Sage Removes Barriers for Technology in Math Classrooms

If you are not yet using programming with your math and science students, you might have a couple of excuses why.

1) I don't have the time to learn (give me 30 minutes)
2) My school won't let me install the software.

Technology in schools is difficult especially if you are working with older hardware or infrastructure. Many schools will only install new software at the beginning of the year, but if you are going to start programming you'll want to get started now.

Sage makes programming more convenient than ever while adding in some powerful math packages. You might see your graphing calculator's packaging saying it can carry you through college, Sage will take you from elementary math to your PhD and beyond. Created by William Stein with the intention of being a powerful free and open source alternative to technology like Mathematica.

You might wonder how Sage changes anything. Well Sage contains multiple programming languages so you are not constrained to one, but more importantly the Sage Notebook provides the ability to program in the cloud. While there are other options out there, Sage makes it really easy and puts it all together in a dead simple interface.


Let's explore the Sage Notebook (the cloud based version).

There are so many options for logging in, you can create a Sage Notebook account, use your Google/Yahoo/OpenID credentials or you can browse the worksheets without logging in.

Much like Geogebra, you can browse the public worksheets of other people in the community of users.

Click New Worksheet. Once in the worksheet, you can click on the drop down menu that says Sage and see how many options you have for languages. This covers the many programming languages one would need. If you are just starting out, you may want to use Sage, Python, or R (statistics).

If you read this blog, you know I love Python for its simple syntax and ease of use. With Sage you don't have to give that up, the syntax is essentially the same.

To see what really makes Sage a great fit for math try entering a fraction and hitting Shift+Enter. In Sage, fractions are treated like an actual object. You can multiply it, add two fractions, and all of the other manipulations you would do on paper.

A feature very popular in Wolfram|Alpha is the equation solver. Try this out in Sage:

It couldn't be easier to graph:

Once you have a worksheet you can share it with people so they can interact with it or publish it for viewing. In fact most of the examples in this post can be seen here. Just click on the buttons in the upper right of the workbook.

This is just meant to whet your appetite, there are so many different ways this can be used, especially when you consider all of the different functionality and the ability to work online and save/share your work. The documentation is very helpful and there are numerous tutorials created by the community to help you learn. Take a look at Sage's tour for more examples of what is possible.

You will not be disappointed as this is no toy but a powerful full mathematical suite. Student will love this for the same reason they love Geogebra. It takes abstract concepts and manipulation of symbols, variables, and functions and treats them like objects in a game. Now you can play with the math as opposed just focusing on calculating.

Being able to quickly see the effects of an equation or its graph means students can draw conclusions faster rather than being unnecessarily distracted by the arithmetic or plotting of points.  I hope you will take me up on this invitation to use this free tool. The hard work that the Sage community has put into making this available to all should not be in vain.

If you are already using Sage (and I know many of you are) be sure to share in the comments or on Google+ how you are using it.

Stay connected and check out the other tutorials on BrokenAirplane by following the links on the top and the most popular posts on the sidebar.

Google Doc Discussions for Hybrid Learning

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Google Documents rock! Where else can you get a free document editor that you can share and collaborate with others? Recently, Google released Discussions which were an improvement on the comments you could embed within a document. With discussions, you could leave a comment and have it be sent to a recipient, who could in turn reply in conversational form. Now students could work together to refine their work and teachers could give feedback all leading toward beautiful work.

With recent improvements, you can track when the last time a page was accessed and what they said. This was rolled out without much fanfare, but for educators, it makes a big difference! Typically to get this kind of data you would need to use a classroom management software like Moodle or Edmodo, both fine tools but they require you to leave what you are doing and go somewhere else on the web. All of this is within the Google Apps that you are already using.

This summer, Patrick and I are working on a hybrid multimedia/graphic design summer school class. We wanted students to be able to work from all over the city without having to come into town. Plus Patrick wanted to be able work with students while he and his Graphic Novel project students are exhibiting at Comic Con (congratulations to them by the way). A concern with the hybrid class was "seat time", how would the school be able to certify that the students had worked long enough to qualify for the Carnegie Credit Hours? 

