A Comparison

Today I visited Jamie's class at Highlands Elementary to see another math-focused design project with the same age group as I worked with. The class was slightly smaller (20 students versus my 25) and also had fewer teachers (just Jaime and Jen, an aide, plus Amanda). Jamie had mentioned in his initial presentation to our class that he was interested in Andy Goldsworthy's work, and this artist has been the model for the projects.


Today, students went outside and built structures with stones from the dry riverbed behind the school, and then were to write a fraction pertaining to the stones they had used. (For instance, '2/9 of the stones are red.'" The class was definitely more exploratory than my classes at Marcy. I felt I needed to plan every minute of each session, and if students finished what they were doing before we had moved to the next thing, it felt like things got out of control, and the teacher needed to ring a bell to bring the kids back together again. At Highlands, the students were given very minimal instructions and were able to stay busy the whole time. Every one of them didn't necessarily stay on that task all the time, but for the most part they did, and those that got off track didn't need to be corralled, but came back on their own. Jamie never had to raise his voice or scold students to get them to listen or behave. At the same time, having class outside and having class in a small classroom are pretty different scenarios, and that alone might account for some of the differences I saw. The way the classroom is organized and run is such a foundational aspect of school, yet there are so many factors that influence it that it's hard to say how things 'should' be done, or how best to achieve an atmosphere best suited for learning. Behavior and discipline seems to be a chicken-and-egg problem-- which comes first, children who misbehave and require disciplining, or disciplining that's not appropriately suited, and causes more misbehavior? How do you foster a classroom environment where children listen and do not distract others, but yet can explore and learn on their own? Certainly different groups of children will need different levels of control in the classroom, from a strict set of strongly enforced rules to a lenient policy that lets children do whatever they want at that moment. The former seems to be the old-fashioned practice of generations ago, and the latter that of the Montessori system. Both Marcy and Highlands are somewhere in between the extremes.

Day 4, Pat's class

The final day of working with Pat's class of first and second graders included two projects. The 'wrap-up' project was actually first, since I thought it was the more important of the two and wanted to make sure we would have time to do it. The second project was another take on patterns that they could continue after I left.

We started with a short presentation / discussion about where in the world we see patterns. The students were always eager to comment on each image. I was also very impressed by how they would use a new word I had introduced right away. For instance, I had described an image as having a radial pattern, and then the next three students I called on told me about other places where they saw radial patterns, in such a way that they understood the term.


After talking about some examples of patterns, we headed outside for the students to get a chance to find patterns for themselves in the front yard of the school. The students really got into this, shouting, "I found a pattern here!" right and left. It was great to see them make the connection between the classroom activities and the world around them.


We came back inside and the students were asked to draw the pattern they had found. After giving them some time to complete this task, the students laid their drawings in the middle of the classroom for everyone to see, and took turns describing what they saw to the rest of the class.

patterns circle

Moving to the next project, I introduced the students to the concept of fractals by showing several images and asking them what they noticed. When a student described an image as "looking like there are smaller trees on the branches of the bigger tree" I was able to expound upon this to show them the definition of a fractal. In particular, the students recognized the images of fractals that are also on their math textbooks!

From here, the students learned to construct a Sierpinski Triangle by following the rules of how one is formed. There were several times that students would ask "What now?", unsure of their understanding, but when given a prompt / hint / encouragement, they generally did know what to do.

s tri 2

S tri 1

All in all, I think it was a successful program. Things certainly didn't always turn out as I intended, but Pat was really pleased with what they children learned and produced!

Final Day: Destruction

On the last day with the 5th and 6th graders we had them test out their designs. The problem we gave them was to have them build something that could withstand a lot of weight using only 100 popsicle sticks and glue. I was apprehensive about whether the kids would enjoy the project or even finish in just two days, but many of them did. In fact, when we went to class early, there were kids working on their designs rather than having recess.

Most of the designs were very basic, just flat bridges that were heavily glued and had multiple layers of sticks. These turned out to be very strong. We came to class with about 60 lbs of weights to test them and three were still standing after holding all of the weight. A lot of the kids that had put effort into the designs had bridges that failed around 15 to 20 lbs which was a little unfortunate, but I think they only used about half of the sticks we gave them.

