Archive for the ‘provocations’ Category

growing our Reggio-Inspired Mathematics inquiry project

Posted on: October 29th, 2015 by jnovakowski

So the final session I presented at the Northwest Math Conference in Whistler was on the Reggio-Inspired Mathematics inquiry project that began in Richmond and has grown to include six Lower Mainland districts, thanks to the support of the BCAMT.

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Along with our publications, articles and materials, I was happy to share our new blog that was created to archive resources to support educators as they consider teaching and learning mathematics through a Reggio-inspired lens. The blog can be found HERE. There’s a photo album of mathematical provocations, downloadable instructional resources as well as links to archived articles and presentations.

After the session, several teachers from around BC asked how they could be involved. Thanks goodness for an online community and technology that will allow us to connect virtually!


how materials inspire inquiry

Posted on: October 15th, 2015 by jnovakowski 2 Comments

Building on our Creating Spaces for Playful Inquiry series, there will be several professional learning opportunities in our district this year that focus on specific aspects of playful inquiry. On the professional development day on September 25, Marie Thom and I hosted an afternoon at Thompson Elementary focused on how materials inspire inquiry.

A variety of art materials were presented alongside natural materials found in our area to inspire attendees to think about the changing of the seasons, what stories live in fall and to consider a connection to place and the cycles that autumn brings.

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Some of the teachers attending mentioned that they had never used charcoal pencils or watercolour pencils themselves and this was part of the intent of the session. We wanted teachers to consider the affordances of different materials and what they each offer so that they can make intentional decisions about which art materials they may provide to students. We emphasized the notion that students need to also learn how to use the materials, take care of them and to consider what materials might be more suitable for different projects. Just like with tech “apps”, we want students eventually to be able to have a repertoire of materials that they can choose from to use to help them think about an idea or to represent their thinking.


By looking closely and observing leaves, nuts, branches and other objects outside or brought into the classroom, inquiry naturally emerges and students wonder aloud, creating an opportunity for teachers to seize the moment and create ways for students to investigate their question, to look even more closely or test their ideas. Working with art materials may uncover new ways of thinking about the object or their questions.

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If this is an area of interest for you, two professional books we recommend are: The Language of Art by Ann Pelo and In the Spirit of the Studio: Learning from the Atelier of Reggio Emilia by Leila Gandini and Louise Cadwell.


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.

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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.

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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.

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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.

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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.

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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.


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.

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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.

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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)

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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:

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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.

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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.

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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.


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.

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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.

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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.

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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.


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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.

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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.


more measuring in kindergarten

Posted on: April 25th, 2015 by jnovakowski

One of the things that is fascinating about using open-ended provocations in mathematics is that every experience with the materials is so different. Materials are chosen intentionally and often set out together to suggest an investigation but where the students take things makes it their own and often goes much deeper with the mathematics than what we may have intended.

Earlier this month I spent part of a morning in Stephanie Merrick’s kindergarten classroom at Hamilton elementary and the students had been using the materials from the Reggio-inspired measurement kit. The students in the class listen carefully to each other and are experienced with engaging with materials both independently and collaboratively.

I did a short mini-lesson on comparing linear measurements reading a book called Big and Small that compares different sizes of animals. We discussed how the term “big” is too general and that we need to use more specific language like longer, taller and shorter when comparing, I then modelled this using a set of matryoshka dolls, ordering them and using the comparative language. The students were then invited to use the materials and investigate measuring and how to compare measurements.

The provocations placed out on the tables…

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And the students began measuring and talking about their measurements. We also placed some tubs of materials on the carpet. One student sat down not the carpet and started measuring his leg with cubes which then inspired others to measure parts of the themselves.







This pair of students lay down the panda matryoshka dolls and measured their lengths with gems and then recorded the measures.


As the girls were undoing the pandas to put them back together as a set, they began filling them with the gems they had been measuring with and wondered about the capacity of each doll.


During this visit I had a Queen’s student working with mean she interviewed Stephanie and captured some of her thoughts about teaching mathematics through Reggio-inspired practices. Specifically, Stephanie was asked how she thought student learning was affected.

  • “Having everything hands on and play-based lends itself to extension. It lends itself well to students finding their own extensions”
  • The practices and materials help students, “learn where they are at.  If students are ready to learn more, they will explore it naturally.”
  • The teacher noticed that it “takes away from my own micromanaging as they find where they will go next independently.”
  • “It is engaging.”
  • “It is easy to say to students ‘can you show me that in a different way with a different material?’” and the practices and materials provide these prompts.”