With Discussions, that problem was resolved. With the class a mixture of synchronous face-to-face video conferences, and asynchronous independent work students could demonstrate their mastery as well as seat time with time logs in their Google Doc. We are really excited about the prospect of conducting a full class without a classroom. More on our successes and struggles will appear in the next few weeks I am sure but I figured that many could benefit from this and I wanted to get the tip out as soon as possible. Enjoy!

A few improvements to discussions in Google Docs - Original Article

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Autodesk123D Brings Free CAD to Everyone

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As as an educator, I am strongly in favor of free software. Classrooms have a difficult enough time without having to pay for expensive technology. While I personally favor Open Source, I have long been puzzled at why more companies do not provide free education software. It is in their best interests to ensure a continuous cycle of users and how could a company guarantee that better than by providing them an opportunity to learn their software at a young age.

Autodesk, has taken steps to support the maker and STEM community by releasing Autodesk123D for free to the public. Autodesk is famous for its CAD (Computer Aided Design) software which allows for fast and high quality designs of most major products on the market. Many who could have learned this software were unable to because they were unable to afford the high cost for a software licence. Free alternatives exist but they have either a steep learning curve, or were not powerful enough to do effective designing.

Note: Students who are members of the FIRST Robotics Competition have access to free student versions of all Autodesk Software. As if you needed another reason to start a robotics team.

Autodesk 123D's website provides you with the option to download the software (Windows Beta currently), as well as search and find already created models. This can expedite the process when you only need to modify a design as opposed to creating it from scratch. You will also find resources for printing out your model when it is done. Yes, that's right, the 3D Revolution is here and the cost of printing a prototype for fun or marketing has dropped dramatically.

Once you have downloaded the software, you will find introductory videos to get you started. Clicking on Learn More brings up the Support Website which has great videos to take you through the steps to make your first design and beyond. Considering how much Autodesk training usually costs I am happily surprised at their realization of how much this will benefit them in the long run by creating a larger base of users.

Autodesk123D has the feel of Autodesk Inventor with enough features to create a design. It is similar to Google Sketchup in many ways while being oriented towards CAD more than architecture.

Users will be able to get practice working with the workflow and part hierarchy which is critical to good CAD design. This allows the designer to see how parts are connected and see the settings and features of each part and sketch.


The design buttons are similar to Google Sketchup so if you have any experience with that software you should be able to pick up the process faster. It starts with a sketch which is then extruded (pushed/pulled) to the size you want. Like Autodesk and Sketchup you can specify the exact measurements. The other buttons allow for the insertion of Primatives or basic shapes, duplication and reflections, and assembly. The familar view block and zoom/pan tools are there as well.

My other favorite part of this program is the wise decision by Autodesk to not cut off its effectiveness by cutting it off from the rest of the community. Autodesk123D allows for saving and opening in its own special extension but will also work with STEP, Autodesk 2007, DWG, and STEP files. This allows users to access the FIRST and VEX CAD libraries of premade parts. One can also open Google Sketchup files showing they are willing to play nice with others.

This is a great piece of software but also a great decision by a company who is and will likely remain an industry standard for a long time based on decisions like this. This product is capable of inspiring and empowering design and creation and I hope more companies decide to provide free and useful versions of their software for training but also for those businesses and organizations that cannot justify an expensive software licence. There are so many tools out there that make this an exciting time to be apart of STEM. The more people who have access to these creative softwares, the better for us all.

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Use Google App Inventor to Create Your Own Android Programs

Update: App Inventor is being integrated into MITs Mobile Learning Center. Don't wait, start using it today with Google! (see the announcement on the Google Research Blog from App Inventor's creator Hal Abelson)

Whether it is for the fun of it, or out of an actual need, everyone can learn programming. Like any skill it requires a lot of practice and perseverance but programming does have a steep learning curve. There have been great leaps in providing the masses with the ability to create their own websites/wikis and with Python my 9th grade math/physics students have learned a lifelong skill, not to mention the powerful 3D Software like Alice and Blender (such an amazing time to be alive)!

Yet, with an ever growing population of mobile phones and the likely true prediction that they will replace most of what we do on a laptop, there is a need for those who can program for the mobile platform as well. Our phones are with us 24/7 and there are already so many great applications out there, but sometimes you have a great idea or need for something new. Google App Inventor is free and now open to everyone and the interface and tutorials are easy to follow in the way you have come to expect from Google.

