Zome Workshop

Year: 2007 Authors: Paul Hildebrandt

Core claim

A structured, discovery-based Zome workshop can engage students in mathematics and related subjects through hands-on challenges and guided discussion.

Topics

discovery learning, hands-on workshop design, mathematics education, team challenges

Domains

geometry, polyhedra, fibonacci numbers, educational design, visual manipulation, constructive play

Methods

guided discovery, team-based challenges, facilitated discussion, workshop scheduling

Media

Zome parts, struts and balls, workshop handouts, loaner kits

Paper text

The text below is the locally extracted OCR/Markdown version of the paper. Raw PDF files remain local and are not published here.

Paul Hildebrandt Zometool Inc. 1400C 1st Avenue Longmont, CO 80501 USA Email: paulh@zometool.com

Abstract

How to conduct a Zome workshop for students, teachers or parents. Discusses the discovery learning philosophy, preparing for the workshop, conducting the workshop, follow-up activities and available resources for educators.

1. Introduction

If you want to get kids excited about mathematics, but don’t know where to start, try a Zome workshop. Zome is a powerful manipulative that applies to many of the (US) national standards (1) and integrates with other core subjects such as science and language arts. And it’s fun! Here’s some structure and content developed for K-8 gifted students in the summer of 2006. Based on the “discovery learning” model, it can break the ice in the classroom, facilitate lot of learning, and leave students begging for more!

2. Discovery Learning

Discovery learning “is based on discovery guided by mentoring rather than on the transmission of information,” (2) i.e., the discovery process is as important as the learning that results. In a nutshell, you pose challenges and students try to solve them. With lots of ways to solve a challenge, an unusual approach may lead to unexpected discoveries. Some teachers dread the moment they can’t answer a student’s question. Fortunately, this happens fairly frequently with Zome. It’s liberating to say, “I don’t know. But that’s a great question. Any ideas on how we could find out?” That’s when learning quickens!

3. Preparing for a Zome Workshop

3.1 Familiarize yourself with Zome — work with Zome before conducting a workshop. This is not so you can know all the answers, but rather so you are better able to guide the discovery process. See through your students’ eyes. Unstructured play is a good way to start; then work through some of the challenges or lesson plans listed in Teaching Resources.

3.2 Organize the learning space — organize the workshop space into 3 areas: 1) tables, where students can work in teams, 2) a discussion area for the whole group, and 3) plenty of floor space to accommodate larger projects as the workshop progresses. Allow at least $20{\mathrm{m}}^2$ (215 sq. ft.) per team (4-8 students.)

Tables — use round tables if possible, with enough chairs for teams of 4-8 students, and include about 100 Zome parts per participant (see “5. Loaner Program” in Teaching Resources for cheap access to Zome parts.) Place the tables in a U-shape along 3 walls of the room, with plenty of space between them for bridges, towers, MetaZome structures, etc.

Discussion area — separate the discussion from the tables and arrange seating so that students are encouraged to focus on you and and other participants during discussions. The temptation to continue “playing” with Zome is too great (even for adults) when it is close at hand! It’s best if they can’t see their own models during discussions (except as you invite individuals to share their work with the group.)

Space for larger projects — the advanced challenges are an exciting part of the workshop, in which teams build large and complex models. Structures like the “Tallest Tower,” “Longest Bridge” or “MetaZome” can have dimensions of several meters. Adequate space helps you control the chaos.

Figure 1. set up

3.3 Rhythm and attention span — Find a natural rhythm for the activities: alternate between challenge sessions, in which the students are engaged in hands-on activities, and group discussions, in which all attention must be focused on one speaker at a time. Don’t let basic challenge sessions exceed 15-20 minutes without a discussion break. Initial discussions should be limited to 5-10 minutes. A number of studies (Johnstone & Percival, 1976, and Burns, 1985) suggest that even adults’ attention begins to flag after 15-20 minutes in any one activity. In a lecture or discussion, the first 5 minute period has the greatest impact on learning. Attention will increase with student’s interest, so advanced challenge sessions may tend to be longer.

3.3.1 Two-Hour Workshop Schedule

*times are flexible, but in general, no session should exceed 20 minutes in length

4. Conducting a Zome Workshop

4.1 Initial assessment — on arrival, encourage participants to try out Zome for a few minutes. (If parents bring kids to the workshop, advise them to arrive 15 minutes before the end of the workshop to see their kids’ creations, take photos, etc.) Use this time to assess each participant: some will dive in and start building structures, some may sit back with their arms crossed, some may walk around the room looking at others’ work. Your assessments are important to building a successful workshop for all the participants. Use the information to assign challenges, change the composition of groups, avoid conflicts, etc. 4.2 Initial discussion — After the initial assessment, move to the discussion area to talk about 1) the structure of the workshops, 2) the rules, and 3) what the students learned about Zome during the “hands-on” session. During this third part, assign challenges and finalize the composition of the teams.

