’t go back in and add new sites, unless I’m missing something.

Tammy shared a couple others that are of interest to me personally, but I don’t think they have relevance to math teachers or other consultants.  If you are interested, they are BibMe (creates a bibliography for a paper using one of several possible formats), using the advanced search filter in a Google search to filter by reading level for struggling readers, and tripit, which helps with travel planning and organization.

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Web Tools for Classroom I

At ISTE 2011, I attended two sessions aimed at showing off as many web tools as possible in 60 minutes. Tammy Worcester showed her Top 20 Favorite Web Tools, giving herself an average of 3 minutes per tool. Brandon Lutz kicked it up a notch, and showed off 60 in 60. He gave us one per minute, for an hour. There was some overlap.  I made a Venn Diagram because I’m a math geek. In the next three posts, I’ll discuss the tools they shared, and what I see as their use for me.

I’m not going to discuss all 74 unique things I saw. Some of them are of no interest to math teachers. If you really want to see them all, you can click on one of the links above.

Overlapping Tools

Because I think it is interesting to see the tools that they both recommended, I’ll start with the overlap.  I will discuss all six tools that they both shared.

Tiny URL – This is a URL shortener. I use bitly, and I know many people are fond of Google’s version.

Plurk – I had never heard of Plurk, but I definitely plan to check it out. According to them, it is like twitter, but has better threading of responses. One thing that drives me nuts in twitter is that if I reply to someone’s comment, I have to seek out other replies, because I only see the replies of the people I follow. Apparently Plurk does this better.

Evernote – My boss and my consulting colleagues have been raving about Evernote for months. I don’t use it because I haven’t needed to. Evernote lets you create, modify and synch documents among all your devices. I do the same thing using the QuickOffice app on my iPhone and iPad, and storing the documents on Dropbox. I annotate PDF’s on my iPad using GoodReader. If I ever encounter something I can’t do with these tools, I’ll give Evernote a try. I know it’s good because people have been bugging me to try it for months.

Dropbox – I was pretty clear about how much I love Dropbox when I wrote my Ode to Dropbox several months ago. They have had a security breach recently, and there is some question as to whether or not files are encrypted on their storage, but I still love it. I don’t keep anything there that is sensitive or could jeopardize my privacy. It’s the best way I have found to store and share my presentations and handouts.

Qwiki – I’m not sure I see use for this for math teachers, but it is pretty neat. I see this having great value for teachers of struggling readers. It is a search engine type site. When you enter a search term, it brings back information on the topic, which it then presents to you. It reads aloud the text that scrolls up, and brings in images and other links. Share this with your colleagues. The best way to explain it to you is to get you to go there and try it out.

Wolfram Alpha – It was interesting for me that both presenters shared Wolfram Alpha, even though neither one was a math teacher. Readers of this blog probably don’t need a description of this one.

In my next post, I’ll look at the other tools that Tammy shared.

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Math Teacher Networks

I started teaching in the dark ages.  When I began, there was no internet, email, social media, or cell phones.  We had just gotten computers in classrooms for teacher use for things like attendance and marks entry.  Our PD focused on how to use technology like PowerPoint and Word.  I started teaching way back in 1992. My first computer, purchased in the mid-80’s, looked like this:

Recently, I had the opportunity to meet Dan Meyer.  He was younger than I expected, and I got thinking about how different the start to his teaching career was than the start to mine.  He never taught in a world that didn’t include the internet.  He probably can’t even remember a world that didn’t have internet.  He has been connected in ways I only dreamed of in 1992.

When I started teaching, I was in a small rural school.  I was the only high school math teacher.  My two resources were a curriculum guide and a textbook.  When I got stuck, there was no other high school math teacher within a half hour drive that I could talk to. I couldn’t email anyone, because email didn’t exist.  We had to use long distance calls sparingly, because the cost was high.  Essentially, I spent the first 8 years of my career alone in my planning, preparation and reflection.  It seriously hindered my growth.

I hope you young teachers know how good you have it these days.  Young teachers like Sam Shah, Kate Nowak, Jason Buell, Sarcasymptote (Greg), Dan Meyer, Shawn Cornally, and Dan Anderson are connected in ways I couldn’t have imagined in 1992. Many of them have probably never met each other in person, and yet they remain in close contact through their blogs and Twitter.  When Dan and I talked about some of them, it seemed strange to me that he had never met them.  In my mind, they exist in the same world and should know each other.