Some of you might have reasons why you might skip over this post:

• "I don't have the time to learn to program."
• "I don't have an Android phone"
• "I don't have an idea of what I would want to make"

Let me say that I was able to get an app up and running in less than 30 minutes. It is the goal of this blog to share with you amazing technology in a way that you can get started using it tomorrow (Geogebra, Python, Audacity, to name a few examples). Even though I do have an Android phone, for those of you who don't, you can use the built in emulator to test your apps on the computer. If you still think that there is nothing you would want to make, keep in mind that every one says the same thing when they start to create. Whether it is art, writing, or programming, the important thing is to just get in there and start, then when you see your potential you will come up with many more ideas.

In order to start making your apps:

1. Setup your computer (download the software and make sure JAVA is updated).
2. If you are using a phone:
• Set up the phone to work with the computer and make your first app.
3. If you are not using a phone use the built in emulator to make your first app. 

I am going to let Google show you how to make the first app in which they use a meowing cat as their Hello World app (to each their own) as they do an excellent job of using pictures and descriptions to walk through the steps and I see no reason to try and do it better.

HelloPurr App

While creating this app, you will find a WYSIWIG Drag and Drop interface that makes building and designing an app very simple. The interface is a simpler implementation of the iPhone app designer in my opinion.

On the left are all of the commands and sensors that you can use in your app. This ranges from simple buttons and pictures to more sophisticated sensors like the Barcode scanner, videos, messaging, and even the ability to interface with their VEX Robots! 

On the right are customization features like color, layout, and other aesthetic features.

To make all of these components work together, they need logic and connections that determine what happens when you push on a button, turn the phone 90 degrees, etc. The actual programming occurs in the Block Editor where you connect conditions to methods (fancy name for a function) and make the magic happen. This setup is very similar to the Alice software environment in which kids from elementary school and beyond can make 3D JAVA like programs. 

There are tutorials from the basics to more advanced, and while one cannot do every possible thing that they could do if they were to program the application in the full Android SDK, it is powerful enough to make some very useful apps for class or general productivity. Not to mention that our students are understanding the basics of computer science which is applicable to any programming language and situation.

The App Inventor community is growing and is strongly committed to it's success. I think educators see how powerful it is for people to be able to create a useful or fun app without much programming experience. Keep in mind that students are still learning quite a bit about logic and algorithms, App Inventor just makes the syntax a bit more kinesthetic/visual (if only they all could be).

There are a few new resources out that I would like to highlight to get you started:

1. The Official App Inventor Tutorials - The link may change once it moves over to MIT but the instructions will show you how to make a quiz app, a don't lose your car app, and more.
2. Google App Inventor Book - I have reviewed most of the books out there on App Inventor and I enjoyed this one the most for its clarity and use of visuals. While App Inventor is colorful and easy to use, it is not just fun but a powerful development tool. The author delves right into the parts of App Inventor that would be useful for making professional and powerful apps like media, databases, sensors, game logic and more.
3. My colleague Michelle Hutton (former president of the CSTA) spent her time at Google developing tutorials and curriculum to get you and your students going on App Inventor.

Enjoy and if you have created a cool app using the App Inventor be sure to leave a comment about it to inspire the rest of us!

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Physics and Math for Everyone with Exploriments

Last week I spoke at the CUE Conference and having arrived early, I was able to check out all of the vendors. About 90% of it was similar to last year and SMART/Promethean boards and projectors always have a huge presence. I also saw a few companies promoting Augmented Reality, which you can see in the video below.

The research is showing that when students can interact with learning in a visual, kinesthetic way they are more likely to remember the content.

I am not promoting or encouraging these tables/tables/boards etc as they are expensive and do not promote learning in and of themselves. However, when you can make the content itself interactive, then your students can really get into it.

I have created a few of these myself with Geogebra, and also some modules with Python but I have always wanted something more complete that would support the learning in the classroom. PhET is definitely the kind of thing I am referring to. It is interactive and has lots of features. Plus it is asynchronous so students can learn from it even when I am not specifically working with them. You can find these and many more free applets on my Math and Science Resource page. My only frustration with these are how few there are and sometimes they are intended for college students and are thus over complicated for high school students.

Exploriments - Amazing Science/Math Modules


Back to the CUE Conference, I came across a booth whose demure appearance understated the excellence of what they were promoting. Exploriments has created amazing Shockwave based demonstrations, experiments, and explanations.

