## the new playground at Grauer: where’s the math?

Posted on: September 18th, 2018 by jnovakowski 1 Comment

Last year the families, staff and community fundraised for a new playground for Grauer Elementary. Grauer is a small school with only five, six or seven divisions (depending on the year) and it is hard work for a small school to raise \$60 000! It was very exciting when the school reached their goal and is such a good example of an authentic numeracy experience for students to think about. In the BC curriculum, numeracy is defined as an application of mathematics to solve or interpret an issue or problem in context.

Last Saturday, I joined staff, parents and community members coming together to install the playground (self-installation with staff support from the playground company saves thousands of dollars). As Ms Partidge and I helped to read the specifications for the installation of one of the fire poles, we commented to a couple of parents around us how much mathematics was involved in the process.

I shared some of the photos from the installation day with the two grades 1 & 2 classes. All of these students had been to The Studio last year with me and had spent some times exploring the idea of “what is math?” so I framed this investigation as “where is the math?” I knew for some students this would create some dissonance as even young children can sometimes already have a very narrow view of what mathematics is and think that it is about counting, numbers and “plussing”. Part of this investigation was to disrupt this thinking. Of course counting, numbers and arithmetic operations are important content areas of mathematics, but they are not the only content. This investigation was one avenue to create meaning for learning mathematics, having students make connections to math beyond the walls of the classroom. The students came up with some initial ideas and we will continue to add to our thinking over the next couple of weeks.

The students were invited to design and create playgrounds and to consider where, when and how mathematics would be applied/used. One group of students followed the kit diagrams to create a Playmobil playground set – there was lots of math talk during that collaboration! Some students chose to draw and paint a playground from their imagination and some built playgrounds with blocks and loose parts, including a playground for animals.

After our first time together, I noticed the students were very interested in the photographs of adults using the levels and measuring tapes so I ordered some (not toy) tools to add to the construction area of The Studio. It was great to watch the students use these tools in authentic ways.

One of the classes had gone outside to look closely at the playground twice, creating detailed labelled diagrams or maps of the playground.

We extended this experience in The Studio by asking the students to create “math maps” indicating “where’s the math?” on recordings of their playground creations.

And what are are we assessing in terms of mathematics? These types of investigations and explorations lend themselves to informal formative assessment and gives us a sense of mathematical language the students have and where students are along a learning trajectory around different concepts and skills such as spatial reasoning, comparison of size and quantities and measuring. This type of assessment, that focuses on observing and listening to the students’ play and math talk is so important at this time of year and informs our instructional plans and focus for the fall.

When students engage in this type of learning through materials we make their learning visible through a sharing session at the end of our time together and capturing photographs, videos and students’ thinking so that we can revisit and reflect on the experiences, make connections to new learning experiences and consider questions for further investigation. The following are examples of documentation panels that we create to post in The Studio to help make our learning visible.

Grauer_playground1_Sept2018 copy

Grauer_playground2_Sept2018

I’m looking forward to seeing where the students take us next on this investigation.

~Janice

## May thinking together: How can we weave Indigenous content and perspectives into the teaching and learning of mathematics?

Posted on: June 12th, 2018 by jnovakowski 1 Comment

The First Peoples Principles of Learning is a foundational document in the redesign of BC’s curriculum frameworks. The Principles were developed by FNESC (First Nations Education Steering Committee) and the poster in English can be found HERE and in French can be found HERE. As Jo Chrona would say, the FPPL are much more than the poster – they are principles that are inclusive of all children in BC while honouring Indigenous ways of being and knowing. FNESC has developed teaching resources such as the In Our Own Words resources for K-3 and the Math First Peoples resource for Grades 8&9 (currently being updated) but much of the information and ideas in the resource can be adapted for all grade levels.

On May 17, Leanne McColl, Lynn Wainwright and myself attended the 8th annual K-12 Aboriginal Math Symposium. Educators from across BC attend this symposium. Information about the symposium can be found HERE and there is a tab on the website that links to archived resources.

I have attended this symposium for years and was fortunate to share a project from The Studio at Grauer at this year’s event. Some of the slides from my presentation can be found HERE , under May 2018.

A focus of my presentation was on three of BC’s mathematics curricular competencies. These competencies are part of the learning standards for the K-9 mathematics curriculum and are aligned with the First Peoples  Principles of Learning and the Core Competencies.

