2015 June Archive - Mathematics and Science in SD#38 (Richmond)

Archive for June, 2015

summer professional reading and opportunities

Posted on: June 24th, 2015 by jnovakowski 2 Comments

Thought I would share some of the professional books I have on my summer reading list and yes, of course I hope to dive in to some fiction as well!

Learning by Choice: 10 Ways Choice and Differentiation Create an Engaged Learning Experience for Every Student by A. J. Juliani

50 Things You Can Do With Google Classroom by Alice Keeler and Libbi Miller – I follow Alice Keeler on twitter and she always has great tips

Let’s Find Out!: Building Content Knowledge with Young Children by Susan Kempton

Building Proportional Reasoning Across Grades and Math Strands, K-8, by Marian Small – I read anything by fellow Canadian Marian Small, always learn something new

Doing What Scientists Do: Children Learn to Investigate Their World by Ellen Doris

Making Number Talks Matter: Developing Mathematical Practices and Deepening Understanding, Grades 4-10, by Cathy Humphreys and Ruth Parker – Number Talks have taken off in our district and I’m looking forward to reading another perspective on this practice

Intentional Talk: How to Structure and Lead Productive Mathematical Discussions by Elham Kazemi and Allison Hintz – we bought a set of this book for teachers in the district to read over the summer and participate in a slow chat on twitter, using the hashtag #intenttalk

Creative Schools: The Grassroots Revolution That’s Transforming Education by Ken Robinson and Lou Aronica – it’s Sir Ken, enough said

Math is a Verb: Activities and Lessons from Cultures Around the World by Jim Barta, Ron Eglash and Cathy Barkley (NCTM)

Critical Maths for Innovative Societies: The Role of Metacognitive Pedagogies by Zemira Mevarech and Bracha Kramarski (OECD)

Creating Cultures of Thinking: The 8 Forces We Must Master to Truly Transform Our Schools by Ron Ritchart – a group of Richmond educators attended a series with Ron Richart this year and I am looking forward to reading his latest book that continues to focus on thinking.

Another new book that is not in the photograph is Creating Thinking Classrooms, published by the Critical Thinking Consortium here in BC. I have a long history with TC2 and respect the work of Roland Case immensely. I’m looking forward to making connections to our redesigned curriculum with this book.

*****

There are all sorts of professional learning opportunities over the summer. Check in the External Pro-D Opportunities conference on Richnet for more information. I have listed two that may be of interest below:

As part of the Festival of Forestry, there are two Forestry Tours this summer, one on Vancouver Island and one in the Lower Mainland. More info can be found HERE.

There is a K-3 Institute at the University of Victoria from Augsust 17-19. More information can be found HERE.

And for those of you that are thinking ahead to the Provincial PSA Day in October, you can check out the BCTF site HERE for more information.

Specifically, the BCAMT is hosting the Northwest Mathematics in Whistler – for more information and to register, go HERE.

The BCScTA is having their annual Catalyst conference in Richmond – more information and registration can be found HERE.

Have a restful and adventure-filled summer!

~Janice

cedar weaving

Posted on: June 17th, 2015 by jnovakowski

Back in April, the Richmond School District’s Aboriginal Education department hosted Alice Guss of the Squamish Nation for a morning of cedar weaving. Alice is an artist, storyteller and drummer and has been involved in the field of education for over twenty years. She does workshops around the world in drum making and weaving.

More information about Alice can be found HERE.

We invited Alice back to Richmond as part of our National Aboriginal Day celebrations and this week she worked with two of our QTL (Playful Storytelling through First Peoples Principles) classes at Steves and then joined teachers from the project after school.

Kathleen Paiger’s kindergarten class and Ellen Reid’s grades 1 and 2 class at Steves Elementary listened to Alice singing and drumming and learned about how cedar is harvested for the purposes of weaving and making practical items and regalia. Alice shared some of items that are made from different parts of the cedar tree.

The students learned how to weave a cedar bookmark and they were quite interested in the texture and smell of the wood.

