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# Week 4: Zoom on zoom

Prezi is a powerful  tool for making presentations. In this brilliant and popular manifesto, Alison Blank uses Prezi's zoom capability to make the point that math is not linear.

If you get dizzy watching, slightly unfocus your eyes when you press the "next" arrow.

Part 1

What math concepts would you teach using virtual manipulatives that can zoom in and out? Why and how?

Part 2

Make a Prezi presentation and link it here.

• I believe that Prezi would be great to teach many mathematical concepts. Ultimately, it depends on the creativety of the person using this application. I believe it would be great for introducing or review the steps to solve word problem. I love the fact that you can zoom in on specifc information and this is key when solving word problems. I would have Prezi zoom in on the important facts or data presented in the word problem and have the scholars determine if that information is necessary or needed in solving the exercise. I would alsu use it to guide the scholars in the steps to solving any word problem as we sort through the information, what we are solving for, and what operations or skills are needed to complete it. I would also incorporate the use of virutal manipulatives that are related to the exercise solved so scholars would have a visual as to what was happened or what is needed. After going through the steps, taking notes, and the use of virtual manipulative; we would solve the word problem and represent the answer in words along with our virtual manipulatives.

Here is my Prezi link. http://prezi.com/hff60tjajrxv/writing-an-algebraic-rule/

• You used the body of that android to organize your presentation in a very intuitive way. The process is over the head, visually showing "thinking." It all starts over one hand and then goes to the other.  This is a beautiful and efficient way to build infographics.

As you said, "flying" from one step to the next tells the story - and zooming can show what is important in that story!

If I were to make a Part II to your Prezi, I would show the numbers "plugged into" the formula 3x+1, with zoom on inputs and outputs.

• Part 1:  Prezi is useful for zooming in, such as one would do with a magnifying glass - the first thought that comes to my mind is zooming in on a sunflower to demonstrate the Fibonacci sequence (and also demonstrate the difference between the actual pollen-bearing flowers and the bracts).  Prezi would also be very valuable for demonstrating how many different topics relate to each other while using a relatively small (and nonlinear) space.  My first impulsive thought would be to use Prezi to show how human beings of different cultures can have similar aesthetic preferences (such as the Golden Ratio; zooming here and there on the Prezi world map template could give a great visual of any 'universal' type theme).  The relationships between different branches of mathematics (or any other discipline) could be demonstrated in this way also.  Prezi gives an advantage for demonstrating conceptual/abstract relationships, as trying to put these ideas into a conventional linear slideshow is like trying to put the proverbial square peg into a round hole.  For example, one could start with a circle (or triangle, or any other shape/idea) in the middle and radiate out to various other topics, often returning to the center to remind the viewer of the main idea.

Part 2:  My Prezi is at

I was really indecisive about presentation ideas.  I thought this would be a nice warm-up to introducing the Cartesian Coordinate System.  I think that giving quick bio of mathematicians  might make the subject less intimidating for students.

• Non-linear tools work great with "sidetracks." In your example, we may be exploring Fibonacci - but have a little sidetrack about the anatomy of sunflowers - and then go right back to the main path.

Your map idea takes the same design to eleven: by clicking on different parts of the map you can trek into that place's math, so to speak.

The designs where side ideas radiate from one central idea are called "mindmaps" - yes, great for exploring hierarchical or taxonomic systems.

I feel that the curly stylized tree you used as the background really fits the story! The separate facts are on branches you can "climb." I agree that seeing mathematicians as people makes a lot of difference. There are some modern projects where kids interview contemporary math professionals about their lives and interests... Maybe kids could use your presentation as an example for theirs, and an inspiration for interview questions? Most mathematicians have tutored at some point of their lives, for example, to make the ends meet. "Have you tutored any royalty?" - a cool interview question right there!

• Part 1

I really think that a lot of math concepts can be used using this virtual manipulative. I think the best math concepts that would fit this format is an overarching concept that can be broken down by steps or smaller concepts. I think that this format helps to emphasize to students how to break up a large concept into smaller parts in order to learn and understand the material.