The students were engaged with the materials for almost an hour. During that time both Stephanie and I were able to sit alongside every child in the class and capture a glimpse of their understanding about measurement. The current prescribed learning outcome for measurement in kindergarten here in BC is: use direct comparison to compare two objects based on a single attribute such as length (height). Every student in the class was able to compare two objects (ie. two ribbons, two of the matryoshka dolls, their legs or arms, etc) and use the specific math language of taller. longer or shorter. Many students demonstrated understanding well beyond this outcome and measured using non-standard and standard units and were able to explain the differences in lengths or heights of the objects they measured using units. For example, one of the matryoshka dolls was eight cubes tall and another was four and a student said that the taller was was four cubes taller. As Stephanie suggested in her comments above, the provocations and materials provided the opportunity for students to extend their own learning.


what can your pattern become?

Posted on: April 3rd, 2015 by jnovakowski 1 Comment

Sharon Baatz, a kindergarten&grade 1 teacher at Woodward Elementary has had the Reggio-inspired patterning kit since February. Having already investigated patterns with her students in the fall, the kit gave her and her class a chance to re-visit the big ideas with some fresh materials. Sharon mentioned that her students particularly enjoyed working with the nuts and bolts and that she found the grid and spiral mats really helped her students expand their thinking about patterns.

Sharon sent me some documentation she created about an inquiry that began in her class, emerging from a student’s observation: What can your pattern become?

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I visited Sharon’s class last week and asked them the big question of “what is a pattern?” and again, as for most five year olds it seems, they were able to provide lots of examples of what a pattern was (orange, white, orange, white, orange, white, etc) but had difficulty defining and describing the concept. We struggled through that conversation but  got to some ideas around repeating, alternating and being predictable. I then asked the students to consider the question: What stories live within patterns? I knew this class engaged in the story workshop process so I hoped this question would inspire them. We set out materials on the tables and Sharon followed one of her classroom routines and asked a child to name students to go and choose where to begin their investigations.





Not currently in the kit, but materials I have been using to extend students’ ideas about patterns, is a collection of bare wooden blocks. I find that many students focus on colour or shape when patterning and I wanted to provoke their thinking by having them work with materials that were all the same colour and the same shape.

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We saw some very creative thinking with the materials and the students focused on position and creating height by building with the blocks.

We came together at the end to share and I asked the students if they found any stories. One student commented that she made a zigzag pattern and that could be a path going somewhere. What a great inspiration for a story! This was some new thinking for the students and Sharon explained that she is interested in exploring the idea of math workshop to parallel what she is doing with story workshop.

Our practicum student from Queen’s University interviewed Sharon and captured these reflections:

  • She felt that the openness is good for children because it inspires growth and “encourages different levels of thinking”
  • Sharon liked one of the picture books in the kit and she used it as a “spring board” by showing it to students first to look at patterns
  • Sharon noticed the “social skills that these practices develop” such as working together and sharing
  • Sharon noticed that the “students were very engaged”
  • Sharon liked the “vocabulary the materials and practices encourage” 
  • Sharon likes that the all students can achieve to their own different levels, and that the students often get pushed to further, higher levels of achievement

Sharon’s reflections made me think about our redesigned curriculum and the core competencies. Many teachers have wondered how those will be enacted in the classroom and I think the above examples speak to this. We saw lots of evidence of communication, creative and critical thinking and personal and social development.


thinking about the big ideas of number in grades 2&3

Posted on: April 2nd, 2015 by jnovakowski

On Tuesday, I visited Anna Nachbar’s grades 2&3 class at McNeely with our Reggio-inspired number kit. Anna had attended a session I presented on the project at our Elementary Math Focus Day on December 1 and said she would be interested in investigating the materials with her class. Most of the classes that have used the kits have been Kindergarten or K&1 classes and I really would like us to look at how the materials and Reggio-inspired practices are applicable with older students so this was a great opportunity!

When I looked over the kit list and then the number learning outcomes for grades 2 & 3, I designed some new provocations that would get at some big ideas for those grade levels, using the existing materials with a few little add-ons. Provocations are intended to be inquiry-based and take on different forms in terms of structure. I don’t like to call what we are doing “centres” or “stations” as to me, this brings images of students being grouped or “signing up” to go to certain places to do specified tasks/activities and then rotating through them, often in a timed manner. Instead, I like to invite the students to think about what they are interesting in investigating and begin there (noting if there is a lot of children at one area, asking them to think about how they could handle that problem). Some students may stay with one provocation (that becomes an inquiry for them) for an extended period of time while others may move from area to area or choose different materials to engage with. Aligned with Reggio-inspired philosophy and practices, I believe we have to trust that students are competent and capable of managing themselves and making reasonable choices. When they need support with this, we can coach them through this. One of the things that I have noticed throughout this inquiry project and that many teachers have commented on is that they are astonished by the high levels of engagement and independence that the students demonstrate.

