Showing posts with label math. Show all posts

Reflections on Coding to Help in Geometry

Hopscotch block codes for animation.
Recently my Geometry students were tasked with using Hopscotch, a basic "coding" app for iPad, to create a simple animation.


Objective: Use Hopscotch to understand Conditional Statements.
Instructions:  Create an entertaining and engaging animation for your classmates using multiple characters with multiple "If...." commands. Then create a ShowMe video that demonstrates your knowledge of "If...Then..." statements and your animation commands.

I had multiple reasons for assigning this task, some of which are listed here:
1. Expose students to coding structure.
2. Working with "IF...THEN..." conditional statements.
3. Use commands such as: rotation, change by x, and change by y.
4. Interpret movements in the coordinate plane, work with coordinates, and design something using math.
5. It is playful and open ended. It is a creative expression of math.

The final reason I tasked students with this project was to expose them to conditional statements. It seems Common Core has done away with the need to learn "IF....THEN..." statements as they relate to geometric proofs. To be honest I always struggled with teaching this concept really effectively and students always struggled to really grasp it, but then again there is probably a small percentage of us who really love mathematical proofs.

However, I do believe that conditional statements are very important for our logical development as well as for our future generations of computer programmers and software engineers. So to expose them to this type of language in a playful way seemed like a good idea.

Here is what I liked:
1. Kids got creative.
2. Kids asked questions about how to animate- they were genuinely interested in a math task.
3. It gives immediate feedback. Simply tap play to see how the changes in animation.
4. Kids tried things that I never thought of- such as adding emoji's as text objects.
5. Kids were proud of what they made and bragged about what their classmates made.
6. Prior to the bell ringing, kids coded in Hopscotch rather than played a game on the iPad...(alright there were still some that played games).
7. Kids were working with (and therefore learning) the basic ideas around translations and rotations in the coordinate plane without being told to learn about translations and rotation. By the way these transformations are our next unit of study.
8. It gave some students who may not do well on a traditional paper assignment the opportunity to demonstrate an understanding of content.
9. There were not many guidelines. Student work looked different based upon what they were interested in creating.

If you are on an iPad you can view this student sample by opening this file up in Hopscotch. http://hop.sc/1cm1muo.

Looking back on the assignment I realize it wasn't the perfect assignment. At least, it wasn't perfect in the way that all students aced the part of the chapter test on "If...Then..." statements and proofs.
But again, this raises another question on assessment- when using projects to create an understanding of concepts how realistic is it to expect our students to transfer that knowledge from a project to a traditional paper assessment?  Isn't my real end goal for our students to be able to transfer their knowledge from the traditional paper assessment to a real life application such as creating a computer animation?

Would love to hear your thoughts....as it appears I am still learning!


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Sharing Knowledge, Inspiring Creativity

If you have read any of my other posts or pages on this blog you will know that I am a big proponent of teacher created (hacked) interactive books made for the iPad using iBooks Author. See our summer project here. 

So, in honor of attending the #NCTM conference this year in Denver and in hopes of inspiring creativity in others and generating feedback (kind critiques) of my own work I am posting two semi-polished interactive books. After downloading them to your iPad please revisit this blog and leave a comment giving feedback to the work in progress. Thanks!

You will need to download these books from an iPad and chose to open them in the free iBooks app.


Geometry: Transformations75 MB Download to iPad
Geometry: Circles70 MB Download to iPad















About the Books

Both of these books are created in iBooks Author and are only viewable on the iPad. However, if you wanted them in ePub format we can provide that format you will just lose most of the interactive features. 

Both books contain student friendly text, images curated from creative common sources, HTML widgets that allow for exploring patterns and relationships, and quizzes both embedded and online. In addition to these features, the books contain videos, some that are embedded that will play offline and others that are streamed from YouTube.



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Soccer Ball Math

The Ball Story

It happened to me yesterday. Like all non-expecting, well-intentioned, hard-working coaches who happened to be in the wrong place at the wrong time. 

I was positioned 10 feet outside of the goal frame instructing my goal keeper on a few points. The rest of the team lined up around the 18' mark, poised and ready for taking shots on our keeper. 

Just as I turned ever so slightly to face the next shooter and motion for her to take the shot. That's when it hit me, literally. That's when the cry of all self respecting men rang out around the world. That's when the wayward shot from the foot of the quietest girl on the team came like a comet screaming for my manhood and hit me square, causing every woman and child in viewing distance to pause, gasp, and then burst out into laughter.  

I dropped. 

I cried.

They laughed. 

The Ball Story Problem

Being a soccer coach I am fascinated with the different designs of a soccer ball. However, the traditional design offers geeky teachers a challenging math problem involving areas of two dimensional regular polygons that are linked together to form a three dimensional solid. 

So, in honor of attending NCTM 13 in Denver this week (and of course the story above) I thought I would share this problem. The students do an entertaining job of explaining the problem in the video below. 