When it came to the actual destruction, a lot of the kids seemed excited. They all gathered around, made predictions about how much weight their bridges would hold, where they would fail, etc. The bridge that I made held all 60 lbs of weight and then a kid asked if he could sit on it, too. I let him (he probably weighed 60 lbs) and the thing went down.

One of the funniest parts to me was when a kid proudly walked up to me, stated that he in fact didn't design, he just put sticks together and that his bridge was still the strongest. When I turned his platform bridge over, there were diagonal cross-bracing members. I informed him that those diagonal members helped to secure the entire structure, that without those his bridge would have been much weaker. He laughed and finally admitted that maybe he did learn something after all.

In the end, working with the kids was a lot more fun than I thought it would be. They are at a point where they don't want someone telling them what to do, they want to figure it out themselves. In this regard, I think the way Erin and I set up the class was very successful. The kids all got engaged in at least one part of the class and it seemed like they all had a moment of success along the way. I hope that the kids will take what they have learned to their future structures and physics courses and whoop the competition (I am pretty sure they all have to do similar exercises in future courses).

Day Three, Pat's Class

For the third day, we went back and revisited tessellations from a week ago. I began with a presentation focusing on three of Escher's works that we had discussed on the first day presentation.

The first design is a tessellation created from a square using translation--like last Tuesday's project. The next design uses a triangle with rotation. The last image makes use of not one but two different shapes, one of which is created out of the negative space left by the other.

square birds Escher.png
triangle birds escher.jpg

The project that the students completed was to create a tessellation like the second Escher work--that is, using a triangle and rotational transformation. I used Escher's design as the template for the example:

demo rotational tessellation

Like before, I showed the students the process to follow (cut from one side, move to the other--this time, since the shape is a triangle, moving the piece means rotating it, not just sliding it over; cut from half of the bottom of the triangle and flip over to the other half). However, this shape turned out to be much more challenging than the first project, and the students needed a lot of help from the teachers in the classroom.

rot. tessellation piece

Once the students completed the shapes, they did as good a job of tessellating them as in the first project, recognizing the need to rotate the shapes to make them fit, rather than laying them in a row.

rot. tessellation birds

Because of the difficulty of the project, we ended up not having time for the second tessellation and wrap-up discussion. The second project was going to be to start with a shape of the student's choice (cut out of an index card), traced side-by-side in rows into the paper. Then in the negative space created by the first shapes, the student would draw in another image--like the third Escher work. The wrap-up presentation and discussion about patterns we find in the world would have to wait till Thursday.

Marcy Design/Play: Session IV Observations, etc.

During our final day with the first graders in Teferi Fufa's class, I observed:

Children drawing slight variations on their costume ideas
Children talking amongst themselves, sometimes off topic
Children only drawing one or two ideas
Children quickly drawing their ideas
Children mimicking what they had seen either on the board, in the book, or from their neighbors

Before this class sessions, Jillian and I were discussing the merits and drawbacks of giving examples on the board, because we started to notice a pattern of mimicking in the kids.
Jillian brought up the good point that it might not be a bad idea to expose them to as many examples as possible, mimicking or no, because they are essentially absorbing these examples (even more so by doing them themselves). At a later time, they can hopefully draw on these examples, add to them selectively and creatively, and determine which might be an appropriate fit for a given situation or problem.

As for the various skills the students are using, they are developing fine motor skills, cognitive and critical thinking (some of them a bit of meta-cognition), deductive and selective reasoning, and different modes of communication (verbal, visual, etc.)

I think it was a bit early for a few of them to be thinking about the iterative process, and to truly be comfortable with the idea that the first idea they throw out on the page might not really be the best one, and that new fresh ideas can actually improve with different versions. I think this is a new way of thinking, and we at least planted the seed with our exercise. I also think that a few of the students are starting to grasp the concept that one thing can represent another, but by in large this is still an area of thinking that they are still developing and most may not be comfortable with the concept.

Iterative Process

I forgot to mention that on our last day with the first graders, we also introduced the concept of iterative process. Naturally the kids kind of had a frightened deer in the headlights look when I asked them if they knew what iterative process meant, which is what I expected.

I then explained that this was just a fancy big word way of saying "doing something again and again". I explained that sometimes it is important to try something one way, then try it another way and even another way in order to get all your ideas out, because sometimes your first idea isn't always the best one.