4.2.1 Workshop structure — briefly explain the structure of the workshop to the group. During hands-on activities, it’s o.k. to experiment, create and build, to talk in a classroom voice with team members, and even walk around the room and see what other teams are doing. During group discussions, one person speaks at a time and all attention is focused on the speaker. Again, keep the discussion area completely separate from the work area. Seeing models is a distraction; being within arm’s reach is too great a temptation.

4.2.2 Workshop rules — frame the workshop as an educational event and not a free-for-all by discussing the rules. Demonstrate rules such as (a) how to disassemble models — by actually taking a model apart (“why not just jump on a big model when we’re ready to take it apart?”), and (b) the tip, “if it works, it works perfectly” — show students how to “sight” one ball through the hole of another to discover which strut fits between the two. This demo can lead into the meat of the initial discussion, in which students share their first impressions of the tool.

Figure 2: Building the “longest bridge” at a Zome worship for gifted children, Denver, July 2006

4.2.3 Discussion — “So what can you tell me about Zome?” “The balls have different shaped holes… Some struts are twisted; some are straight… Only certain struts fit in certain holes… There are different colors and different lengths of struts… Blue struts are ‘squares’… Yellow struts are triangles… Red struts are ‘hexagons’… The struts come in short, medium and long lengths… if you put a short and medium together, it makes a long… Reds and blues are the ‘same’ length, but yellows are shorter…” Let participants struggle with ideas. Use questions like “what do you think?” or ask the group, “do you agree? who has a different idea?” to keep ideas flowing. It also saves you from having to know it all!

4.2.4 Assign challenges based on your initial assessments and the initial discussion. I tend to make the assignments during the discussion based on participants’ initial observations. For example, if an entire team builds “pincushions” during the free play period, they’re great candidates for the basic challenge, “How many holes in the ball?.” Or a table may have several guys who only seem interested in building cubes with the long blue struts. You found the “Lego heads.” They’ll be good candidates for the Super Structures strand (i.e., build the longest bridge and/or the tallest tower.) It’s a fair bet that by the end of the workshop they’ll have a gut feeling for triangulation, among other basic engineering concepts.

The Rules

• Maintain relaxed, focused attention. While building, converse quietly about your work. During discussions, listen to the speaker. You can’t give attention to one person while talking to another.
• Tighten your model as you go. Gaps between the shoulder of the strut and the ball face accumulate and lead to trouble, especially in dense models like the “pincushions” and trusses.
• “If it works, it works perfectly” (…and if it doesn’t work, it doesn’t work at all!) Struts should never be bent, twisted or under tension in finished models (the reason for this will become clear as you work with Zome.) But it’s o.k. to bend struts to fit them into a tight position. To see if a strut will fit between two balls, try looking through one ball to the other ball. The holes will line up!
• Disassemble models carefully! Hold the strut close to the ball and push the ball with your thumb to release it. Do not rip models apart, jump on them, throw them against the wall, or use any other form of destructive testing. The parts will break. If you do break a part, give it to the workshop leader (rather than mixing them in with the good parts!) Think of the next students to use them (3).
• If you use it, put it away. Leave the space cleaner than you found it!

Another approach: you can simply pre-assign basic challenges by team, table etc. Such arranged marriages will also meet success. Any strand you choose will lead the students to real, exciting learning. Once the teams return to their tables but before they begin the hands-on work, explain to each team their challenge in detail, especially if you are using challenge cards (see Teaching Resources.) Often participants don’t read the card and simply build the illustrations.

4.3.3 Address problems and facilitate learning — At this point, begin the hands-on session. The first few minutes can determine the effectiveness of each team for the whole workshop. You may need to encourage, redirect or reconstitute them. In some cases, an individual or group may ignore the challenge altogether and go their own way. Treat these departurers with courtesy; much learning may occur in such a context.

With vigorous protests, participants leave their models to join the discussion setting every 20 minutes to refocus attention. One at a time, have a volunteer bring her model to the discussion area, explain the challenge and what the team discovered. Facilitate a brief discussion and encourage the other participants to applaud the volunteers for their efforts. Assess participants with the goal of assigning a follow-up challenge. Some may wish to complete what they started and others may want to follow an individual path. Many want to work in teams to build larger and more elaborate structures, such as “tallest tower, longest bridge” or a MetaZome structure. Conduct the second hands-on session in the same way as the first. At this point, it’s a fair bet the teams will be galvanized and motivated, and their questions may go beyond your current grasp. Once again, a great opportunity for learning: “I don’t know; how can we find out?”