The students then enjoyed listening to Alice’s stories and she said them in some dancing to her drumming, with the students taking on different animal roles.

After school, a group of teachers involved in our QTL project along with some other interested educators, came together. Alice shared her family’s history and we learned about the story of The Chief in Squamish and of the two-headed serpent, a story important to the Squamish people. The teachers then learned more about the importance of cedar and how cedar trees that have been culturally modified (stripped for cultural purposes) can not be cut down by logging companies. An article about culturally modified trees can be found HERE.

The teachers learned how to weave a small cedar basket. There was lots to be learned during the process about persistence and learning new things and also about the natural properties of the cedar. The completed projects were cherished by the teachers and were all one of a kind.

It was an honour to have Alice join us in Richmond again and we hope to have her back again next year!

~Janice

BCAMT Reggio-Inspired Mathematics Cross-District Inquiry Project

Posted on: June 16th, 2015 by jnovakowski

With growing interest in Reggio-inspired practices in BC schools, neighbouring school districts expressed an interest in collaborating with Richmond teachers as they explored mathematics through this lens. A grant proposal was submitted and accepted by the BCAMT. The grant supports cross-district inquiry by providing funds for dinner meetings and materials.

Structures we have used to collaborate and make our professional learning visible include a google doc, a Pinterest board, blogging and the use of twitter, using the hashtag #BCAMTreggio.

We hosted two dinner meetings, one in February at Annieville Elementary in Delta and the second in May at Thompson Elementary in Richmond. During the first meeting, Richmond teachers shared examples from their classrooms and reflections on their learning. Teachers were provided with planning time to consider who they would move this project forward in their districts.

During our second meeting, we created some materials and reflected on our project with teachers from Surrey, Delta and West Vancouver sharing examples and reflections.

We have been able to share our professional inquiry at the Richmond Elementary Math Focus Day, at the Surrey Teachers Convention and the Vancouver Primary Piazza.

A group of teachers from Burnaby came together with Angela Meredith (Early Learning and Literacy Consultant for Burnaby), Ron Coleborn (BCAMT President) and I one day after school on Monday to discuss the project and how it would connect to their ongoing inquiry into Reggio-inspired practices. The Burnaby team is interested in looking at mathematical thinking in the Reggio-inspired classroom and how different teachers may take that up and have different entry points into the project.

We have been able to do some cross-district visits as well. I have visited classrooms in Delta and West Vancouver and teachers from Richmond have visited in Delta and Surrey teachers have visited in Richmond classrooms. It is always rich and inspiring professional learning to be in another classroom environment and think about what you see and what that makes you think about in terms of your own practice.

Two articles about this project have been submitted to the BCAMT journal Vector as another way to share our professional learning with others.

Big themes that we are continuing to look at are:

1) the affordances of materials, particularly loose parts, to support and represent mathematical thinking

2) the design of provocations to inspire mathematical thinking, inquiry and to uncover curriculum

3) the tension between an emergent, inquiry-based approach and having a required curriculum

4) opportunities for cross-discipline, co-constructed inquiry

5) the conditions needed for the teaching and learning through these practices

6) the pedagogical content knowledge needed by teachers to teach in this manner

7) assessment tools to support teaching and learning and that support students in showing what they know, can do and understand

With a second grant from the BCAMT, we are looking forward to a second year of collaborating with teachers from a growing number of districts.

~Janice

playful inquiry dinner series

Posted on: June 14th, 2015 by jnovakowski 1 Comment

This spring we held a two-part dinner series, sharing our stories and experiences inspired by our visit to the Opal School in Portland in January. Braunwyn Thompson, Michelle Hikida, Hieu Pham-Fraser and I facilitated the series which involved us sharing what we noticed at Opal and what we took from our visit and investigated in our context.

The series was called Creating Spaces for Playful Inquiry in the Classroom: Teachers’ stories inspired by Portland’s Opal School and the sessions were held in the Diefenbaker library on April 18 and May 7. Over 50 educators attended the series including K-7 classroom teachers, teacher-librarians, learning resource teachers and administrators.