This concept tied in nicely with our exercise of having them design three different costumes for the same character. Quite a few of them chose the second or third iterations as their favorites, and when I worked with these kids, I tried to emphasize the fact that trying something new, something that wasn't their original idea, worked out really well in the end.

Final day with First graders

Thursday marked the last day that Jillian and I would be taking part in our hour long sessions with the children in Mr. Fufa's first grade class. We had decided (along with their teacher) to take a shot at designing costumes, with the understanding that the children would further develop and possibly create those designs with their art teacher before the play.

Upon arrival, we reviewed with the kids one last time on what it meant to "plan, do review". By this time they were quite familiar with the phrase, even without prompting on the board with text.

We then went over (with class input) the different ways we had done these three steps:

PLAN: Talking about what we would do for the day, brainstorming, and learning about different design techniques.
DO: Drawing, diagramming, modeling, writing.
REVIEW: Talking with our peers, talking in large group, talking one on one, and presenting individually in front of the class.

Some of the kids seemed to get a bit confused between the PLAN and DO phases, most likely because they were thinking the DOing would be the actual play, which means that in their minds, the PLANning was the stuff we were DOing: the drawing, diagramming, modeling, and writing, which is also a fine way of looking at the process.

After our brief discussion, we told the kids that we would be helping them design their costumes. This was made a bit difficult due to the fact that the kids do not yet know what characters they are going to be playing yet. Despite that setback, we asked the kids to choose the character they like the most, and then began by giving them a few examples of different ways that they might go about designing different costumes. We did this by giving three examples of an oboe costume on the board.

Then the kids were given the directive of designing three different costumes, and pencil and paper. Again we walked around with the help of the teacher and aides, and talked one on one with the children and developed those designs that were ready for further development (materials, fasteners, backs of costumes, clothes underneath, etc.)

At the end of the class, we asked the kids that were ready to to cut out their favorite design (a few of them were ready to evaluate which of the three designs were most appropriate, given a variety of parameters) and then place these models inside the stage sets they designed on Tuesday.

We then gathered in large group and had about 5 children stand up and discuss what they had drawn. They were by in large able to answer the questions we gave them as they pertained to design, which was really nice to see.

To wrap up our sessions with the first graders, we again reviewed the different ways we had designed. We then asked them to brainstorm quickly different ways they might be able to use these techniques in the future and they were able to come up with different instances in which it might be appropriate, and given a specific design problem (planting a garden) they were able to identify certain techniques which might be more or less helpful.

outside of the classroom

One of the final things that we asked the students on our last day was: where else could you use the process of plan, do, review that we taught you?

At first the students were not quick to answer, but then we gave them some suggestions. How about if you were going to do a garden. How would you plan that?

One girl said she would make some drawings and sketches. They giggled when we suggested that they could model it too, but agreed that it was possible. Another student said that you could do drawings to plan where the flowers would go.

We reminded the students that they can use the design process for many things: building forts, baking, painting a picture, rearranging their bedrooms . . . the sky is the limit.


the final act (again & again)


Leah and my last day in Mr. Fufa's class was very productive. After our excitement and success on Tuesday it was difficult to come up with a follow up lesson for Thursday. Mr. Fufa suggested that we do something that brought the student's attention back to their art class, and the fact that their art teacher would continue to guide their development of the play in our absence.

We decided to have the students plan and draw their costumes. Also, at the same time, we wanted to introduce them to the idea of iteration.

At the beginning of class we opened a discussion to review all the ways we had implemented the design process over the past two weeks. We asked the students: how did we plan things? The students answered that we had talked about ideas, brainstormed and made lists.

Next we asked: how did we do things? The students answered that we had drawn, diagrammed and modeled things.

Finally was asked, how did we review things. One student raised his hand and said: "well, we finished our work and gathered in the center of the room and sat down and then we talked about it."

Yup, that's pretty much it.



The students fell into work pretty quickly. Our guidelines for the lesson were: draw three different iterations of one character's costume. Many of the students copied Leah's drawn examples, but at least they did it with their perspective character. The students became more focused and excited when questioned about their designs. "What is your costume made out of? How would you connect it to your body? What would you wear underneath it? What color is it?" The students started to draw with more detail with further encouragement. They started to put labels on their drawings of the different materials and connections.


