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Space Filling Shapes Geometry Playground

Formative Evaluation

Toni Dancu and Nina Hido

2007

formative, mathematics, geometry, spatial reasoning, Geometry Playground

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Table of Contents

Background .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3  

Goals .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4  

Methods .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4  

Findings .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4  General Observations ................................ ....................... 5  Affect ................................ ................................ ............... 5  Common answers to “What made it fun for you?” ............. 5  Interactions Between Groups ................................ ............ 5  Exhibit Features ................................ ............................... 6  Materials .................................................................................................... 6  Ease of Tessellation ................................................................................. 6  Graphics and Labels ................................................................................ 6  

Next Steps .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7  Post-evaluation Decisions ................................ ................ 7  (Based on discussions with Paul, Nina and Toni) ................................ 7  

Acknowledgements .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7  

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Shape Filling Shapes

Dancu and Hido

2007

Draft Label

Background

Shape Filling Shapes is an exhibit prototype for the Geometry Playground exhibition. Visitors explore rotating and stacking blocks using the skills of spatial reasoning. The exhibit is exploring the mathematical rule of tessellation.

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Goals

The goal of this evaluation is to:

• Observe how visitors use this initial exhibit prototype. • Start to understand the benefits and challenges with the differently shaped blocks. • Start to learn about how visitors use and respond to the label text and

photographs. • Look for promising next steps for the exhibit.

Methods

Informal conversation with visitors in the prototype area on the museum floor on Sunday, August 8, 2007 12-4:30pm. Notes on the exhibit set-up: Groups were recruited to try out the exhibit. There were 3 different shapes to try, so they were all covered to start, and then uncovered one at a time. Almost all were done in this order: wooden Truncated Octahedrons (TO), expandable foam Stellated Rhombic Dodecahedrons (SRD), foam Rhombic Dodecahedrons (RD). Adjustments that were made throughout the testing time: After the 5th group, the TO’s came unstuck from the board, so we had much less of a starter seat to work with. There were only 2 stuck down after that. This definitely increased the difficulty of fitting these shapes together. Towards the end, I moved both large SRDs together and placed them where visitors had to walk by them to get to the exhibit to see if that would make them more noticeable (it didn’t). Also at one point, I switched the order they did the shapes in because most visitors were finding the RD to be easiest.

Findings

Rhombic Dodecahedrons (RD) Stellated Rhombic Dodecahedrons (SRD) Truncated Octahedrons (TO)

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General Observations • Visitors for the most part were very engaged. All of the groups wanted to try all

three (one visitor was pulled away by family after trying two shapes). • Almost everyone had at least one person in the group (most often the parent) who

was looking closely at the label and using the pictures to guide them towards an end result.

• Most visitors thought they were done when they’d either used all the pieces, or gotten their stack to look like the photo on the label. In fact, for the RD, there were a couple of extra pieces after a pyramid was built, and this was confusing for visitors. Visitors responded with such comments as, “Wait, there’s another one, did we do it right?”

• No visitor made any unprompted comment about the large SRDs we had nearby the smaller blocks. They went relatively untouched the whole time I was watching, let alone visitors talking about them being the same shape as the small ones.

Affect • Most visitors seemed engaged. I had mostly groups that included kids, where kids

were the most active participants. • Many visitors said the one they liked best was the one they found the most

challenging. This was typically the SRDs.

Common answers to “What made it fun for you?” • “It makes you think. It makes your mind work.” • “It was challenging.” • “It was fun to figure out how they fit together.” • “You get to build it and it’s tough.” • “It’s like a 3D puzzle.”

Interactions Between Groups • When the group was a child-parent dyad, the parent would read the sign, and

often say to the child, “No extra space.” Then they would provide some instruction. Examples:

o Right off the bat, mom said, "You want no wasted space." o For the SRD initially, dad said, “You've got to get a base first." o For RD, a dad said, “Look at the sides, see how they go?” The son was

still struggling a little, so the dad said, “How many sides do you see on top?”

• When there were siblings, some worked together, while some got bothered by the other. Examples:

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o The teen sister said to her brother, "No, wait that's not how it goes.” Boy “Yes it is!”

o One figured out the different shapes a little quicker than the other, and was trying to show the other boy how to do it.

Exhibit Features

Materials • 10 visitors said they liked the foam material the best. The most common reasons

were that it stuck together the best, and that it felt good. • 2 parents thought the wood would be most durable. Note: It is possible the shape of the SRD, rather than the expandable foam material, allowed the shapes to more easily stick together.

Ease of Tessellation • Overall, most visitors found the RD’s the easiest to put together. Some found the

SRD’s challenging, which led to greater enjoyment. o “The foam was the best because it was hardest.”

• The TO’s were definitely a lot harder for visitors once there was less of a seat to start from. After they were unstuck, 6 groups said they thought the TO’s were either the hardest one, or just confusing for them to figure out. Without the seat, visitors experienced frustration and a few wanted to move on .

o One teen said, “I wasn’t in the mood to figure it out. The orange one was too frustrating.”

Graphics and Labels • Visitors definitely used the label pictures to figure out how to build with the

structures. It appears that the experience would really change if the pictures weren’t there.

• Visitors seemed to appreciate the labels and graphics. Some mentioned the end result and one visitor mentioned doing your own thing:

o “The sign and pictures helped a lot.” o [What made it fun for you?] “How it is more of a puzzle. You’ve got to

put it together without the picture it would have been a lot harder.” o “This one was good [RD], to get it into a pyramid - it had a clear end

result we were trying for.” o “The foam one was a little hard at first, but the pictures helped, like what

the end result looks like. But it was also fun to do your own thing. [Did you feel like the picture was what we wanted you to do?] Kind of, but I also just did my own thing.”

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Next Steps

Post-evaluation Decisions

(Based on discussions with Paul, Nina and Toni)

• Explore ways of engaging visitors in indefinite explorations (i.e., without a pyramid goal in mind). Some possible adjustments to encourage free-building:

o Changing the graphics to depict stacking in progress rather than a finite pyramid.

o Altering the bases to reduce the pyramid base look/use.

Acknowledgements

This material is based upon work supported by the National Science Foundation under Grant number NSF/DRL 0610436. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.