For the first session we prepared documentation panels of our experience at Opal focusing on learning environments, questions and mathematics. We prepared provocations for the educators to engage with as they came into the space. After each of us shared our stories about playful inquiry, we enjoyed dinner provided by The Healthy Chef and then we broke out into facilitated inquiry groups. Each group was mentored by a Richmond colleague who has visited Opal School. Areas that educators were interested in exploring were – morning meetings, intermediate provocations, including all learners (non-enrolling teachers), provocations in K and early primary, learning environments, inquiry questions with curriculum in mind and outdoor learning spaces.

The educators left the first session with the goal of trying one thing with their students and bringing something back to share for the next session. We provided a small kit of loose parts and some acrylic frames to place questions in.

For the second session, after a short introduction, we broke out into our mentor groups to share what we had tried. All of the groups reported back to to the whole group and all were very inspired the richness of the inquiry experiences and provocations that had been provided. We are still trying to figure out how to compile and collate our ideas so that we can be inspired by each other!

Our provocations for this session focused on cross-curricular big ideas and provocations that Michelle, Braunwyn and I had provided to students.

For both sessions, a range of resources were shared, many from the Opal School. Opal School publications can be ordered HERE.

We wil be continuing this series during the 2015-2016 school year and are excited to announce that Susan Harris MacKay will be a presenter at the launch of the dinner series on September 24, 2015. Registration will be available through Richnet in early September.

An article by Susan Harris MacKay on the principles of playful inquiry (click to link to pdf)

MacKay principlesofplayfulinquiry

~Janice

loose parts and mathematics

Posted on: June 14th, 2015 by jnovakowski 1 Comment

Back in January, Michelle Hikida and I introduced the Reggio-inspired patterning kit to her grades 2 & 3 class at Diefenbaker and we considered the affordances of different materials to support mathematical thinking and inspire inquiry. A blog post about this experience can be found HERE.

Later in the term, Michelle approached the concept of fractions in the same way, laying out a variety of materials and asking students to show what they knew about fractions. What happened surprised her and caused some reflection. Instead of representing their understanding of fractions with the loose parts and math materials, they represented the symbolic notation of fractions. With discussion, Michelle realized this is what they knew about fractions, that they didn’t understand the concept but were familiar with the symbolic notation.

For example, students initially represented fractions this way:

This made Michelle think back to the experience when she introduced patterning. Students in grade 2 and 3 have previous school experiences with patterning and have a place to start when demonstrating their understanding. For fractions, although students may have had informal experiences at home, the concept of fractions is not formally introduced until grade 3 in our curriculum. Michelle spent some time working with loose parts and math materials to use an inquiry approach to develop understanding of fractions. By asking questions like “What is a half?” and “How could you show what 3/4 means?” the students were able to develop and represent a conceptual understanding of fractions using loose parts and math materials.

I visited the class a few weeks later and students had already made big jumps in their conceptual understanding and were able to represent fractions both concretely and pictorially, connecting to the symbolic notation.

Another example of representing mathematical thinking with loose parts is from the grade 3 class at Quilchena. Although we had also looked at creating representations of what multiplication and division meant, for this class students were given loose parts to represent specific multiplication equations. The following example shows that the student understands that 5×2=10 by showing five groups of 2. If the student had used the loose parts to represent the equation by making a 5 and then a 2 and adding “symbols” made of other materials, it would not show evidence of conceptual understanding, just a representation of the equation.

I think this is where as educators, we need to be keen “noticers” when students are using materials and consider the following questions:

How are student using the materials?

What are the materials offering the students (or not)?

Do some materials have more affordances than others for specific concepts?

Are the materials supporting students’ thinking and understanding?

Are our questions or provocations supporting thinking and understanding?

What do students need in order to use loose parts successfully? What do we need to do as educators?

For me, this is a matter of responsiveness and awareness. To be responsive to what we notice in our students, we need to take time to observe, notice, and be curious about their learning but we also need to be aware and knowledgable about the mathematics that the students are investigating so that we can respond and provoke their thinking.