Encouragement and interest on a teacher or adult's part can go a long way toward getting a student to develop their work. A word of praise or inquiry can challenge them to do more. And, like I've observed before, thinking on your toes is a must for a teacher. On Thursday, many students drew their characters fairly quickly and started to get bored or off task, so Leah and I decided to have them paste their characters on their stage where they would be standing during the play...they had to have a reason for the placement and we encourage them to explain why.


a more refined understanding of language, words and labels
a more refined understanding of people's roles in the world (esp. designers)
some math concepts (logic, sequence, pattern)
narrative and immediate feedback to their work
exposure to the iterative process . . . practice makes perfect
learning to question their peers
observing and learning from their work
asking questions of their work
listening quietly when someone else is sharing their ideas

Analyzing and synthesizing part and whole (we asked them to place their developed characters on the stage.)
receptive language (they were able to process what we had explained to them and produce work.)

Something that we didn't implement, but I wish we had were the questions that Mary Jo taught us our first week of class.

Without judging, what did you notice?
What does it remind you of?
What emotions do you feel?
What does it make you wonder?
Now, what is the big message?

The thing is we just ran out of time . . . but this would have been a good way to synthesize prior teachings with what we were trying to teach them at the time.

Day Four, Anne's Class ~ 4.22.10

As I came in to class today, one of the kids eagerly showed me the dodecahedron that she didn't manage to finish building on Tuesday but "perfected" on her own time.

I congratulated her on doing a good job, but more than that, I was gratified by how some kids were interested enough with things that I showed them that they were willing to pursue the subject on their own free time, even though it was an ungraded class for them.

Day Four - 09.jpg

Today, the kids wanted to make something with their hands. So, for the first half of this class, we cut patterns and tessellations out of paper.

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Starting with a quick example that I made out of paper, I showed them how to fold paper and multiply shapes by cutting holes in the folded paper. The key here was to illustrate how what they cut often turns out to be an unexpected shape once they unfold the paper, depending on how they folded it.

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Because the colored paper was letter-sized and square folds were easy to make, most kids folded it that way. But some realized that it didn't make a concentric pattern like the example I showed, and asked me to show the folding procedure again. I asked them to look at what their friends were doing, and urged them not to be afraid to experiment with folds and cuts in order to find out for themselves what happens when they do different things.

For the second half of the class, I showed them various slides of images that could be interpreted in various ways, ranging from geometric shapes (often found in psychology tests) to images from gestalt theory.

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When we were covering the geometric shapes, half the class (the girls) were "hogging" the screen trying to point with their fingers what they saw on the screen. With one image made up of black and white circles (left image below), those near the screen all saw straight lines, while the others (the boys) who were at the back of the class all saw a square.

I asked the girls to back up and take a second look, but they persisted in keeping that image they first saw in their mind, and insisted on it being lines. After a couple minutes, I began to hear some "Oh!"s and "Woo!"s from them.

I had anticipated a similarly lively argument/discussion with the gestalt theory images but what had happened was quite a surprise to me. There was a disagreement, but not between the students. All the kids saw the same thing! It was the student helpers who saw things differently, and one representative from both the kids and student helpers actually went up to the screen to "fight it out". (right image above)

Day Four - 07.jpg

Regardless of how we tried to tell them (comparing lines on the screen to parts on our face), they simply could not see the old lady. But when I went on to the next slide, which was a rendered version of the same image, the kids were greeted with shock and astonishment. "Wait! Go back to that previous slide again?" "Oh!!!" Some still didn't get it, but it took too long so we had to move on. Kids can be very retentive of first impressions, however I observed that (at least at second grade) they don't care a lot about questioning their own perceptions based on what their peers see.... yet.

It was the last day of class, so I wanted to end things off by showing them some "fun" stuff, like street art dealing with optical illusions. It turned out to be a revelatory kind of disappointment however. While the student helpers were blown away by it ("This is crazy!"), the kids actually didn't find anything strange about them. To them, some random guy squatting precariously on a window ledge while getting rescued by cartoon Batman and Robin (middle image below) was perfectly normal. After all, they see it on TV all the time!

Day Four - 10.jpg

Oh well, guess it was fun after all. While I found some of the readings not to be fully applicable to second graders (such as 16 Habits of Mind), because they have not yet reached an age where they develop such sensitivities, I made lots of observations about the kids based on watching their reactions to stimuli and the unknown.

In a way, these past four teaching sessions felt like one big developmental psychology field session for me. I hope that class for the kids were as meaningful to them as it was for me.