Too often, I want to demonstrate a concept but a powerpoint or whiteboard explanation will not suffice. Sometimes there is a YouTube video but there are far too few quality videos out there. Additionally, if your school is suffering budget setbacks like the majority are, then it is difficult to afford the expensive lab equipment and materials. Yet, with Exploriments, much like Geogebra and Khan Academy, this levels the playing field so all students have an opportunity to learn even if their resources are limited. All of the benefits of online learning software come along with it:

• Students can learn at their own pace any time (could be given for homework before a lab or lesson).
• Repeatable and accessible anywhere that has a computer with internet.
• Interactive learning and teachers can follow along to see how they are progressing.

There is a free trial which allows you to explore the quality and thought that went into designing these simulations. However, the cost is far cheaper than any science video set or even the cost of a single lab experiment for an entire class. In the full version, you have access to:

Physics - Electricity, Electrostatics, Weight vs Mass, Motion (1D), Projectiles, Force, Friction, Momentum, Moments, Simple Machines, Gravitation, Oscillation, Pendulum, Spring, Pressure, Fluids, Light, Heat, Vectors and the list goes on!

There are experiments and demonstrations that would be expensive (electrical charges) or impossible (gravity at high altitudes) that are brought into the classroom and easily accessible for you and your students.

The math portion is growing as well as currently offers number sense and basic algebra. Chemistry has just started with compounds, but the representatives spoke with me about all of the modules they are working feverishly to add. If you have a subscription, you have access to all of the newest stuff.

If you are a math/science teacher, I strongly encourage you to check Exploriments out. I think that you will see that these can help your students learn and understand in a way not possible before.

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Geogebra CUE Conference Resources

This is an online version of a presentation that I gave at the 2011 CUE Conference in Palm Springs. This presentation is designed to give an overview and some of the functions of Geogebra. For more resources please check out the BrokenAirplane Geogebra page.

Click on the link to start using Geogebra. Then click on download. You will be presented with two options.

• Choose Webstart if you would like to install Geogebra on your computer. This is the best option as it will not require the Internet but it requires administrative access on your computer. Talk to your school's IT person about getting this installed.
• Select Applet Start to run Geogebra from within your browser without installing anything.

The first example is in reference to helping students understand Slope. This is a critical concept for students and also crucial to completing my Slope Art project. I have my students create "sliders" which allow them to change the values in the slope-intercept equation y=mx+b. Students can move these values back and forth to see the effects it has on the equation. To learn how to use sliders, check out my Interactive Math post about Geogebra.

In the following example, I use sliders once again but to demonstrate how to make any quadratic equation and see the effect of changing the coefficients of a,b, and c.

Geogebra is just as powerful with Geometry as it is with Algebra and you will find it excellent for creating proofs and constructions.

To create the perpendicular bisector (see the pictures on the right):

1) Use the new point tool and the line tool to create three points, A and B and make a line through them. 

2) Create a new point C and place it more than halfway on line AB.

3) Using the compass tool, create a circle with a radius from A to C and the center at A. Then create another circle with the same radius and with the center at B.

4) Then create new points at the intersections of the two circles and connect them with a line. You have created a perpendicular bisector!

Often, students need or want to see a concept again. Click on the "View" menu and then "Navigation Bar for Construction Steps" this will put a playback control at the bottom of Geogebra that you can replay for your students again and again. There is a way to animate movements as well in Geogebra.

Geogebra can explain math in a way that paper cannot convey. Here is a link to a visualization of the Unit Circle and its relation to Trigonometry.

While there are many more features, one that has been beneficial to me as a math/science teacher has been the ability to easily and clearly work with data. While Excel and other software provides this functionality, it is often too complex for younger students. With Geogebra you can quickly make graphs and equations that can be manipulated and modified.

There is so much that Geogebra can do I hope that you are interested in learning more. Be sure to check out the resources on BrokenAirplane as well as links to other great sites about Geogebra. Thanks for stopping by.

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SAM Animation is the Standard for What Educational Software Could Be

A couple of months ago, I was contacted by our organization's COO about SAM Animation software. He was really excited about it and at first I'll admit I didn't see the point. That was until I downloaded and tried out the software. I have not seen anything else that makes it so easy for students and teachers alike to create movies and animation to demonstrate learning.