The BC Numeracy Network has archived different types of resources to support the redesigned curriculum. Under the Connections tab, there is a page dedicated to resources that support the weaving of the First Peoples Principles of Learning into mathematics teaching and learning.

In the Richmond school district, two of the four goals of our Aboriginal Education Enhancement Agreement (AEEA) are focused on all learners (not just those with Indigenous ancestry) developing an understanding about the First Peoples Principles of Learning, our local First Nations community and Indigenous worldviews and perspectives as part of engaging in the process of reconciliation through education.

Teachers often ask me about where to start in this area and are concerned about not doing things properly or that they do not have enough knowledge themselves. I suggest that teachers contact someone in their district about local protocols and then try something in collaboration, maybe inspired by one of the above suggested resources. Look for authentic connections within your community and across disciplines in the curriculum..  Some of the things that I have done to continue to learn more in this area are: read articles and books recommended to me, seek out opportunities to learn from elders and Indigenous community members and colleagues, get involved with district or university-based collaborative projects,  connect with your district’s Aboriginal Education team, attend workshops and tours offered through museums, cultural centres and local Indigenous organizations. There are lots of opportunities to learn and see connections to mathematics…we need to go forward together with an open mind and an open heart.

To consider…

How can the First Peoples Principles of Learning be embedded in our mathematics teaching and learning? How do BC’s mathematics curricular competencies reflect these principles?

One of the principles is that “learning takes patience and time” – how does this principle bump up against some ideas around the teaching and learning of mathematics?

How might we work towards the goals of our Aboriginal Education Enhancement Agreement within our mathematics classrooms? What role could mathematics play in the process of reconciliation?

What does it mean to use authentic resources, stories and elements of culture in our mathematics teaching? How is this affected by the land and the story of the place where we live and teach? Who can help us think about these ideas? Where can I learn more and find resources?

What opportunities do your students of Indigenous ancestry have to see their community, family and culture represented in the mathematics they are learning at school? Within our diverse community, how do all students see themselves reflected in their mathematics experience? What is the relationship between our students’ mathematical identities and their personal and cultural identities?

What interdisciplinary projects might connect mathematics with Indigenous knowledge and worldviews?

~Janice

## April thinking together: How do the core competencies connect with mathematics?

Posted on: June 7th, 2018 by jnovakowski

The Core Competencies are at the centre of BC’s redesigned curriculum and underpin the curricular competencies in each discipline, such as math. An overview video about the Core Competencies can be viewed HERE. Drawing from global education research and through provincial consultation with stakeholder groups, three Core Competencies were identified – Thinking (creative and critical), Communication and Personal & Social (positive personal and cultural identity, personal awareness and responsibility, and social responsibility).

As we develop awareness about the Core Competencies during the school year, we consider the ideas of “notice, name and nurture” – looking for evidence of core competency development or application in our classrooms and schools.

In our district, we have created Core Competency posters in both English and French, overviewing all the core competencies as well as posters specific to one core competency (all available through the district portal). These posters are up in classrooms and schools to create awareness and develop common language around the core competencies.

In The Studio at Grauer, much of the work we do in mathematics has elements of the core competencies involved. In the mathematics curriculum, each of the curricular competencies is linked to one or more of the core competencies. The COMMUNICATION chart in the photograph below is an example of how I make this focus clear to myself, teachers and the students when we work together in The Studio. I often identify a specific curricular competency in our initial gathering meeting, that we are going to focus on together as we work with a mathematical idea. For example, I might say to the students,
“Today as you are thinking about comparing and ordering fractions with materials, practice explaining and justifying your decisions to a partner – that will be our focus when we come back as a whole group at the end of our time together today.”

Other times, I will ask the students to reflect on their last experience in The Studio and consider what they need to work on around communication, either personally or as a class.

