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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Presentations of Learning Keep Us All Informed and Accountable

Twice a year, we take a break from our normal curriculum and classroom schedule in order to have Presentations of Learning (POLs). This is a week long event in which every student shares with their classmates, teachers, family, and community members what they have learned over the last semester.

The word "learn" always needs clarification for the students and so I am sure it is important to define it here. When we are referring to learning, we are not necessarily referring to "book smarts" or testable learning (although sometimes that is requested as well). Many of us focus the conversations around the Habits of the Heart and Mind but others use other similar themes or essential questions.

We ask the students to reflect and present upon the previous semester and to describe the challenges they have experiences and the growth that they have seen in themselves. They can provide evidence through project artifacts, their Digital Portfolio, anecdotally, or other various means of convincing us that they have used their time well this semester.

Remember, this is not a focus on things we have already graded them on because that would be a waste of time. I have other ways of assessing that. This is a chance to have a conversation with them and realign my perspective and goals with theirs. It is so rare that we have the time to get a student's perspective and I consider this a critical part of heading into the second semester.

The presentations last for about 10 minutes with a few minutes for question and answer afterwards. If we do not feel that the presenting skills meet our criteria or that the reflection is honest and has depth then we ask them to redo the presentation. We explain to them that this is not a "failure" this is a "not yet". Every student eventually passes but it takes refinement and time for some more than others.

We invite teachers, students, and family members to come see them because it provides a great opportunity to see a student in a different light than they may be used to seeing. It also gives a powerful opportunity to immerse themselves in our classroom/school culture. Since our entire school conducts POLs, we also ask our students to see POLs from the 10th, 11th, and 12th graders. This is an eye opening experience and they get to see the huge amount of growth and maturity that our students gain over 4 years.

How could you start implementing POLs in your classroom or school? Create an essential question of what you would like the students to reflect upon. Make it clear that this is not about grades necessarily  and that honesty is honored more than brown nosing (telling us what we want to hear). Then take 3-5 days depending on the schedule and listen to what your students have to say. It will definitely be worth your time. Invite others to come see the presentations and help ensure that this is taken seriously and given great importance.

Do not be lax or go easy on the students. Refinement requires honesty and growth will not come if you are not willing or able to say the things others might never have before. But also be open to hearing a new perspective on a student and perhaps insight into how you can better help that student and what they can do to help themselves.

Do you conduct Presentations of Learning? What criteria do you use to assess their learning? How has it impacted your students/school/community? Leave a comment and tell us how.

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New Robotics 2011 Game Logomotion Released!

Do I seem more tired than usual? If so it is because the FIRST Robotics Competition had its Kickoff this Saturday and we have worked all weekend. If you are a subscriber or longtime follower of BrokenAirplane then you know how passionate I am about the power of Robotics to change a students life. In my opinion, robotics teams are the purest form of learning and allow students to unleash their creativity and potential while learning valuable STEM skills (Science, Technology, Engineering, and Mathematics).

Each year the game changes, and each one is always so unique and well designed that even after doing this for years, I still get as excited as my students to start designing (perhaps more so). This year's game is Logomotion and it celebrates the 20th year anniversary of FIRST Robotics. Watch the 3 minute video to find out what it is all about.

Pretty amazing huh? What is even more amazing is that thousands of teams are working right now to create their own unique designs. Completely led and run by students with feedback from mentors, just wait and see the incredible stuff students come up with.

Our team went to the San Diego Kickoff and had a blast. It is their Rookie FRC year and I am excited to share it with them. We are a relatively small team of about 8 students but thanks to the incredibly generous support of our sponsors NASA, JC Penny, our after school program, and private donations we are well equipped to handle the job. I am also incredibly grateful to the 3 engineers and 1 math teacher/programmer who have joined the Chaos Vortex team. 

I will provide updates on our progress as the season progresses. If you know a FRC mentor at your school, please give them a smile and an encouraging word as we tend to work an extra 20+ hours in addition to our regular teaching duties. We love every minute but after a couple of weeks it gets pretty exhausting.

Let me know if I or my team can do anything to support other teams. We are rookies but we have a few years of VEX under our belt and we love to help! We are always looking to start new teams and if you would like to come by and see our VEX or FRC team in action let us know so we can help get you going for next year.

6 weeks until ship date.

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Share Math with Students and the World

If you have been playing with Geogebra learning the basics, sliders and animation, and hopefully some of your own, it won't be long before you want to share this with your students.

Of course you can show it on the projector if that is an option for you, but what happens when your students go home and need to remind themselves? Or perhaps you would like them to play with a concept before they come to class the next day. Whatever the reason, there is going to arise a need to share Geogebra files with your students outside the classroom.