This is a really high quality piece of software, that has been rigorously tested and refined in the classroom. It began a few years ago at Tufts University funded by the National Science Foundation. The software was released to the public and quickly gained a following of tens of thousands. Try out the free download by going to SAM Animation and clicking on the "Download Demo" button. The demo will let you see all of the amazing features and I am sure you will see how powerful this software can be.

SAM Animation software can be used to create stop motion or time lapse movies. 

Stop motion is where you take a picture, move the object, take another picture, and so on. This is how animation was originally done with films like Snow White and it is still how claymation movies like Wallace and Gromit or the Nightmare Before Christmas are made. With this, your students can create instructional videos using a variety of props and tools. Students of all ages love making movies, and there are many examples on the SAM website (some by Kindergarden children). For example check out this Life Cycle of a Tree video. Students are creating videos about science, math, history, the arts, and more.

Here is my former robotics team having some fun with this year's FRC Game Pieces

Time lapse movies are equally amazing to create and watch. A time lapse movie is used when you have something you want to capture but it takes a long time. For example, a sunrise/sunset, the sprouting of a seed, the solving of a Rubik's Cube, building of a robot, etc. This is the type of technology used for many parts of the award winning series Planet Earth. 

You might think to yourself that this sounds way too complicated, but within 5-10 minutes (I promise) of installing the demo you will have figured out the main idea and can start recording right away. You will need a webcam (every one we have tried so far has worked) and the installed demo.

After creating a project you will come to the stop motion page.Where capturing action is just a click away. There are two great features that you will discover right away. First, each picture that you take shows up in a timeline on the bottom and can easily be deleted with a single button.

The second main feature, and my favorite, is called Onion Skinning. You can see this in the window on the right. SAM Animation will show you in a ghost-like form where your last picture was taken so you can make sure you are positioned correctly for the next shot. This is perfect to make sure distances are realistic as well as being able to pickup where you left off when class ends.

Double clicking on a frame will bring up the editing window where you can draw, type, and even Chroma Key which is the professional term for replacing a background with another image. This allows your students to create a video in space, underwater, or anywhere else.

Recording audio is a snap, and a joy as you can record afterwards or import sound into the animation. 

If you would like to create a time lapse animation, simply click on that tab and you are presented with options for how often each picture is taken and for how long you want it to continue to snap the shots.

There are a many more features but if I don't have you convinced yet, here is the best reason why your classes will love using SAM Animation software. If you have used Adobe Premier or another expensive video software, then you know about the time lost to rendering or crashing while saving. With SAM, you click on File and then Export, and up pops a host of options like Flash, Quicktime, formatted for iPod, etc. that you can save to. Then for those of us who work on antiquated computers/networks, you can choose how fast your Internet speed is so the save is far less likely to crash your computer or slow down your network.

From speaking with Melissa, co-founder of iCreatetoEducate, every decision and feature has been driven by teacher and classroom feedback. From how easy it is to use, to the consideration of varying needs and technology, this software is a shining example of what educational software can be when there is passion and a love of learning driving it.

If you are interested in giving your students an innovative and exciting way to learn and share their learning with the world, then check out SAM Animation for the free demo and examples. I also suggest the iCreatetoEducate site where you can find support for SAM and suggested camera and props to help make your animations, and some great examples and tutorials. You will find the service and support to be excellent and product will continue to wow you every time you use it.

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Greenshot for Windows Makes Screenshots Easy (and its free)!

If you are writing worksheets, technical documents, blogging, etc. You will invariably come across the need for a screenshot. A screenshot is just what it says, a picture taken of whatever you have showing on your screen. When I started this blog, I quickly developed a need for a screenshot tool that would be fast and versatile (and of course preferably free). After looking through the various options, my conclusion was to definitely go with Greenshot.

Greenshot runs in the system tray in the lower right of your screen and has a very simple interface allowing you to customize your settings about where your captured screens are saved to and whether or not to capture your mouse as part of the snapshot (even if you do, you can delete it later).

To capture a full screen simply hit Ctrl + Print button. Since the Print button is vestigial, left over from when this button would send the text on the screen directly to the printer, it breathes new life into the button.  If you would like to capture a portion of the screen hit Print by itself and then click and drag the region you would like to capture (keep in mind some computers have added the "Function/Fn" button to essentially add more keys, for my computer I hit Fn + Ctrl + Print or Fn + Print).