The following are documents that show the links between the Core Competencies and the Curricular Competencies in Mathematics:

SD38 K-5 Math Connections between Core and Curricular Competencies

SD38 6-9 Math Connections between Core and Curricular Competencies

SD38 K-5 Math Communication

We have woven self-assessment and reflection about the core competencies into our projects and learning together throughout the year. During the last school year, there was a requirement for students to do a “formal” self-assessment to be included in the June report card. For students to authentically self-assess and reflect, they need to be familiar with the language of the core competencies and be able to connect to learning experiences they have had throughout the school year. During the third term last year, the grades 3&4 class from Grauer visiting The Studio weekly to engage in a mathematics project around the work of Coast Salish artist Susan Point. At the end of each session together, we had the students share their learning – what did you learn? how did it go/what did you do? what’s next for your learning/what are you wondering about? Sometimes students turned and talked to someone near them, other times, students shared their learning and thinking to the whole class.

Every few weeks, we had the students do a written/drawn self-assessment and reflection. We have found that using question prompts to support reflection and considering evidence of learning has been the most authentic and personalized way to have students think about and connect to the core competencies. We developed some recording formats to capture students’ thinking, with the clear intent that students are not expected to “answer” all the questions – that they are they to prompt and provoke reflection and self-assessment. A team of Grauer educators were working together on an Innovation Grant project around creative thinking and growth mindset and we wove these ideas in to some of the self-assessments.

Here is one example of a recording form:

Grauer_Competency_Math_Reflection_May2017

As we are coming to the end of another school year and are thinking about the student self-assessment of the core competencies component for year-end communication of student learning, we might consider the following questions:

• What opportunities have students had to experience and develop the core competencies in their mathematics learning?
• What opportunities over the school year have students had to name and reflect on the core and curricular competencies in mathematics?
• How have we made the core competencies and curricular competencies in mathematics visible in our classrooms and schools?
• How have the core and curricular competencies language and ideas been embedded in the mathematical community and discourse in our classrooms and schools?
• What different ways have students been able to share, reflect on and self-assess their mathematical thinking and learning?

~Janice

## 2017-18 primary teachers study group: session six

Posted on: June 6th, 2018 by jnovakowski

For our sixth and final primary teachers study group session of this school year, Megan Zeni hosted us at the outdoor classroom at Homma. Megan shared the story of the space and how it has developed over time as well as shared the logistics of her “prep teaching” position in the outdoor classroom.

We explored the different spaces in Homma’s outdoor classroom to consider opportunities for storytelling and play.

We had lots of great conversation about risky play and the gross motor and social-emotional learning that happens when students engage with large materials, building and play in outdoor spaces.

As we left the Homma school grounds and walked towards the south arm of the Fraser River, we considered the story of this place. The boardwalk and buildings along the river help to uncover the story of the people of this place and how the river has been used over time.

It has been a great year of primary teachers coming together in different places and spaces to think about how outdoor learning experiences can inspire different types of stories and curricular connections.

Looking forward to another year of learning together.

~Janice

## Story Workshop series – 2018

Posted on: May 24th, 2018 by jnovakowski

A group of district teacher consultants and school-based teachers came together this spring to facilitate a three-part Story Workshop after school series. This was in response to many requests and questions  from teachers in our district about Story Workshop. The facilitators of the series were: Sharon Baatz, Louesa Byrne, Michelle Hikida, Carrie Bourne, Lisa Schwartz, Marie Thom and myself.

A goal of this series was to honour the work of Opal School educators who developed the structures and practices of Story Workshop as a way to connect the arts and literacy. Opal School educators draw upon social-constructivist learning theory and have been informed by the early childhood educators in Reggio Emilia, Italy as well as American educators such as those working with Harvard’s Project Zero initiatives. Opal School has a deep commitment to equity and access for all students and to develop student agency.

They are many other ways we might engage our students in storytelling experiences – oral, digital, writers workshop etc but the focus of this series was to create awareness and understanding of Story Workshop as developed by Opal educators. The Opal educators have developed five structures or stages of Story Workshop. Some stages are more for the educator to consider and some take more time than other stages. Some of the structures such as negotiation or congress might involve small groups of students and an educator instead of the whole class. Over the series, we hope to develop a deeper understanding of the process of Story Workshop and what it offers the students in our classrooms and what it offers us as educators.

In our first session on April 9, we focused on the stages of Preparation and Provocation. We watched and discussed the Opal videos and Michelle, Louesa and Sharon shared examples of these stages of Story Workshop from their Richmond classrooms.

We watched and discussed the first two videos of the series and used the following questions to frame our small group discussions:

What do you notice about the materials the teachers are using?
When you look around your own setting, what unexpected materials might you use in new ways?
What do I want the children to learn?  How can I support this learning?