For grades 2&3 the students are learning about 2 and 3-digit numbers with some very big ideas around place value that are foundational at these grade levels. The following provocations were designed to have students play with these ideas and to uncover their conceptual understanding around number.

The following prompt directly guides the students’ inquiry. It asks them to choose three digits from the baskets of different materials (various wood numerals and pebbles) and then to investigate different numbers you can make with the three digits. I also put out mini-clipboards and many of the students enjoyed writing down all the numbers they made. One pair of boys wanted to know the number of  “combinations” possible and tested their initial theory using various digits. Anna commented that this same problem or investigation was in the math resource they use at McNeely but as teachers, we noticed that there was something about doing this kinaesthetically with the materials that enabled students to come up with most of or all of the combinations (rather than just doing it more abstractedly with just pencil and paper).



Some of the students also began to play with creating very large numbers and were excited to learn how to read them.



Another provocation we set out was a collection of hundred charts, a basket of pebbles and the question: What can you find out about numbers?


At first we noticed some discomfort amongst the students. They weren’t quite sure what to do and looked to us to tell them what to do. With the ball toss back, “what do you think you could do to find out about numbers?” the students began with something familiar – looking for number patterns. This was a start and it will be interesting to see where they take this. Anna has built such a strong sense of community in her class and the students were kind to each other and collaborating so well that even though this type of inquiry-based mathematics was new to them, they were able to adjust and engage.


The following set of materials were presented without any direct prompt. Students used the materials to create games, build and record numbers, etc.


For this provocation, I set out a collection of 1, 2, 3 and 4-digit number cards as well as some pieces of yarn. The invitation was to consider different ways that the students could compare, sort and order the numbers. One student began by making a venn diagram using two pieces of yarn but then wasn’t sure to go with and then said, “Hey, this could be a number line instead!” and lay the yarn out. I watched as two students worked together, taking turns placing the number cards in order along the number line. I watched one student notice a misplaced number and kindly say to her classmate, “do you think this number goes here instead?”



Another provocation asked students “Where do you see numbers in your world? How are they used?” and I had some photographs of addresses out for students to look at with some large wooden numerals. Two boys excitedly explained to me that they were going to make “their” numbers which they explained was the numbers on their homes.


On one table I placed some baskets of glass gems with no direct prompt accompanying them. They were left alone for half of the time (we spent an hour together) and then a group of girls visited the table and began creating patterns. When I noticed this, I asked the students “how do these patterns help you think about number?” This led to a discussion about labelling patterns with number, how many “elements” are in the stem or core of a pattern and then how many terms or groups are within their repeating patterns. This would lead very nicely into an introduction to multiplication, emerging from this experience.


I currently have a Queen’s University student working with me on an alternative practicum and she was able to “interview” Anna a bit and get some of her reflections on the experience.

  • Anna admitted that “I did not know what I was going to see.  I knew the materials were all natural but I did not know how Janice was going to make it grade appropriate.”  Nachbar then added that, “She did make it very grade appropriate,” and was thinking about how she could use similar provocations, materials and practices for other ideas in mathematics, such as multiplication and division.
  • Anna noticed that “All students can be successful and take something from the experience” as the materials and provocations provided multiple entry points, allowing students to enter the activity at their level.  She also believes that these materials and practices would be successful combined with direct teaching.  Nachbar felt that there is “a place for open-endedness” but there must be a balance of this with direct teaching.(Janice’s note: a mini-lesson involving review or teaching of a concept usually proceeds a set of provocations which can be seen as a time to practice, apply and go deeper)
  • Nachbar’s big question was “at what point do you step in a guide the students?” 
    • (Janice’s note: Anna and I had this conversation together and I think like in any situation, as a teacher, you read the situation and respond differently in different contexts and for different students. I think sometimes we feel we need to jump in but often giving the students a little time to struggle lets them figure things out themselves and settle in. When students are off-task and not engaging, we need to think about why and be responsive to that. Sometimes we need to re-direct, pair them up with a classmate, etc).

Anna’s questions about guiding the students also made me reflect on our experiences at the Opal School in Portland and the teachers’ discussion of the ball toss, a metaphor that emerged from Loris Malaguzzi of Reggio Emilia as well as the Harvard Project Zero work around Making Thinking Visible and the use of the “reflective toss” to guide and further inquiry. So I think the timing of providing guidance is important – being responsive, giving time for students to sort things out themselves but also what we say, what language we use is also important. How do we support and extend students’ thinking instead of directing it?

It is so inspiring to think and learn alongside a teacher like Anna who is open to professional inquiry. I am hoping to find some time in my schedule to get back to visit the students at Anna at McNeely this month.