Fab@School, one of our 2010 DML Competition Winners, recently shared this post from "Paula White, a gifted resource teacher at Crozet Elementary School in Virginia. It is cross-posted at I Education Apps Review, a wonderful website that focuses on the use of iPad and iPod Touch applications in schools."
I'll write more about Fab@School in a separate post, but for today I wanted to bring them into view by sharing Paula's writings about her students and the digital fabricator she uses in her classroom. Paula's approach to describing the learning potential of games is brilliant, period. What I really appreciate, too, is that she has exactly the right amount of impatience for the Digital Media and Learning movement to build more apps. If anyone out there is at all interested in designing or developing new ways of learning, here is your muse.
Its not about thinking outside of the box -- its about thinking ABOUT the box -- what it looks like in two dimensions or three, how it behaves, what its dimensions are and how you can pack it.
For the past year I have had a digital fabricator in my classroom and have watched my students think -- or not think -- and create, or attempt to create, in 3 dimensions. What got me really interested in the realm of spatial thinking was a situation where I asked my students to recreate a shape net of a shed on the computer to scale.
The idea was to then print them out and compare them to the original. (See a description of this lesson here.) I watched two girls literally attempt to recreate the net on the computer, not using the 3-d capabilities of the software we were using.
So I began looking for spatial visualization and spatial reasoning apps to put on our school iPods that would help kids see the world differently, beyond the literal translation of Recreate this sheds net. I also wanted to be able to tie in specific mathematical standards (if parents asked why their kids were playing), so these were the NCTM ones I targeted in the apps discussed below.
- Apply transformations and use symmetry to analyze mathematical situations
- Predict and describe the results of sliding, flipping and turning two dimensional objects
- Identify and describe line and rotational symmetry in 2 and 3 dimensional shapes and designs
- Use visualization, spatial reasoning, and geometric modeling to solve problems
- Create and describe mental images of objects, patterns and paths
- Use geometric models to solve problems in other areas of mathematics, such as number and measurement
- Recognize geometric ideas and relationships and apply them to other disciplines and to problems that arise in the classroom or in everyday life.
Games are abundant, of course, but I was really hoping to find real life applications of geometric thinkingkind of like Bungee Stickmen, which includes mathematical calculations as you have to determine how far the bungie cord will carry the guy jumping off the bridge and make sure he doesnt crash. I found several other balance gamesTightwire and Jenga, but real life applications of any of these standards were hard to find. I suggest several at the conclusion. As you read along here, be imagining ones youd want and add them in the comments.
Of course, in thinking of 3-D manipulation and movement, I thought of Tetris and Blokus, but looked for additional ideas in areas besides just games. I found Sketch Me! which shows half a picture and has the player draw the other half. Jigsaw Lite is a National Geographic game that has kids jigsaw back information about animals and their habitats. Art Lite asks the user to put back together famous works of art. I looked for things like varying ways to do activities kids had experiences withlike using a number line and found the app, Number Line. It shows kids fractions, decimals and percents (not all at the same time), and kids have to put them in order on a number linethat they can never see wholly at the same time either. They have to envision the number line in space almostand be able to leave spaces for quantities they havent even seen yet. Once kids get the hang of it, they like the challengebut understanding of fractions, decimals and percents is a necessity to play.
In thinking of paths, predictions and everyday life, I do like the River Cross app where kids have to figure out how to get some animals, humans and food across the river in pairs where one doesnt eat another. However, there arent enough versions, so I have my kids make up additional quandaries like that. Kids can also fool with Labrynth and Labrynth 3-D to explore space and paths, but I wish there were more sophisticated games or apps that included a fun way to explore the coordinate plane. Ive begun seeing Blokus as almost a path game, since the better you make your connections branch, the more likely you are to increase your options for playing throughout the game.
I include Knots Guide in my path spatialization tools, as the manipulation of tying knots in space is incredibly visual. If you experiment only a short time with knots, you will find yourself involved with a type of spatial reasoning which is not so much geometric as topological. The manipulations that you make as you mess around with a knot are clearly spatial, understanding, describing, and predicting the effects of these manipulations requires a sense of how the knot occupies space, and how the parts of the knot are related to one another in space. (http://www.ccs3.lanl.gov/mega-math/workbk/knot/knnctm.html)
There are plenty of apps that allow for exploration of placing shapes into predetermined spaces. Thats an incredibly difficult skill for some thinkers. I found Pentan Lite, which is a game where you place pentominoes on a board according to a predetermined shape. Tanzen is similar, as are Fragmental and Tetras3D, which are 3-D. One of my favorite apps is MetaSquares, an app where you make different size squares on a pegboard-but the squares can be on different axes, so they are transposed. Some kids have a really hard time with this kind of seeing. This one stretched MY visualization skills!
Games like Bejeweled, Line Up, Clear it and Manic Marble all support kids scanning for similarities and visual patterns and then planning moves to put objects together spatially. They involve translating and transposing objects and some of them allow rotations as well. Flipsy is particularly hard for some kids, as you can flip the board and when more than one color is on the board, you have to think ahead to what will happen with different colors moving and some disappearing as they flip. Unblock me is similar to Flipsy, but doesnt rotate. Theres also Cubic Square, which is similar to Rubics Cube.
Unfolding Space, Illusions and Patterns LE allow students to explore moving shapes that turn, twist and transpose as you watch. I found three art apps as well that do similar movesArt Tree, Atomic Toy and Fast Fractal. These support students imagining how things move in space and how they can change. And while these allow users to look for similarities and differences, and explore all kinds of movement, shapes and symmetry, I simply could find no app that supported the NCTM standard:
- Describe a motion or series of motions that will show that 2 shapes are congruent
The creation piece of the NCTM standards
- build and draw geometric objects
- create and describe mental images of objects, patterns and paths
- identify and build a 3-D object from 2-D representation of that object
- identify and draw a 2-D representation of a 3-D object
were also slim pickings in the apps, as far as I could find. Of course you can use the drawing apps to have kids draw shapes, but I would love for someone to build an app where kids could create shapes with various materialsstraws, toothpicks, etc. I would also love to see a Design a Box app that provided various specifications as to what was going in there. How about a Pack the Trunk activity with suitcases or coolers or tubs?
And how about an app where kids find certain shapes within others and highlight them with different colors, similar to the coloring you can do in the Unfolding Space app? And, is there an app that lets students play with the four color map problem? I would also love to see some apps that had critical thinking and visualization in it like these graphing games: http://www.ccs3.lanl.gov/mega-math/workbk/graph/grgsm.html
What kinds of apps would you like to see to help students think in 3-D? And do you have ones to add to those listed here?
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