~Janice

inclusive learning communities: grade 8 math at Boyd

Posted on: June 14th, 2015 by jnovakowski

Our district is providing release time for teachers to investigate how to better create inclusive learning communities in their classrooms and schools. Schools needed to submit proposals and the projects are being facilitated by members of our district support team. Shelley Moore is working with the grade 8 math teachers at Boyd to consider ways to differentiate instruction in their classes. Because math was the content area, I was asked to be involved. This is the first of the ILC projects with the rest of them beginning in schools in the fall.

We met to look at the curriculum outcomes that we might look at together. We discussed the value of performance-based assessment and beginning with performance tasks to see what the students already know about the concepts involved. We decided to look at the outcomes arounds surface area and volume of prisms and cylinders.

We taught lessons in two grade 8 classes with other teachers and resource teachers being able to come in and observe. Photos and video captured how the students engaged with the mathematics. We asked students to first create rectangles with an area of 12 square centimetres to see what their understanding of area was. Many students found all the possibilities. We then asked them to build a rectangular prism with a volume of 24 cubic centimetres. Many students were able to find more than one prism with this volume. The students were then asked to figure out the corresponding surface area of the prism, recording how they did this using pictures, numbers and words. Students were asked to share what they found out on the whiteboards in the classroom. A final task was to ask the students to share their understanding using a screencasting app on an iPad or to create a net for a rectangular prism with a volume of 24 cubic centimetres. A particular focus of the lessons was on use of mathematical vocabulary and seeing what language students used when communicating their thinking.

After the introductory lessons in the two math classes, the math teachers, resource teacher and Shelley and I met to review the evidence of students’ understanding of surface area and volume by looking at photos, video, student work and debriefing the lessons. The teachers noticed that most students had a good understanding of area and surface area but had not yet generalized a “formula” for surface area of a prism. The students had a good understanding of volume of a rectangular prism and the teachers wondered if they would be able to generalize this to other prisms and cylinders. They also noted the high engagement of all the students and the value of having tools like grid paper and cubes to support the students’ understanding.

With the information from this performance task, the teachers and Shelley were able to put together class profiles and develop learning goals for all students in the class. Lessons were developed with entry points for all students.

A framework was developed looking at the concepts for this particular “unit” and what an assessment continuum would look like for “not yet meeting, meeting, fully meeting and exceeding expectations” as well as modified expectations for each outcome. Shelley did another lesson with one of the grade 8 classes and we viewed photos and video as well as some student work to discuss student learning.

The teachers in this project commented that they valued the collaboration time and through the experience came to understand what “differentiation” could look like in their classrooms. One teacher commented that “inclusion is good for everyone” after seeing evidence of this in the classes. The teachers involved felt they could see how this planning framework could be applied to the whole grade 8 course and how well it complemented the middle years IB program at Boyd. They are curious what this might look like with a more abstract content area like algebra and are interested in how technology might support a more inclusive learning community. So although the “ILC” project is formally over for this group of teacher, they are hoping to continue their own professional learning in this area next year and we will be looking for ways to make this happen!

~Janice

primary math mornings at Quilchena

Posted on: June 13th, 2015 by jnovakowski

I have spent most Monday mornings of this term at Quilchena Elementary, teaching in the primary classrooms and meeting with the teachers during a collaboration block. The school principal brings all the primary students together for a block each week for choir which provides time for the teachers to come together to collaborate and plan.

The teachers wanted to focus on number sense and over the weeks we looked at the importance of understanding number in different ways.

In Jessica Preswick’s Kindergarten class, we often began our classes with a short number talk involving dot cards or ten frames. Through the students “subtilizing” what they see and then describing it, we are able to get insight into the students understand of number. We also had students use materials to decompose a quantity into parts, for example, showing all the ways to make seven.