Exporting a Worksheet
Luckily, Geogebra was built for easy sharing. Once you have created your Geogebra Worksheet that you want to share, click on "File" and then move your mouse over "Export". This brings up the sharing options.

There is the option to take a screenshot of your worksheet which can come in handy, but you probably want to share the whole thing, interactivity and all. Click on Export as "Dynamic Worksheet as Webpage (HTML).

From there add in your information to describe what the worksheet is about. I would recommend that you don't leave this section blank as I have seen many unlabeled worksheets that have made no sense at all. It is a great idea to add instructions and descriptions to make the worksheet as helpful as possible.

Don't be afraid to check out the advanced tab as well. These options allow you to restrict certain options like right-clicking, reseting the construction, hiding the tools, etc. This is not for the purposes of restriction but to ensure that the student only does what you want them to do. If you give too many options for a construction where you only want them to drag the sliders, they could get confused.

Finally, click "Export" and decide where to save the file and what it should be called and like magic, your Geogebra Worksheet is there all packaged into one HTML File. This makes it easy to email the file to your students. If you have a website, you can add this as a page by placing it in your website's folder and linking to it.

It used to be much more difficult to share Geogebra files on the web, but now it is all inside one self contained file. Keep in mind that if your computers have updated JAVA, the files can be used without access to the Internet. This came in handy one day when the network was down.

If you are going to embed the file into your blog or anywhere else, you can follow the directions on Kate Nowak's Blog but keep in mind that if you resize the file you are going to not shrink down the file but cut off some of it. That is why I usually will provide the actual file or link to the file by using the Geogebra Uploader.

Here is a link to the Quadratic Coefficients Exercise mentioned in the previous post on Sliders and Animation in Geogebra.

If you are interested in embedding the sketch into your blog, there are some excellent instructions on the Mathematics and Multimedia blog.

Community
Geogebra has been around for long enough that there are quite a few people using it. That is the power of Open Source, people who might not previously have been able to learn and contribute to this project can freely use it on any computer in the world. In fact the problem is almost too many resources.

Let the community support you right away in using Geogebra. What are you planning on teaching today? Trigonometric functions, quadratics, Derivatives, Addition? Type in _________ (your topic) geogebra worksheet and I would be shocked if you couldn't find something that you could immediately use in your classroom.

Here are some great resources that you can always rely on for great Geogebra Content:
Geogebra Wiki - The main site keeps a great collection of Worksheets that you can add to covering a wide variety of topics. There may be a Geogebra Institute in your area. Click the link to check it out. There is also a YouTube Channel dedicated to news and features in Geogebra.

Geogebra Math - Created by Linda (of Math247) and Maria (of Natural Math), legendary in the math community for their innovations and contributions. You will love these Worksheets.

Mathematics for Middle School - This is another blog where it is clear that the author (Andreas) is committed to creating great resources to share with educators and her students. The focus is on arithmetic and algebra which is so important as these abstract concepts demand visual explanation.

Mathematics and Multimedia - This blog will really take you deep into mathematics. The tutorials not only demonstrate topics but also proofs or concepts that cover a large span of topics. Guillermo has done a masterful job with this blog.

I will continue to do Geogebra tutorials and topics and if you have any ideas, suggestions, or questions about what you would like to see, let me know and I will either directly message you in the comments or Twitter or create a post to help you out. Remember to sign up for the CUE Conference in March and I will see you there!

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Make Math Move with Sliders and Animation in Geogebra

It is incredible that within the first few hours of posting the Geogebra Basics post, hundreds had already checked it out via Twitter, Facebook, and the BrokenAirplane RSS feed. There are so many people who are interested in learning more about using Geogebra in their classrooms and I hope you are getting the hang of the basics and perhaps tried a few things of your own.

The next two features, are one of the most requested and often used features for Geogebra because they promote interactivity and understanding. Once you get the hang of it, your students will never look at an equation the same.

Sliders

This is one of my favorite features in Geogebra. Graphs/Functions show changes over a range of numbers, but what happens when you change the equation? These relationships are the core of the equations but students often miss it as they try to plot the graph.

Step 1: Open Geogebra (steps 1-3 in the basics post).

Step 2: Look at the bottom of the Geogebra window. On your left you will see the word "Input" and next to it is a text box to type in equations, variables, and more.

Step 3: Lets create some coefficients that we can play with. In the Input Bar, type in m=0 and hit "Enter" on your keyboard. It is important that you follow these instructions literally, so do not use an uppercase M (although you could use any letter in the future but for the example follow carefully)

After hitting "enter" you will notice under "Free Objects" a new object m which is set equal to zero.