4.4 Closing the workshop — Use the same discussion format after the final session. Often participants are exuberant about their work and will want to show it off to friends, parents, take photos, etc. Use this enthusiasm to reinforce the learning that has taken place. Draw parents into the excitement when they arrive.

Despite the pain of disassembling their creations, participants must clean up. It’s a good time to remind students of the final rule, “Leave the place cleaner than you found it,” so that the next workshop participants can have as much fun as they did.

5. An Example: the MetaZome Challenge Strand

Here’s an example to illustrate how a basic challenge, “Can you build the shapes of the struts?” (Shape and Number 2) can lead to profound results. To start the initial discussion, you ask, “so what do you know about Zome so far?” Trevor: “The struts are different colors and different shapes.” You repeat: “The struts are different colors and different shapes. What are the different shapes?” Diana: “Triangles, squares and hexagons.” You: “Triangles, squares and hexagons. Does everybody agree with that?” Students: (general agreement, with some dissenters.) You: “Most people agree, but not everybody. Who doesn’t agree? Why not?” Julia: “The blue struts are rectangles, not squares.” You: “The blue struts are rectangles, not squares. Does everybody agree with that? O.k., what else? How many sides does a hexagon have?…”

Figure 3. Some possible strands showing how basic challenges build to more advanced explorations (the chart progresses from bottom to top.)

So you challenge Julia and her team to build the shapes of the three struts. After the discussion you meet with the team, answer questions, and encourage them to walk around and see what other teams are doing if they get stuck. They build the Golden Rectangle quickly but stumble on the equilateral triangle and regular pentagon. The team at the next table is building red, yellow and blue “pincushions,” and discover triangles and pentagons quite effortlessly when they “connect the dots.” Soon Julia’s team triumphantly bids you back to their table. They’re ready for the next step in the challenge: “Great! Now can you use your rectangles, triangles and pentagons to build a ball?”

They dive in. You notice that they are struggling with 5 rectangles around a pentagon, and ask if the pentagons look the same on either side. Diana notices that the blue struts seem to “dish” inward on one side but outward on the other. In 20 minutes they have two whole MetaZome balls. “I wonder… could build a giant blue strut to connect these two balls?”

The rest is history. After their presentation, you challenge them to build a MetaZome Atomium (pictured in Shape and Number 8,) and suggest they join forces with the “Super Struts” team. They can use the help, and this team recently discovered that super long struts can be built up from any two consecutive lengths (short/medium or medium/long) based on Fibonacci numbers. The second hands-on session passes quickly. Parents are invited to the final presentation and are already snapping pictures of the proud members of the MetaZome construction crew and their creation.

6. Conclusion

This workshop is a great way to get started teaching with Zome. As you become more familiar with the tool, it’s likely you will increasingly find applications for Zome in the classroom. You can also schedule follow-up workshops at regular intervals to reinforce and “hardwire” the new learning.

7. Teaching Resources

Except for Zome Geometry text, all listed resources are available (electronically) for free at http://zometool.com/educators.html.

1. Zome Learning Adventures (K-8) — Middle school students engage in 3 standards-based challenges in a 30-minute video.
2. Zome Challenge Cards (K-12)— 24 illustrated “discovery learning” challenges written for use in Zome workshops
3. Zome Lesson Plans 1.0 (K-12) — Standards-based lesson plans written by teachers for teachers
4. Zome Geometry (11, 12 & beginning college) — supp. textbook by Hart and Picciotto, published by Key Curriculum Press
5. Zome Loaner Program (all levels) — teachers may borrow mass quantities of Zome parts for 2 months at a time, essentially for the cost of shipping. See http://zometool.com/educators.html.

Notes and References

1. National Council of Teachers of Mathematics (NCTM) standards as addressed by Zome are summarized in an appendix to Zome Lesson Plans 1.0, pp. 201-208, 1998
2. The Boyer Commission on Educating Undergraduates in the Research University, REINVENTING UNDERGRADUATE EDUCATION: A Blueprint for America’s Research Universities, 1998
3. Broken parts may be returned for free replacement to Zometool Inc., 7475 W. 5th Avenue, Suite 204, Lakewood CO 80226. As of Spring 2007 we are implementing design and material improvements to make all Zome components virtually unbreakable.