Once you have captured the screen, an editor window will open (unless you have changed the options to directly save or copy to the clipboard). From here you can:

• Add rectangles, circles, lines, and arrows to add emphasis.
• The color, thickness, and transparency of these shapes can all be configured.
• Add text
• Highlight
• Obsfucate - This is a wonderful tool allowing you to blur out or hide specific parts of the picture or text. You might find this helpful if you want to blur out portions of a bank statement, hide your address in a picture, or share a student's work without divulging the name.
• Crop the image down to just the right size.

It's pretty cut-and-dried from there. You can then send the image to the printer, save it as a JPG, PNG, etc, or copy it into the clipboard for inserting into a document or presentation. Once you get the hang of the keyboard commands it is a breeze and a joy to make presentations, documents, etc. Rather than feel like something you have to break away from what you are doing, it is seamless enough to keep your workflow.

I would highly recommend Greenshot for Windows and hope it makes your life a bit easier.

Greenshot can be found in my Free Software for Educators List

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Living in the Cloud

So having had my Cr-48 Laptop for a week and seeing what it is like to live completely without a hard drive, I must say I had no idea how much I rely upon software. Even though I save almost no data to my hard drive, I still am unable to live fully in the cloud.

That is fine with me, as Chrome OS has not even reached version 1.0 and it has a long way to go, yet it is ironic that living completely in the cloud had the same feeling as roughing it in the mountains. There are so many creature comforts that are just not yet there yet, but it wasn't too long ago that I was educating people about the surge in Open Source technology so I have great expectations for its potential.

In this post I wanted to share the great cloud/web apps that are out there now and also what I would need to see emerge to feel completely free to soar among the eagles.

First in 100 words or less, what is the cloud and why would I want to "live in it"? The cloud is the term given to the applications and network storage that work together so you can sync up your data online. This allows you to work from any computer (Apple/PC/Linux, Home/Work/In-Laws, etc). It also affords you the assurance that even if your computer is lost or broken, your data can be recovered.

As always out of respect to your time and pocket, I will recommend only that which is free or worth the cost and tested by me.

It would be impossible to have a cloud computing post without including the giant that made it popular. Google has provided so many different ways to work online and all of them are free.

Google Apps
Books (Store), Blogs, Chrome, Gmail, Calendar, Documents, Photos, Sites

Aviary
Bundled into Gapps or you can run them separately is the Aviary suite. In it you will find:

• Image Editing
• Screen Capturing
• Vector Editor (think Illustrator/Inkscape)
• Visual Effects Editor (very cool, lots of amazing potential)
• Music Creator (ability to create beats and tracks)
• Audio Editor (an online Audacity with a built in library of samples from Quantum Tracks)
• Image Markup
• Color Editor

The Aviary applications are amazing and some are even better than their desktop counterparts. If you have a creative bone in your body, you should definitely give them a try.

Dropbox

This is the cleanest, simplest, best way to sync your files. Simply install the software on any and every computer you want to synchronize and then simply drag and drop your files into the Dropbox folder and it is automatically backed up. Then you can access your files from any of the computers, online, or even from your phone.

Evernote

I don't personally use this app but I know many others who I respect that love it. Evernote allows you to capture files, images, text, and more then share it and store it.

The cloud applications are getting better and better but I am still unwilling to leave my software. As more and more developers start moving familiar features into the cloud then the age of the Personal Computer is going to draw to a close and it will become more and more about having a constant Internet Connection.

My wish list for the cloud:

• To be able to sync settings (display, sound, hotkeys, etc). Google Chrome lets you sync quite a bit right now but everytime I am on another computer I am never as productive as when things are just right on my fine tuned computer.
• A great screencaster. I currently use CamStudio and as more and more people are creating video tutorials, the need for this is going to increase.
• A better way to connect the files on my computer to the ones on my phone. I still feel like there are two worlds, the mobile one and the desktop one. Merge those two please.

Far from complaining, I love the technology I have and am old enough to remember how far we have come from code on floppy disks/punch cards. With everyday I feel empowered to do more and more and the opportunities my students are able to explore and achieve are mind boggling. What will the technology world look like in 1 year? 5 years? 20 years? 100 years!?