These virtual networks of  math teachers are powerful, and lead to rich discussion and professional learning.  We are in an exciting time in education.  We are all getting better because of the willingness of these young teachers to explore and share.  What strikes us older folks (and probably puts fear into the hearts of textbook publishers) is that these people are not sharing their stuff for profit.  They are sharing for the good of their profession.  I commend them for that.  I would be a better teacher today if such opportunities had been available to me in 1992.

Thank you for sharing.

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Ode to Dropbox

A colleague recently tweeted her love for Dropbox.  I made fun of her, and replied that if she was going to write an ode to Dropbox, she should at least include a referral link for extra space for herself. I have since Googled “ode” and discovered that it is another one of those things that English teachers make you write that has a lot of rules. I must state, therefore, that I know this isn’t an ode. The truth is, though, Dropbox has changed the way I work.  In this post, I’m going to describe the basics of Dropbox for those of you who haven’t heard of it, and then I will explore some great uses for teachers.

Basic Explanation

Dropbox is a service that stores your files in the cloud, and syncs them automatically to any computer you set up, regardless of platform. I sync my work computer, my home computer, my iPhone, and my iPad. When I work on a file at work and save it in my Dropbox folder on my laptop, that file is automatically updated at home on my desktop. In the past, I would have emailed files back and forth to myself, or carried them on a memory stick, and constantly worried that I was overwriting a file I needed with an older version of itself.  Dropbox is much more convenient. It also allows me access to those files from any computer with an internet connection through the Dropbox website, in the event that I need something and don’t have my own laptop there.

Dropbox gives users 2 GB of storage at no cost. The free storage available can be increased by referring others.  For every referral, you get an extra 250 MB of storage, up to what they say is a maximum of 8 GB.  Through referrals, however, I have worked my way up to 8.25 GB of free storage. It’s not listed on their site, but I think I read at one point that the free maximum was being increased to 10 GB, which might explain how I got to 8.25.

People who use Dropbox regularly and need more space can purchase that space.  $9.99 per month gets you 50 GB of storage, and $19.99 per month will get you 100 GB of storage.  I have a neighbor who runs a small business.  He uses Dropbox as his company server because it is cheaper than installing all the hardware needed to set up his own.

Dropbox also allows you to share selected files and folders with people. I share a photos folder with my mother, so she can access full resolution pictures of her grand-daughter. I share a presentations folder with a colleague so we can share our work presentations with each other. Dan has shared a folder with me into which he is placing his programs as he hammers through Project Euler. These are just a few of my shared folders.

Uses for Educators

As an educator, I have found many practical uses for Dropbox.  When I visit a school and do a presentation about our new math curriculum, my presentation is often a large file with embedded video and pictures.  Participants invariably want a digital copy of the presentation, but it is too large to e-mail.  In the past, that meant asking participants to bring memory sticks, and copying the presentation to their sticks one at a time.  With Dropbox, I just put the large file in a public folder, and share the link to the file with the participants.  Problem solved.

Another benefit of Dropbox for educators is the ability to collaborate easily on files.  It’s not Google Docs, where multiple people can edit simultaneously, but it allows multiple people to access and revise the same file, always maintaining the most recent version. Way back in August, I worked with a group of teachers on some planning. They wanted to share their work, and asked me if they could email me documents, which I would then forward out to the rest of the group.  After explaining that I wasn’t their secretary, I showed them Dropbox, set up a shared folder and gave the entire group access, and let them post their stuff to that folder.  Four months later, members of that group are still contributing items to that shared folder, thereby reducing the planning workload for everyone.

A colleague, Russell Lyons, recently showed me how he is using Dropbox in his classroom, and it is brilliant. The iPhone Dropbox app allows you to take a photo right from within the app.  That photo is instantly synced to your account, making it available to any computer you have set up.  So if you don’t have a document camera, but would like to model good student work, you just snap a photo with Dropbox, and project it within seconds from your classroom computer.  The quality is surprisingly good.  This picture below is one I took at one of my sessions. Within seconds, I was able to discuss this group’s work with the whole class by projecting it on the SMART Board. It should be noted that they were working on this problem, from Andrew Shores’ blog.