I teach using PowerPoint presentations and I LOVE learning a new visual to teach from, especially when the format is very visually appealing and has a great iPad application. My students love anything that they can do on their iPads. I really like the Prezi presentations has a path directed by the creator so the users know how to navigate from frame to frame. This is also very important for math presentations that usually have a specific order to learn concepts.

I think this program would be great to teach to students and offer to them to use for projects and presentations. I was also thinking about how well this program would work for those vritual field trips that we learned about in the math terms from Week 1. Students can use hyperlinks, videos, and type information into each frame along the path and take their users on a journey through their project, a new concept, or a virtual field trip!

Part 2

This is a link to my Prezi on the order of operations. I really enjoyed working with this program and I would really appreciate any feedback.

I did find two things about the Prezi program that I did not like. One is that it does not have a nice way to incorporate Math Type software. You can see in the Prezi presentation that I created that I imported the Math Type equations as pictures. Maybe there is a better way of doing it that I haven't found yet. Does anyone know it? The other thing that I was not able to figure out was how to hyperlink. Did anyone find a way to do that? In my presentation, I copied and pasted links for students to practice the order of operations.

• I really like the "path" tool in Prezi, as well. You can lay out the paths that loop, or "radiate" from one central idea and come back to it, or are linear like a story with the beginning, the middle and the end.

I have seen a few good Prezi examples that don't use the path tool, as well. For example, this one starts from a path (explaining why PowerPoints that are too long are boring) and then you can just click around: http://prezi.com/jukqtsincrom/the-destruction-of-linear-learning/

Since you asked, here is somewhat more detailed feedback about your presentation. I can see you thought it out and made it with heart! Now you and other teachers and students can use this real resource you created.

• The visual analogy of "the path" (shown with footsteps) is attractive and effective. You are making the point that you want a certain step-by-step procedure followed at all times.
• Zooming on steps will help students to pause and recall what those things are.
• Embedding pictures and the video is strong; links work well for when you can't embed the media, but I would represent it with pictures or screenshots as well for preview reasons.
• Mnemonics and international info as a sidetrack - nice! Appropriate.
• (This is a purely pedagogy comment). Somewhere toward the end, I would sidetrack into alternative ways of thinking about the order of operations, for example, TreeForms or "nested syntax". As a coincidence, there is a somewhat heated discussion of the topic going on right now on the Math Future email list, which you can read or join here: https://groups.google.com/forum/?hl=en_US&fromgroups=#!topic/mathfuture/_e59kezqz1g
• You may want to title your Prezi, so others find it easier.

I think MathType only works on Windows at the moment: http://www.dessci.com/en/support/MathType/works_with.asp#!target=prezi

• Thank you for all the great feedback!

• Part 1:

I think when you are a teacher, students whether older or younger, adults or kids...or in the middle, WILL get BORED unless you keep your lesson or presentation of thoughts INTERESTING. The virtual manipulatives work well in just about every math concept. For me, I think I truly would plan to mix it into almost every week of teaching in a middle school classroom.

Some concepts seem more obvious like geometry...the turn a 3D shape really ALIVE in a virtual manipulative seems like it would be a crime NOT to...in order to really show it, you almost have to...IF you are like me & you are a terrible drawer! Certainly, some textbooks will show good pictures but the idea of showing the building bocks layers at a time into that shape is really impressive to watch through a virtual manipulative.

Truly though, I pray that the urban school I end up teaching at has a decent amount of technology to assure kids get to experience it in this way. Last week, in the classroom I am helping out in, the teacher was doin simple linear equations ...she was working along in a power point that every once in while would have a jazzy shadowy number OR a simple colorful pencil circle around something. It REALLY had the kids paying attention. And, isnt that what its all about...its our biggest challenge as teachers I think.

So, I say...use it often ...in as many cases as possible & keep the presentation of lessons visually stimulating & you can't go wrong!

• Part 2: PREZI

Hi guys,- Please note, I updated my link & comment here thanks to Katherine!!

click on link above to view my prezi! -Lisa

• Lisa, when you are on the page for your prezi, you can hover your mouse over the title where it says "untitled" and a blue link will pop up that says "edit". If you click on that, you can change the title. The same thing works for the description.

• K,

Thank you sOOOO MUCH! I really appreciate you taking the time to show me this stuff...its been driving me crazy :)
Much Appreciated!-Lisa

• For some reason, I imagined your songs as a smart rap. Catchy!