Do you have any "cloud" tech that keeps your data safe and allows you to be productive everywhere? Share it with us in the comments.

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Sine, Cosine, and the Unit Circle in Geogebra

I have received some requests for this applet so I decided to post it for anyone who wants it. Seeing the connection between the trigonometric functions and the unit circle unifies a lot of mathematics. It also makes sense of these functions that must typically be memorized or looked up.

If you have not yet used Geogebra, be sure to use my getting started with Geogebra post. It has helped quite a few teachers start using Geogebra. It really does not take that long to learn.

Customize this applet for you:

• If you would like to see it full screen, double click on the animation. 
• To turn off the animation, right click the slider and uncheck Animation On. 
• See how I made this applet by clicking on View and then Construction Protocol. You can use the forward and backward buttons on the bottom to step through the construction as well.
• If you would like to see the values of Cosine and Sine change as x changes, go to View and Algebra View.
• To change any aesthetics or animations you can right click on any of the Dependent Objects in the Algebra View.
• Finally, if you turn on both Algebra View and Spreadsheet View from the View menu and then right click Cosine or Sine in Algebra View, you can turn on Trace to Spreadsheet to collect the values cycled through from pi to 2*pi.

Enjoy, and if you have any suggestions for other applets you would like to see, let me know. A special thanks to Guillermo of Mathematics and Multimedia for his post on Embedding into a Blogger post.

Be sure to check out all of the BrokenAirplane Geogebra resources.

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Why I love my Android OS Smartphone

It is no secret that I love Google. Everything they make is so well integrated and well designed (ok Buzz and Wave had promise but oh well). I even helped test out Google Apps for our school and knew that it was going to be far more useful than Outlook for coordinating our meetings and working with our students.

So when the time came for a new phone, I knew I was going to go for an Android phone. I knew I would enjoy the email and calendar integration and maybe even a few apps but I had no idea how much I would enjoy it. When I first got my Android phone I was blown away by its potential. I kept remarking that this was the first phone that actually felt like a "smart phone" or a phone from the future.

Why I am writing this post, almost 2 years after I first got an Android phone? Well, our school provides our parent and students comments bi-annually. As fulfilling and enriching as this is for them, it is extremely time consuming to write 75 or so comments (especially when I have the FRC season underway). 

A couple of semesters ago, I realized that I could write comments while I was sitting in a line bored or riding shotgun up to Los Angeles to visit family. This has significantly reduced the strain and stress of doing comments and has prevented me from having to experience the hours of last minute comment writing that my comments.

Yesterday, I was writing a comment and needed to check the student's grade. I was able to switch back and forth between the gradebook website and my Gmail where I was writing my comments. It struck me just how Android allows me to be powerfully mobile.

How else do I enjoy my Android phone? Many probably misunderstand us smart phone users and think we are just Facebooking or Tweeting all day long (and some may be). Yet, I have become much more productive and efficient since having my phone and it has allowed me to maintain this blog, keep my FRC team, communicate with students and parents. 

Some of my favorite Android apps for Education and features are:

• Dropbox: Having a networked drive that is easily accessible from the net is invaluable to a teacher. I cannot express how much I love backups of my stuff and the Android app is so wonderful with the ability to read and view almost any file.
• Editing Google Docs: Really useful to be able to modify and collaborate on a document without being at a computer (Android 2.2 only)
• Gmail and Google Calendar is so wonderful on an Android phone. Some write things down to remember them, I write them down to forget. Whether it is an idea or an event, I put it into my phone so I can spend my time and effort thinking about other things and being creative. With the updated Gmail app it is even easier for me to do these things. As a project based learning educator, I am always thinking of new ways to help students understand and apply information, and with my phone, I just send myself a little quick email (even at 2am) and no need to fret and concern myself with it anymore.
• Rooting: Although I haven't yet done this for my Android 2.2 phone, rooting my HTC Hero made it much more enjoyable. The boost in speed was definitely worth it.
• Tasker: My favorite Android app (next to Dropbox). It has a learning curve, but the Tasker wiki has some great tutorials. It allows you to customize your phone to your life and have it turn off the ringer at a certain time of the day or at School (based on GPS). There are countless other options to suit every possible need. While I still strongly support Free and Open Source, this app is definitely worth its price.
• Versatility: The phone is basically open, which allows it to be used as my 8GB hard drive, mobile hotspot, robot remote control, and so much more.