Another place I use Dropbox is on this blog. I can’t upload videos on this blog through WordPress, without upgrading my account and paying for the privilege.  Since I have a free Dropbox account, when I want to post a video on this blog, I put it in a public Dropbox folder, and then paste the link on this site.  It’s not quite as nice as posting the video directly here, but it is free.

If you are not a Dropbox user, I suggest checking it out.  Their introductory video explains pretty clearly what they are all about.

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Graphing Software

Last week I was working with a group of teachers who were creating a common assessment for our district.  As they wrote questions, I offered to help with graphics if need be.  One group asked me to produce a graph illustrating y = x, for x>-1.  I couldn’t believe how hard it was to do with the software available to me.  After trying several graphing applications available to me, I ended up drawing it in Word and inserting it into the test. It looked like this:

Before I got to the point of needing to use Word, I tried several applications that I use frequently.  The first one I tried is from Edmonton’s own Ron Blond, who wrote Graphing Tool for the Learn Alberta website. I wasn’t able to limit the domain. This one does very well as a tool for student exploration, because it is easy to add sliders for investigation, but in terms of graphs to insert on tests, it didn’t meet my needs. My attempt looked like this:

Next, I tried the Microsoft Math Add-In. Again, this one is useful with its ability to add sliders for student exploration, but I still couldn’t limit the domain.  That doesn’t mean it can’t be done, but I couldn’t figure out how to do it quickly.

Then I tried the Math Tools grapher in Notebook, which gave me similar problems.  Again, this is a decent tool for student exploration, but exploration was not what I was after.

So I threw out a shout on Twitter, and got several suggestions.  I have tried most of them.  Here is my review.  Please note that I am reviewing these solely based on their ability to create the graphs I need to insert into my notes, worksheets, and exams.  I will play around with them some more and in a future post I will review their abilities as interactive exploration tools for students, which may very well change which one I view as my favorite.

Matt Ruden suggested Omnigraph, which i have since discovered is a Mac application, and an iPad application.  I paid $15 for the iPad application, and it is pretty slick.  It creates really nice graphs, right on the iPad. I’ll just use the one I made that is similar to all the rest here, but I was able to create some pretty neat piecewise functions and some great shaded bell curves.  My biggest complaint is that I can’t create a graph from an equation with it.

Kris Reid concurred with many of the other suggestions, but also suggested using Geogebra.  I have used it many times, but never thought to import a graph from it into an exam.  I couldn’t get an arrow on the end of the ray, but the graph is pretty nice.

Sam Shah and Kris Reed both mentioned Winplot.  How come no one ever told me about Winplot before?  It seems to do everything I need it to do.  Sam warns that it has a learning curve, but it didn’t take me too long to figure out how to make exactly what I needed this time.

Don Chandler recommended Advanced Grapher.  I looked at it online, and it looks pretty good, but I wasn’t going to pay $23 for something that I didn’t need anymore now that I found the other two that will suit my purposes.

So, to summarize, I like Omnigraph because it will do stuff like this:

I also like Winplot because it is a little easier to import graphs into the documents I want them for.

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Flipboard iPad App

When I got back to work on Monday, my boss and another consultant both showed me Flipboard for the iPad.  I installed it on my own iPad (it’s a free app) and I can’t stop raving about it.  Flipboard is an app that takes your social networks (Facebook and Twitter for me) and presents them in a pretty slick magazine format.  It totally enhances my Twitter experience.

Here are some screen shots from my iPad, so you can see what Twitter looks like for me now.  These first four shots show how it takes a tweet that includes a link, and instead of showing something like http://bit.ly/bybT2U, it actually pulls in a preview of the photo or article that is linked, so you can read a few lines and decide if you want to read further, which you can also do right from within Flipboard.

The last two screen shots show what tweets look like when they don’t involve links.

While I highly recommend this app, there are some drawbacks to it.  I can reply to  tweets, but unless I’ve missed it, there is no way for me to write a new tweet directly from within this app.  Another drawback is that the tweets get inserted where they fit, so some of the linearity of Twitter is lost.

My biggest wish, though, is that it would have the ability to be an RSS aggregator.  I’d love to be able to browse all of the great blogs I follow in a similar format.  It looks much like a magazine, and I could check out blog posts in a much nicer format than I currently use (mail client on mac).

There is a little video here that shows what it looks in action.  http://www.flipboard.com/

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