I also started to contemplate how to SHOW the ratio of 2:5. How would you show that 4:10 is the same ratio? It's beyond the scope of your song, but your project made me think further...

Maybe start with 2 birds and 5 birds, but then zoom on their FEET. That's 4 feet and 10 feet! Or their wings. I would circle them to highlight, following your technique. As you wrote in the discussion, and demonstrated in the Prezi, circling important parts helps students with their attention.

• That was such a fantastic manifesto! I could relate to so many of the thoughts she expressed, and it gave me even more to think about with regards to the philosophy of math education.

Something I think would be good to teach with zooming is learning about tangent lines and the slopes of curves at a point. Virtual manipulatives that can zoom in could give a super close-up view of a small part of a curve. I think that could really illustrate how when you choose two points close enough together, the curve looks like a straight line.

I had a lot of fun with Prezi! My presentation isn’t really about math, but when I saw this template, I couldn’t resist. It was interesting to think about different ways to connect the content to the presentation itself: Special Relativity

• Awesome prezi! I like your idea of using zooming to teach tangent lines. They confused me when I learned them and seeing them closer might have helped.

• Katherine,

can you tell me how you get your link to simply show up as a word to click on? (as you have above.. "Special Relativity"

I really wish I had better computer skills...but hey...thats why I took this class :)

thanks!
-Lisa

• No problem! When you're typing your comment in the comment box, just type the text you want for your link, so in my case it was "Special Relativity." Then when you're done, highlight that text and click on the little icon above the comment box all the way over to the left that looks like a globe with something in front of it (it says "link" if you hover your mouse over it). A box will pop up and you will see a space that says URL. Paste in the url of your link and then click ok. You can check that it works by clicking preview at the bottom of the comment box then clicking on the link you just created to make sure everything is working properly. Let me know if that works for you!

• Oh, I am going to use your idea for a project we've been doing on introductory calculus. The idea I am thinking is the tangent line (derivative) as the limit of section lines.

Nice visual joke about "turning the universe upside down"!

Also, I like how the three main points you make are there at the last screen - but you don't see them all together until then. It makes for a strong "punchline" to the story.

Looking at your presentation, I was contemplating "word storytelling" and "visual storytelling." There are some discussions now about new tools supporting new modes of storytelling. Here, you are telling a very classic (and classy) word-based story - but at the same time, you are using the zooming, turning and moving effects to highlight the structure and the key points of the story. Good example of a strong use of a new tool in an old genre!

• I love prezi. I had so much fun making this presentation. I also suggested this site for my other class which we have to make a power point presentation for a final project!

So I thought about items that would be good to teach using zoom in and out. One thing I would teach this way would be fractals. I have made my presentation on the Koch Snowflake.

I hope you enjoy it as much as I did making it. I think being able to zoom in on the different stages of process of making the snoflake would help students be able to see the details.

• Megan, I love your presentation because it's a perfect balance between complex and simple; I think it's just right for sparking a student's imagination.  I also love your final comment reminding students that it all started with a triangle!

• Fractals are the ultimate "zoom objects"! You can zoom in and out infinitely (in theory) - or some many levels in a good software. Actually, I once "broke Prezi" trying to make it zoom too many levels. It froze my computer at the seventh power or so.

What is quite effective in your presentation is the order of pictures from simple to complex. A lot of Kosh presentations I've seen make a more complex diagram of that step where you replace the middle segment, but you just show the next iteration. It almost becomes a little visual puzzle - "deviously simple" indeed! As in "Can you see what we did here?!" And then multiple snowflakes in colors, etc.

Your presentation inspired me to look for Prezi again as a platform for one of my projects, about guided visualization. So you can have some (more complex) words describing the next step in visualization, then the pause for users to picture it in the mind's eye... and then the picture itself!

• Should our Prezi presentation be about a math topic, or can it be about anything (provided we do provide a written answer to Part 1)?

• Your choice,  Sue! It's often nice to connect the topic to the way you arrange the presentation, as in that "math is not linear" example: "the media is the message" type of thing. The Prezi site has some good examples under the Explore tab, sorted by categories: http://prezi.com/explore/