Story Preparation begins with our image of children. Preparation is about preparing the environment; setting up the space, creating an environment that supports children to tell their stories. Opal educators strive for environments that are playful, engaging, naturally motivating, with multiple opportunities for all children to enter into the work.

At Opal, educators convert social-constructivist theory and inquiry into practice by offering provocations. A Story Provocation is a question that is introduced to children to engage and support their interests and curiosity.

The Opal videos can be found here:

Story Workshop – Story Preparation

Story Workshop  – Story Provocation

Educators attending the series were each provided with the book Equity and Access Through Story Workshop.

The videos and supporting text are available at no cost to Opal School Online Sustaining Members and at a small cost to non-members: You’ll find both here.

Educators were asked to make a commitment to something they would try, inspired by the first session, and to be prepared to share a reflection, documentation or an artifact at our next session.

At the second session on April 30, we began by having teachers share what they had tried around Story Workshop with their students. Lisa shared how Story Workshop can be part of a balanced literacy program. Marie talked about different ways to approach Story Workshop with different ages of students and that the process needs time and patience, not rushing towards recording/writing the stories.

We also shared copies of this blog post from Opal for educators to read and reflect upon their own practice and how Story Workshop might be enacted in their classrooms and schools.

We focused on the next two stages of Story Workshop – invitation & negotiation and story creation.

At Opal, the invitation and negotiation time focuses on students being metacognitive about their plans for each day. It is often just a few minutes with opportunities for educators to have a one-on-one check in with students.

At Opal, educators invite children to explore the classroom and materials in search of their stories and this time can last about 45 minutes. Story Creation is a time of looking for and finding stories from the child’s real or imaginary life. Children play with materials, talk to each other, and tell and write their stories.

Sharon and Louesa shared examples from their classrooms:

The Opal videos can be found here:

Story Workshop – Story Negotiation

Story Workshop – Story Creation

Again, teachers were asked to try something around story negotiation or creation and to consider an area of Story Workshop that they would like to go deeper with.

At our final session on May 14, we invited teachers into The Nest and to think about how different materials might inspire different types of stories.

Each educator was given the book I Am A Story by Dan Yaccarino (it comes in both English and French) as a provocation for adults and children to think about different ways that stories can be shared.

We focused on the importance of Story Congress as a way for educators and peers to give feedback on students’ stories. Sharon, Louesa and Michelle shared some of the structures they use in their classrooms for this stage of Story Workshop.

The Opal video can be found here:

Story Workshop – Story Congress

Opal School has online courses available to extend and deepen understanding of playful literacy and Story Workshop. More information can be found HERE.

This was a very well attended series with a waiting list and we hope to be able to offer it again next year. Many teachers asked if we could provide opportunities to visit Richmond classrooms to see Story Workshop in action and we will put something in place for this for next year.

Some of the feedback from series participants include:

“I appreciate how professional the mentor presented so many awesome ideas, so well laid out. This series has profoundly affected my thinking and practice.”

“This series helped me think about Story Workshop, storytelling, oral storytelling, loose parts and how they are different yet integrated.”

“It has helped me breathe. Hearing how others navigate and problem-solve the same challenges I have encountered  has given me comfort and loads of inspiration.”

“This series extended my thinking about Story Workshop by exposing me to more diverse ways to engage with stories – outdoor, leaves/herbs, spindle whorl, clay markings etc.”

~Janice

## creating spaces for playful inquiry: thinking about the hundred languages – April 2018

Posted on: May 16th, 2018 by jnovakowski

For our final session of this year’s Creating Spaces for Playful Inquiry professional learning series, we focused on the Hundred Languages – a grounding element of the educational approach from the childcare centres in Reggio Emilia, Italy. The Hundred Languages concept is based on a poem by Loris Malaguzzi who suggests that all children have a hundred languages (or more) in which to express themselves and that are role as educators (and school systems) is to nurture these languages, not suppress them.

As Richmond educators entered the room, they were invited to they were asked to reflect on how the hundred languages are living in their classrooms.

Hundred_Languages_Provocations_April19_2018

The Richmond educators who visited Opal School in Portland over spring break shared their reflections on the experience through documentation panels.

Carrie Bourne,  Jen Yager and Julie Curran shared what they learned at Opal and how they have taken some of these ideas up in their own teaching contexts.