For more apps, I suggest you check out the updated Best Android Apps for Educators and anyone else who wants to be incredibly productive.

While some might think that constant communication and access to information would be overwhelming and a drain on time, I have actually found the reverse. Of course out of the box, the phone has all of these notifications and reminders but I suggest you turn these off to suit your life. 

The fact is that, I enjoy the ability to get information, make reservations at a restaurant, communicate with my PLN and friends, get directions, and so much more. If you can get an Android phone I highly recommend it. My family uses Sprint because of the unlimited Data plan but there are many great plans out there. Let me know if you have any questions or suggestions on how to use Android to be more productive.

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Modeling Math with Python Programming: The Spirograph Program

Hopefully this software does not remind you of the intense amount of snow some of you are getting. I am often inspired by others to create software and when I was browsing the Math.com site one day, I found a beautiful Spirograph applet that I knew I had to try to recreate in Python. I try to impart this to my students, seeing something that you don't initially understand and learning as you go.

It required me to relearn Parametric Equations, refine my knowledge of Class Objects, learn the controlls functions in VPython and push the boundaries of my computer's memory.

In order to run this code you will need:
Python 2.6 - The interpreter for the code. Check out the programming page if you would like to know more about implementing Python or programming in your classroom.
VPython - The visual add on for Python.
Psyco - Speeds up the code significantly so I could run it on older laptops. If you don't want it or need it, feel free to delete the first couple of lines (before the "from visual")

Enjoy the pictures and the code below, and please share any great code you have or suggestions.

Spirograph Maker inspired by http://www.math.com/students/wonders/spirographs.html

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import psyco psyco.full() from visual import arange,curve,color,cos,sin,display,rate from visual.controls import controls, slider,label iterations = input('How many iterations?') class spiro(): def __init__(self,iterations): self.R = 65.0 #Radius of Fixed Circle self.r = 43.0 #Radius of Moving Circle self.o = 75.0 #offset of pen point in moving circle self.t = arange(0,iterations,1) self.drawing = curve(x = ((self.R+self.r)*cos(self.t) - (self.r+self.o)*cos(((self.R+self.r)/self.r)*self.t)), y = ((self.R+self.r)*sin(self.t) - (self.r+self.o)*sin(((self.R+self.r)/self.r)*self.t)), color = color.green) def fixedRadius(self,fRadius): self.R = fRadius.value self.redraw() def rollingRadius(self,rRadius): self.r = rRadius.value self.redraw() def penOffset(self,pOffset): self.o = pOffset.value self.redraw() def redraw(self): self.drawing.x = ((self.R+self.r)*cos(self.t) - (self.r+self.o)*cos(((self.R+self.r)/self.r)*self.t)) self.drawing.y = ((self.R+self.r)*sin(self.t) - (self.r+self.o)*sin(((self.R+self.r)/self.r)*self.t)) class GUI(): def __init__(self): self.c = controls(x=0,y=0,width=400, height = 400, range=100) self.s1 = slider(pos=(0,40),width=7, length=40, axis=(1,0,0),min=1,max=100,action=lambda: Spirograph.fixedRadius(self.s1)) self.s2 = slider(pos=(0,0),width=7, length=40, axis=(1,0,0),min=1,max=100,action=lambda: Spirograph.rollingRadius(self.s2)) self.s3 = slider(pos=(0,-40),width=7, length=40, axis=(1,0,0),min=1,max=100,action=lambda: Spirograph.penOffset(self.s3)) self.fixedRadiusLabel = label(pos=self.s1.pos, display = self.c.display, text='Fixed Radius', line = 0, xoffset=0, yoffset=20, height=10, border=0) self.rollingRadiusLabel = label(pos=self.s2.pos, display = self.c.display, text='Rolling Radius', line = 0, xoffset=0, yoffset=20, height=10, border=0) self.penOffsetLabel = label(pos=self.s3.pos, display = self.c.display, text='Pre-Offset', line = 0, xoffset=0, yoffset=20, height=10, border=0) self.scene1 = display(title = 'Spirograph!', x=410, y=0, width=400, height = 400) self.scene1.select() WYSIWYG = GUI() Spirograph = spiro(iterations) while(1): WYSIWYG.c.interact()

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