Step 4: Create one more free object by typing "b=0" into the input bar and hit "enter".

Step 5: Next to the free objects "m" and "b" you will see a clear bubble. It is actually an ON/OFF switch for the slider. Click on the bubble for both of them and you should see a slider appear in the graphing window.

Step 6: Back in the input bar, type in "y=m*x+b" and hit enter. Note: The asterisk between the m and x is the multiplication symbol. You must type it this way as you will get an error if you try to just use "mx".

Step 7: It may have seemed like nothing happened, but in fact you just graphed y=mx+b, the equation of a line. The reason you can't see it is because you have your slope (m) set to zero and it is covered up by the x-axis.

So lets see that line and the power of sliders. If you look at the "m" slider, it says m=0. Click and drag the ball on the slider back and forth. Watch as the line changes its slope and imagine your students going "Ahhhhhhh" as you explain and show slope changing. The visual demonstration gives the student the mental connection they need to understand.

You can adjust the "b" slider as well and see the y-intercept change. Although it is called the "y-intercept" students still seem to get confused until you show them that its value determines where the line hits the axis and adjust it to show them how it can change.

As students begin to see these relationships, they can begin to apply their knowledge to new situations and visualize the graphs in their heads before they have to plot them by hand. Imagine a classroom where students and not calculators see the relationships between variables and coefficients.

If you really want a fun demonstration, create three new sliders "a", "b", and "c" (step 3). Then enter in the equation y=(a*x^2)+b*x+c (the "^" symbol comes from holding shift and pushing the number "6") and you can show your students the relationship of the variables and coefficients in a quadratic. Seeing these numbers change,  become positive and negative, and zero really makes it all the clearer that math can represent real things like data and physics.

Changing the range of these sliders can be really useful and you can do this by right clicking on the slider ball and choosing object properties. Changing the interval will choose the range of numbers over which the slider will show. There are many other settings you can change in this menu like color and thickness, and much more. Be sure to try changing the size or color of your lines as well to make them easier to see from far away if you are showing this to a large group.

Animation

It can be very useful to have your students see the sliders move through all of the numbers over and over. This frees you up to walk around the room but also shows an animation of math moving which can be very beautiful and help promote understanding with trigonometric and polar functions.

To activate animation of a particular slider, right click the ball of the slider you wish to animate, and select "Animation On". By default it will cycle through all of the positive numbers and then go through the negative numbers over and over. You can change this in the slider's "object properties" menu and under the "slider" menu and "Animation" setting change the speed of the animation. The three options for an animation are: Oscillating, which is the default back and forth cycling through all of the numbers; and Increasing or Decreasing which will only once go through the positive or negative numbers. It might be necessary to slow down the speed so narration and explanation are possible.


Play around with those, and I do mean play. This is software that really encourages fun in math and I hope that these features will help your students to see that. In the next post, we take a more global look and see how to share Geogebra files with your students and the World! Also, there are an enormous amount of resources out there that I want to share with you from educators already making great stuff with Geogebra. See you next time.

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7 Steps to Interactive Math with Geogebra: The Basics

It's the beginning of the year, and I am so glad I took the break from posting. It gave me a chance to read some great books, work on a few side projects which you will hear about soon enough, get the house finally in order, and spend some wonderful time with my family.

The FIRST Robotics Competition will begin this Saturday and I can't wait to tell you all about this years competition challenge.

Since I wasn't posting over the holidays I was not able to give you a present. So although it is belated, I wanted to share with you one of my favorite pieces of free and open source software, Geogebra (Geometry + Algebra). I remember seeing this software for the first time years ago and seeing the potential for Educational Technology. In fact, I will be speaking at the 2011 CUE conference in Palm Springs this year entitled "Geogebra for Interactive Mathematics".

Should you start using Geogebra? Well tell me if you have experienced this:

• Difficulty graphing on the Whiteboard because of time or quality of drawing skills.
• Confusion with your students about the relationships of variables and their coefficients (e.g. what happens when "m" or "b" changes in y=mx+b).
• Students forgetting a long proof or steps to solve an equation.
• And all of the other frustrations that come with the limits of reality to explain abstract concepts.

If you nodded your head to any of the above, then you need Geogebra. Don't worry though, it is free and easy to get started.

Getting Started With Geogebra

Step 1: Go to www.geogebra.org and click download.

• UPDATE: Since this post was written, there is now a Geogebra for Elementary students. It is the same functionality but with bigger fonts and an easier user interface. 