Marie Thom and I shared some of our experiences from our Canadian Study Tour of Reggio Emilia in March. I shared some ideas I saw about intersecting digital and analog languages through digital landscapes and Marie shared the power of the language of food and the metaphor of the table to bring people together.

After dinner together (enacting the table metaphor) our interest groups met with playful inquiry mentors to share ideas and go deeper with their understanding about playful inquiry.

We collected feedback from educators who have attended this three part series as we reflect on our learning from this year and think ahead to next year.

“Love the opportunity to collaborate with others and hear others share about their thinking/learning and what they are trying in their classrooms. It is thought-provoking and inspiring.”

“Playful inquiry and teaching is a learning process, always growing and changing and best in collaboration with others teachers and peers.”

“This series has kept me inspired when I’ve felt uninspired or simply tired.”

“This series completely changed the lens through which I see my role as the teacher and the roles of the students.”

There was considerable interest in creating opportunities for teachers to visit others’ classrooms to see playful inquiry in action and to be able to collaborate with colleagues from across the district.

Regardless of how how things unfold for professional learning opportunities in our district for next year, we know we have a strong and growing community of educators committed to teaching and learning through playful inquiry. Thanks to all of the educators involved in this series for their contributions and participation!

~Janice on behalf of the Playful Inquiry Mentors

## 2017-18 big mathematical ideas for grades 3-5

Posted on: May 13th, 2018 by jnovakowski 2 Comments

In its fourth year, a group of grades 3-5 teachers came together three times after school to think about the big mathematical ideas for this grade range, considering the pedagogical content knowledge needed to teach and assess student learning. Our first session of the year on October 18 focused on the number concepts big ideas in our curriculum which at gates 3-5 focus on a deep understanding of fractions.

We began with an image from fractiontalks.com – a website curated by Canadian math educator Nat Banting. We considered what students needed to understand about fractions to engage with this task and anticipated how are students might respond to the challenge of figuring out what fractional part of the large square is the shaded blue triangle.

We considered how different materials provided different affordances for thinking about fractions, particularly thinking about different ways to represent fractions – set, area and linear. Some of the text slides from the session and a handout follow.

BMI_October_2017_textslides

BMI_Fractions_2017

Unfortunately, I had to cancel our January session due to illness.

We came together again on April 11 and based on feedback from the group, discussed computational fluency and the role of inquiry in learning mathematics. We revisited instructional routines such as Which One Doesn’t Belong? (wodb.ca) and considered how these routines incorporate questioning, wondering and nurture the curricular competencies in mathematics.

BMI_April_2018_textslides

~Janice

## 2017-18 primary teachers study group: session 5

Posted on: May 13th, 2018 by jnovakowski

On April 12, our study group met on the dyke of the middle arm of the Fraser River. We were joined by “Indigenous Plant Diva” and current storyteller in residence for the Vancouver Public Library, Cease Wyss. A short video about Cease can be found HERE.

As we walked along the river, Cease pointed out different plants to us and shared knowledge and stories about the plants. Paying attention to a plant’s colour, shapes and texture can indicate part of the body or ailment it can provide medicine for. For example, red berries often support blood, muscles and organs.

Cease explained the importance of cattails to cleanse the water along the river as well as providing food and nesting materials for birds. We learned how some plants like dead nettle and chickweed can be used as salves to treat skin ailments and how other plants such as stinging nettle or salmonberry leaves can be infused in hot water to create teas to address different ailments.

We learned to identify plantain (frog’s leaf), dead nettle, chickweed, Nootka rose, sheep sorrel and horsetail, the oldest plant on the planet.

Teachers left with so much new knowledge about local plant species. This knowledge building is an important part of our study group and was something that was requested by teachers to enhance they work they are doing with their students around storytelling outdoors. We can find ways to share this new knowledge with our students and weave this in to our storytelling experiences.

~Janice

## March thinking together: What is computational fluency?

Posted on: May 12th, 2018 by jnovakowski

Computational fluency is defined as having efficient, flexible and accurate methods for computing.

-NCTM, 2000

Computational fluency develops from a strong sense of number.

