## the mathematical affordances of materials: geoboards two ways

Posted on: June 9th, 2015 by jnovakowski

Being part of a professional inquiry project causes you to be curious, to wonder, to take the stance of teacher-researcher. For two years now, teachers in the Reggio-inspired mathematics inquiry project in our district have been thinking about, observing and investigating different aspects of Reggio-inspired practices. Two of those practices focus on the use of loose parts and other inspiring materials and the role of collaboration and co-construction of knowledge and experiences.

Always on the look out for materials that might inspire mathematical thinking, I was inspired by two images I found on Pinterest. Now, I know Pinterest can be a bit of a black hole and there is lots of not so good stuff posted on Pinterest but I look to Pinterest as an inspiration board and trust myself to weed out the not so good stuff. I had seen variations on geoboards and decided to create some materials to pilot in classrooms.

The first was a giant pegboard geobard. I bought a 4 foot by 2 boot pegboard panel at Rona for \$6. I also purchased nuts and bolts to fit in the pegboard holes and bolts long enough to use with elastics. My helpful fifteen year old son screwed in the nuts and bolts on these two large pegboards for me but students could have easily done this as well.

The first board went to Michelle Hikida’s grades 2&3 class at Diefenbaker and it was only half geoboarded. The other half was empty and I gave Michelle a baggie of extra nuts and bolts. She had ideas of looking at line symmetry and congruency in shapes with this format. When I asked her a couple of days after I had dropped it off, she mentioned that the students had been using it to create marble runs. Great idea, but not the mathematical application I had anticipated.

The second full geoboard went to Louesa Byrne’s Kindergarten class at Thompson. As Louesa and I placed it down on a piece of felt on one of the tables, the students couldn’t help but come over and touch it and wonder what it was for. Fyi, the rubber band ball was found at Staples. I purposefully included some glass gems alongside the rubber bands, thinking that the students might use these to measure the area of their shapes or to mark the corners of vertices.

As the students began to investigate the large geoboard, I hung back and observed. The students began to get the feel for the rubber bands and how far they could extend them. I noticed the students made many squares and then added diagonal lines crossing them from corner to corner. Some students used the gems to create patterns along the rubber bands and others enjoyed “bouncing” them on the rubber bands.

Every once and I while I would ask a student what they were creating and a few said “designs” or “nothing, really”…they were exploring the materials. One group of children collaborated together on one side of the board and created their own story world with connected buildings and characters. When I tried to ask them about shapes, they looked at me with a little annoyance. I was imposing my hopes for these materials on the students. Some played along with me and named the shapes they had made or told me how two shapes they made were the same or different but for the most part, the students needed to play and figure out what these new materials could offer them.

After much time creating different lines and shapes with the rubber bands, one student commented that what he had created made him think of the hands on a clock. He went over to where there were baskets of math materials in the classroom and brought back some numeral tiles to add to his “clock”.

I have to admit that I was a bit disappointed overall and then I had to check those feelings and think about why I was feeling that way. Although we know that students need to explore materials for themselves before “applying” mathematics to them, sometimes we think we can move through that process a little faster and we get caught. Caught in a tension between our own expectations or hopes for the materials and where the students are in figuring out the materials for themselves. The more I read about embodied mathematics the more I realize how important the touching, visualizing, moving, experiencing of creating is to the learning of mathematics.

Over time, Louesa said the students continued to create stories on the board and she noticed some patterning. Via email we went back and forth on some questions we could ask the students to consider using the giant geoboard. Now that they had explored the materials a few times, we thought we would try and forge some math-to-math connections and Louesa posed the question: How do shapes help you think about numbers?

During this visit to the class, and to this table, I noticed students more engaged with the geometrical thinking the board and materials inspired. There was more shape making and comparing happening, although there were still some students creating characters on the board, adding gems for eyes.

So although I see many mathematical possibilities for this giant geoboard – shape making, symmetry, patterning, angles, area, perimeter, graphing, measurement, counting, etc., the students may not see those affordances yet. The board will live with them and be a part of their classroom and with time, I am guessing it will be used for all sorts of mathematics, uncovered by the students.

The other project which I also enlisted some family help for was creating tree cookie geoboards. This time of year, I often see bundles of tree branch trimmings along the curbside in our neighbourhoods and I am also quick to hop out of my car, pick some up and throw them in the back of my car. After drying them out, either in our garage, shed or a low temp oven, they are ready to slice up. I have made lots of tree blocks this way and thought it would be interesting to create geoboards with them. I used grid paper to help line up the nails and also created some circular boards. I borrowed some leftover Rainbow Loom bands from some friends to test them out.

In Louesa’s class we presented the boards with a bowlful of colourful elastics and the students were taken with them. Students began by stretching the elastics and creating random, irregular shapes. They then added layers and layers of elastics on top of each other, sometimes random but sometimes repeating the same shape.

Two students began connecting their geoboards together, discussing the different shapes they were creating and the pathways they could use to link the boards together.

A thoughtful teacher visiting from West Vancouver, Misty Paterson, asked me what I thought these little tree cookie geoboards offered that regular plastic geoboards didn’t – what were their particular affordances. After a bit of a pause to think about this, I suggested that both the size and the materials used connected the students to these geoboards in a way that the traditional plastic school geoboard doesn’t. I noticed that the students often picked up the little geoboards and fit them in the palm of their hands. The smaller distances between nails/pegs and the smaller elastic bands are just right for younger hands and allow for the students to examine their shapes by easily holding them up to eye level. And there is just something about the “mini” size of these that the students find appealing. Plastic geoboards are useful and uniform but I also think the recognizable, familiar material of the wood drew students to these geoboards. I could see the students appreciating the texture and smell of the geoboards as well as the uniqueness of each board. I think the idea that they could make something out of a natural material that they might find in their backyards or nearby woods is also inspiring.

We have added a set of six of these tree cookie geoboards to the Reggio-inspired mathematics geometry kit which will be available for three-week loans from the DRC.

~Janice