Step 2: You have 3 options for using Geogebra to accommodate as many possible situations as possible.

• Webstart - This is the option to choose if you want to be able to use Geogebra offline. It requires you to install the software and so make sure you talk with your school's IT department about getting this setup. Good option if you can get it just in case the web is down.
• Applet Start - Allows you to use Geogebra fully in your web browser as long as you are connected to the web.
• Offline Install - Use this option to download a Geogebra installer and share with a student if they do not have Internet access.

Most of the time you will use the Applet Start. This requires up to date Java which most classrooms have if the IT department works on them at least once a year.

Step 3: Open Geogebra. It will look the same no matter how you open it and on which computer, which is a beautiful thing when you are working with students.

Let's look at the construction tools that you will use most often. These tools are used together with others to make objects and manipulate them.

These buttons also store additional tools. I will describe each button and the additional tools in that menu. To see the additional tools, just click on the little arrow in the lower right of each button.

From left to right, you will find:

1. Move, Rotate, Record to Spreadsheet
2. New Point, Intersect two objects, Midpoint or Center
3. Lines, Segments, Vectors, and Ray Tools
4. Perpendicular, Parallel, Tangent, Best Fit
5. Draw Polygon, or Regular Polygon
6. Circle Tools
7. Ellipse, Hyperbola, Parabola
8. Angle, Distance, Area, and Slope
9. Reflections and Translations
10. Sliders, Text, Images
11. Move, Zoom, Show/Hide

A lot of features, and it could seem overwhelming at first. But like any powerful software like Audacity or Inkscape, it is important to play around and get the basics and over time you will grow deeper in your understanding. Most important is that you believe in yourself and your ability to do this! I promise.

Step 4:Lets play around a bit to get the hang of the interface. Geogebra opens up with a nice graph all ready for you so lets add some dots. Click on the New Point Button and then click anywhere on the graph.

You'll notice that a new point has been created and labeled "A". This is also reflected on the left under "Free Objects". This means that you can change or move the point if you want.

Now create another point anywhere you want. A new point labeled "B" is created and the coordinates for both A and B are shown on the left-hand side.

Step 5: Lets turn those points into a line. Click the appropriately named "Line through Two Points" button on the right of the new point button. Then click on Point A and then Point B on the graph. A new line is formed labeled "a" (lowercase to differentiate it from points and you can change all of the names to whatever you would like later).

If you did the previous steps correctly, you should also see the equation for your line under dependent objects (because it depends on Point A and B). It defaults to standard form (Ax + By = C) but you can change that to slope intercept form by right clicking on the line and choosing y=mx+b. You can see this in the picture below but remember that our points and lines are going to differ so my numbers are not the same as yours.

You are probably ecstatic over how much clearer and precise your math demonstrations can be. Let me show you a couple more things today and next time we will go a bit more advanced.

Step 6: Lets make a perpendicular line. Click the next button to the right called "Perpendicular Line". It asks you to click on a point and a line, so click on either Point A, Point B, or create a Point C with the add a new point button from step 4. Then click on Line A.

Your perpendicular line has been created. If you would like to "undo" a step, click Ctrl+Z or choose it from the Edit Menu, but followers of this blog know the power of using Keyboard Shortcuts.

You may need to shift or zoom out, and you can easily do so by clicking on the "Move Graphics View" button. Just make sure you click the "Move" button (the furthest left) in order to click on objects again.

Step 7: As amazing as Geogebra is, you might ask yourself why my CUE Conference demonstration refers to using Geogebra to make "Interactive Mathematics". Well, usually once you have printed out a worksheet or drawn something on the board, it is done and it is difficult if not impossible to play around with it. There are expensive SMART boards that can create Interactive Math but you can do it for free with a computer and Geogebra.

Making sure the "Move" button on the far left is selected, select, hold, and drag Point A. You should see the entire line and it's perpendicular line shift around as well as the equations and points on the left. Check out the video below to see Geogebra in action.

Pretty amazing huh? Math does not have to be dead, now students can play with it, and play they will. Let them loose on Geogebra and they will create amazing art, drawings, and constructions in no time.

In the next couple of posts, I will show you even more amazing things in Geogebra. We should be able to cover:

• Sliders and Animation
• Embedding and Sharing Geogebra files with your students and the World
• And some great resources from other Educators that you can immediately start using in your classroom.

If I could enlist in your help, I want to ensure that the CUE conference and these posts are helpful and relevant to you. If you have a suggestion for a Geogebra topic (or any topic in general) please leave it in the comments, send me an Email, comment on Facebook, or tweet me @BrokenAirplane. Thanks!

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