After much work with subitizing, decomposing and counting, we connected what we had been learning about number to think about measurement by comparing. The students used the language of longer than, taller than and shorter than to compare objects. They ordered objects from longest/tallest to shortest. They also measured some of the objects using cubes and figured how much taller or longer the objects were, compared to another.

We also compared the capacity of bowls and cups by filling them with cubes and then comparing the “towers” of cubes.

In Marla McPherson’s and Karen Maeir’s Grades 1&2 classes, we focused on number talks, developing the students mental math strategies for addition and subtraction. I did need to demonstrate some of the strategies and remind students about the range of strategies they could use sometimes. We focused on students naming the strategies they were using as they explained them to create a consistent awareness of the strategies in the classes. Both teachers created strategy posters for their classrooms. It was amazing to see the students’ confidence with the strategies develop over the weeks and their increased ability to discuss the strategies. We also played card games that focused on them using the strategies to help them develop computational fluency.

In Andrew Livingston’s grade 3 class we began looking at multiplication and division and then moved on to fractions. Approaches we used to learn about these concepts included number talks, use of concrete materials, visual representations, games and use of iPad technology to represent our learning.

Using Cuisenaire rods to learn about fractions…

Using the ShowMe app to explain what we know about fractions…

In June, we introduced some geometric language and materials to the students, focusing on comparing the attributes of both 2D and 3D shapes. The students used the camera and PicCollage app on the iPads to collect examples of one shape.

The teachers felt it was a powerful professional learning experience to have the weekly visits and discussions as a group. It was an opportunity to plan next steps for the week ahead as well as make connections between concepts at different grade levels. An ongoing professional inquiry like we had at Quilchena this term reminds me that collaboration and making time for reflection and professional learning is essential to professional growth.

~Janice

Vancouver Reggio Consortium Learning Journeys Grant

Posted on: June 13th, 2015 by jnovakowski

This year we have piloted four Reggio-Inspired Mathematics kits of materials that were made possible through a grant from the Vancouver Reggio Consortium Society. We applied for the grant in response to teachers that began a professional inquiry project during 2013-2014 and one of the emergent issues was the need for fresh materials to inspire mathematical provocations. The kits have been very well received and from our work with the materials and through our ongoing professional inquiry we have published a resource.

We were invited to share our district’s project at the VRCS’s Sharing Circle. It was an inspiring event with all the teams of educators who had received grants sharing their projects. All of the projects focused on collaboration – such an essential component to professional learning.

It was an honour to hear Susan Fraser speak at the event. She is the author of Authentic Childhood, a very inspiring book. Susan was on the first Canadian delegation to visit Reggio Emilia and the learning journeys grants are her legacy. She proudly declared at the end of the event that we have been inspired by the philosophy of Reggio Emilia and have made it “our own”.

The kits that were made possible from this project have been piloted in sixteen classrooms in our district and our now available for circulation through DRC.

~Janice

diversity of life inquiry at Lee

Posted on: June 11th, 2015 by jnovakowski

During third term, I have spent part of Thursday mornings at Lee Elementary, learning with Sandy Rasoda and her grades 6 & 7 students. Sandy has been teaching this grade level for many years and asked me if we could look at a science unit she has traditionally done by using the science text book and instead, look at the topic of “diversity of life” through an inquiry-based approach.

I looked at the three prescribed learning outcomes for this life sciences topic for grade 6:

•demonstrate the appropriate use of tools to examine living things that cannot be seen with the naked eye

• analyse how different organisms adapt to their environments

• distinguish between life forms as single or multi-celled organisms and belonging to one of five kingdoms: Plantae, Animalia, Monera, Protista, Fungi

After looking at the learning outcomes, I tried to think about the big ideas we needed to get to and what experiences we might provide to the students to help them get there.

On my first visit to the class, we had a short discussion about what makes a living thing a living thing and then went for a walk in the neighbourhood looking for different examples of living things.The students were very curious about the names of many of the plants we found in gardens and along the ditches. We were lucky to hear a frog croaking and to see mushrooms, lichen and moss just outside the school. I took photographs along the way.

What makes a living thing a living thing?