Problem: Find the surface area and radius of the traditional size 5 soccer ball when given the side of the regular pentagonal panels is 4.2 cm. 



Persevering

Simply handing the students a soccer ball and asking them to find the surface area is also a nice way to address the math practice standards of 'persevering in problem solving.' Hopefully after presenting this problem students will ask good questions such as; What do I need to know in order to find the radius and the surface area? What shapes make up the surface area of the ball? How can I find the area of one of those shapes? etc. 

Obviously you can scaffold the information as you see fit for your students. As you can tell from the video we chose to tell them how many pentagons and hexagons made up the surface of the ball. You could also chose to give them more information such as the formulas for finding the area of a regular polygon. Or you could simply hand them a ball and a ruler and tell them to come up with as an exact of a measure for the surface area and radius as they can. 


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Skitch + Clinometer + Keynote = Trigofunetry

I had no idea what a clinometer was until a few weeks ago when we started talking about an extension project for our 9th grade math students. We started with the idea of measuring angles with a protractor and a scope- essentially a coffee stirring straw. Then it hit us to search the app store and see what they had available. This just highlights the shift in thinking teachers take on in an iPad classroom. Somehow our thinking needs to make this shift from "what materials do I have in my room" to "how can this device and its apps impact student understanding?"


I understand the danger of jamming the iPad into our content for the sake of using the iPad and calling a it revolutionary device. But honestly this a perfect exampleof how we can take real life measurements using a device that prior to now very few students would have access to.

After searching a few apps we discovered the clinometer and instantly we had our iProject (iPad project). The clinometer leverages the iPads accelerometer and returns the angle of elevation or declination of your line of sight when looking through a scope attached to the top edge of the iPad. In groups of two to three students they were given limited instructions and supplies and asked to use what they know about trigonometry to find the height of objects larger than them.

Employing the skitch app students snapped a picture of their angle of elevation and calculated the height of their objects. Overall, it was a really fun project that got students out of their seats and calculating the height of objects using trig ratios.

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The Interactive Lecture... Delivery Part 2


A few years ago I studied Classroom Presenter 3 and wrote my masters thesis on tech enhanced interactive lectures. CP3 is an amazing piece of open source software that creates a dynamic interactive student centered conversation in the classroom and in my opinion would make a killer app for the iPad (anyone want to develop it?) The incredible thing about CP3 is that it takes a teacher centered static powerpoint and allows for student input, instant feedback, and an ability to diverge from the linear path of a ppt slide show.


I mention this because video lectures are the foundation of flipped instruction, a style of instruction that I am very fond of and feel compelled to pursue in light of 1:1 iPads. In addition, I am keenly aware of how, like powerpoint, video lectures run the risk of creating a non interactive didactic teacher centered delivery.

This forces many questions. How does a video become interactive? Should video lessons just be explorations that ask questions? Is it best practice to use video to guide students through notes and example problems? How do you ensure students are listening to the lecture and not just copying notes? Are there editing tricks or guided note tricks that make a video more interactive and increase student participation?

Being a math teacher I want my students to see mathematical relationships, recognize mathematical patterns, and learn properties of shapes, functions, and graphs. However, I also recognize that it is important to model problem solving techniques by providing examples that the teacher walks through.

So where does that leave me? As of today I think I am somewhere in the middle of all this. My notes require students to answer questions based off what was said in the video but they also contain examples some completed for them others only partially completed. Here is a sample of where I am at with my vodcasting I like to call em Mathflix. I don't have an allusions of grandeur thinking that I can offer subscriptions for $7.99/month I just thought it was a fun name.



I am interested in your thoughts on how to make videos interactive. Feel free to leave your comments.

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Students using Showme to... well, show me and the World.



My friend Kip introduced me to the Showme App this summer and right away I feel in love with the ability to capture screen annotations and voice narrations as the user is demonstrating something on their iPad.
Now in class I can demonstrate solving and graphing an inequality using Showme, and instead of not being able to hear or see that explanation again, the captured vodcast can easily be linked or embedded in a classroom website for later viewing and reviewing.
As my familiarity with the app grew I thought "wouldn't it be great for students to use this to help their classmates with difficult problems and demonstrate to me what they truly know." We distributed the free app to students and literally watched and listened as they showed me and their classmates what they knew.
However, an interesting thing happened the other day. Being curious about how I could use the showme website to support student learning I started clicking through some topics. After selecting Learn by Topic > Geometry I was blown away by what I saw. Here it is:


You see up until now students have solved problems for basically two people: themselves and their teacher. But now students are solving problems for an audience of millions. When I projected the website for them the other day and showed them how their works was showing up in just two clicks of the mouse their mouths dropped. They were blown away by the fact that their work was published and freely available for anyone to view and use. I wish I could have take a picture of their faces you could see the sense of ownership and pride in their work take on new meaning.

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