(BC Math Curriculum, Big Idea, K-9, 2015)

In BC’s redesigned curriculum, computational fluency has been given a heightened emphasis. In mathematics, there are typically four strands of topics/content and in this iteration of our curriculum, a fifth strand – computational fluency –  has been added and this is reflected in the big ideas and curricular competencies and content.

The meta big idea around computational fluency in our BC K-9 Mathematics curriculum is:

Computational fluency develops from a strong sense of number.

There is a big idea for computational fluency at each grade level:

K: One-to-one correspondence and a sense of 5 and 10 are essential for fluency with numbers.
Grade 1: Addition and subtraction with numbers to 10 can be modelled concretely, pictorially, and symbolically to develop computational fluency.
Grade 2: Development of computational fluency in addition and subtraction with numbers to 100 requires an understanding of place value.
Grade 3: Development of computational fluency in addition, subtraction, multiplication and division of whole numbers requires flexible decomposing and composing.
Grade 4: Development of computational fluency and multiplicative thinking requires analysis of patterns and relations in multiplication and division.
Grade 5: Computational fluency and flexibility with numbers extend to operations with larger (multi-digit) numbers.
Grade 6: Computational fluency and flexibility with numbers extend to operations with whole numbers and decimals.
Grade 7: Computational fluency and flexibility with numbers extend to operations with integers and decimals.
Grade 8: Computational fluency and flexibility extend to operations with fractions.
Grade 9: Computational fluency and flexibility with numbers extend to operations with rational numbers.

As computational fluency with whole numbers is focused on in the earlier grades, it is expected that students will apply number sense and computational fluency and flexibility to their work with decimal numbers, greater numbers, integers and fractions.

For addition and subtraction and then multiplication and division, students develop computational fluency over three years – beginning with emerging fluency, then developing through proficiency and then moving on to extending fluency with increased flexibility and ability to apply strategies across contexts and content.

For example, with addition and subtraction:

In Grade 3, the curricular content learning standard is “addition and subtraction facts to 20 (emerging computational fluency)“.

In Grade 4, it is “addition and subtraction facts to 20 (developing computational fluency)”.

And in Grade 5, it is “addition and subtraction facts to 20 (extending computational fluency)”.

It is also important to be aware of what comes before and after these three stages of development. In grades 1 and 2, students are introduced to the concepts of addition and subtraction as well as the related symbolic notation. They begin to practice mental math computational strategies building on their understanding of five and ten and decomposing numbers to work flexibly with addition and subtraction questions. In grades 6&7, students apply computational strategies that they have developed for addition and subtraction facts with greater whole numbers, decimal numbers and integers.

There is a similar progression for multiplication and division facts.

A note about memorizing…memorizing is one form of learning but is not necessarily related to students having computational fluency. Many teachers in our district report that their students have memorized their addition or multiplication facts but need support with thinking flexibly and fluently with numbers. In our BC mathematics curriculum, the expectation is that by the end of Grade 3 for addition and the end of Grade 5 for multiplication,  that most students will be able to recall their facts. In a previous curriculum, recall was defined as being able to compute within three seconds. For some students, there may be instant memory retrieval and for other students they may bring the sum or product to mind through an efficient mental computational strategy or associative retrieval process.

Number Talks are an essential instructional routine in developing strategies, mathematical discourse and creating awareness about computational fluency. Key resources include:

Number Talks

BC_Computational_Fluency

So some questions to think about…

How would you define computational fluency? What does it look like? sound like?

What do your students need move towards more developed computational fluency?

What do you need to understand more about regarding a continuum of learning and specific strategies related to computational fluency?

What are different ways to develop computational fluency? What instructional routines, games or tasks could we use for practice?

How can we communicate the goals of computational fluency to parents?

~Janice

## elementary math focus afternoon 2018

Posted on: May 11th, 2018 by jnovakowski

On the afternoon of January 26, staffs from twelve elementary schools gathered at Grauer Elementary for our annual Elementary Math Focus Afternoon.

The overview slides (photographs from classrooms not included to reduce file size) from the opening to the afternoon can be found here:

Math_Focus_Opening_2018_textslidesonly

Many school teams brought displays to share how they have been working with BC’s redesigned mathematics curriculum.

Educators could choose from a variety of Richmond teacher-led sessions to learn about instructional routines and practices that are aligned with the BC redesigned curriculum.

FINAL_Elementary Math Focus Afternoon Jan 26 2018 program