What living things can we observe in our community?

When we got back to the classroom the students recorded the living things they observed and added questions they were wondering about.

The next week, I brought a ditch dipper so that we could collect some water samples along with other specimens to look at with magnifying glasses and microscopes. We had petri dishes and pipettes available and there is something about using real science equipment that elevates students’ engagement. We discussed the difference between viewing something with the “naked eye” and with a magnifier of some sort. The students were hesitant with the microscopes and had difficulties adjusting the focus and had to move the illuminator around to get enough light. The students recorded their observations, comparing what they could see with and without a magnifier/microscope.

What tools can we use to examine living things?

During another class, I gave each group of students a set of photographs of different living things we had observed outside. I read a simple picture book introducing the big idea of classification and the five kingdoms and then the groups worked together to sort their photographs into kingdoms. During this task, the idea of sub-categories within a kingdom emerged and students began to consider how to categorize different types of plants and animals by their features. We had given the students the three learning outcomes on a sheet of paper at the beginning of our study and they had this in their science notebooks and used it to record notes and new learning during our investigations.

How do we classify living things?

In-between my visits Sandy provided opportunities to extend their learning about both microscopes and the kingdoms and were given choices as to how they might show what they had learned. Some students did powerpoint presentations, some did booklets or posters and some use movie apps on the iPad to create their presentations. The students had opportunities to teach another grades 6&7 class how to use the microscopes as well as one of the primary classes in the school. Sandy was clearly able to see that they “got it” and this just came from repeated experiences actually using the microscope.

We had such great weather this spring and during one of my visits, Sandy suggested we take the microscopes outside to the picnic benches. The students learned how to safely carry the microscopes and their confidence was growing. One student even commented how great it would be to have a fine adjustment on the microscopes – they were learning the different functions of the microscope and its potential. The students looked at previously collected specimens and also found some new ones to examine.

We also looked at some amazing images taken through microscopes, including some amazing electron microscopes

We then used a Zoomy digital microscope to take our own images of various specimens, including a fly the students found in a windowsill and a ladybug and spiderlings the students brought in from outside.

Using some local examples and examples from recent news items, we discussed how living things have adaptations, focusing on structural and behavioural adaptations. Using the app HaikuDeck, the students created a slideshow of what they had learned about different adaptations.

How do living things adapt to their environment?

The following is one pair of students’ project.

Animal Adaptations – E.K & N.S

I brought in glass slides and cover slips, tweezers and pipettes so that students could prepare their own slides to view under the microscope.

The students also has an opportunity to view prepared slides under the microscope, including microscopic organisms from the Protista and Monera kingdoms.

What do microscopic organisms look like?

At the beginning of June, we asked the students to consider a mini-ecosystem or habitat in the neighbourhood and we went outside with the iPads to take some photographs. The students were asked to synthesize what they had learned about the classification of living things as well as adaptations.

What have you learned about living things in our community?

The minimum criteria for this project was to include living things from two different kingdoms and highlight an adaptation. The students could choose from using the Skitch or Popplet apps.

The following are some examples of the students’ projects:

Throughout this experience I have heard comments from students such as “science is so fun!” and of course this makes my heart sing a little. Learning can be fun…complex concepts and big thinking can be fun. Meaningful engagement with any content begins with the students…where will they find connections? what will make this learning important and purposeful to them?

I think we got there with this class. High engagement and students able to fluently discuss concepts such as the classification of living things and structural and behaviour adaptations of animals and plants in their neighbourhood. The students were all able to confidently use a microscope and teach other students from other classes about how to use a microscope.

“This unit traditionally for me would be a ‘textbook’ unit with possibly one or two experiments. Instead, Janice took us on nature walks where we were out in our environment exploring and learning about Living Things. The students eagerly found specimens they brought back to look at through the microscopes. Every lesson was a hands on lesson where the students questions led them to finding answers and solutions through experimenting with materials from the real world. It was great for me to see how much the kids “loved” being scientists.” ~Sandy

~Janice

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