french immersion Archive - Mathematics and Science in SD#38 (Richmond)

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2018-2019 primary teachers study group: session six

Posted on: June 7th, 2019 by jnovakowski

Our final session of the year was hosted at Thompson Elementary on May 16. Inspired by our core resource, Messy Maths by Juliet Robertson, we created outdoor ten frames using pieces of cotton fabric and sharpies. These ten frame can be used to count quantities of found objects to ten as well as using for grouping smaller objects like pebbles or acorns. And they are washable and re-usable and can be used in the rain which makes them ideal for outdoor learning where we live!

We also used rubber mallets on cotton cloth to create leaf and flower prints to explore the shape, size and symmetry of local plants. This is the just right time of year to do this when the cells of plants and petals are full of moisture.

Teachers shared the different ways we have been using our focus picture book Flow, Spin, Grow by Patchen as we have found growing, swirling and branching patterns outdoors.

We also shared information about the Lost Ladybug Project – a fun way to engage students in looking closely for ladybug species, taking photographs and sharing the location of the find with the world through the website HERE

The Thompson team toured us through their outdoor learning space and showed us their student’s mapping project.

Thank you to Denise, Tanya and Danielle and their teacher candidates for hosting us!

We have surveyed the group and it looks like next year’s focus will be interdisciplinary learning outdoors. We will be able to connect our work around storytelling and math outdoors from the last two years as we move forward together in our professional learning.

~Janice

May thinking together: explain and justify mathematical ideas and decisions

Posted on: May 26th, 2019 by jnovakowski

This month’s curricular competency focus is explain and justify mathematical ideas and decisions. This curricular competency is the same across grades K-12 and is included in the Grades 10-12 courses with the addition of “in many ways“.

This competency falls under the organizer of “Communicating and Representing” is also connected to the Core Competency of Communication, particularly the aspect of explaining and reflecting on experiences.

Elaborations are suggestions for educators to consider as they plan for developing this curricular competency:

mathematical arguments

What is a mathematical argument?

A mathematical argument is the debate and discussion of a mathematical problem or task. This involves the explanation and justification of the reasoning, problem-solving process and the solution. As stated by Small (2017), the ability to create a sound mathematical argument is developed over time.

A common instructional routine in our district is Number Talks. During this routine, students are asked to share their mental math strategies for solving questions involving number operations. Part of this routine is defending or “proving” their solution through their strategy explanation. Other students may agree with, build on or argue with the strategies used. A focus of this routine is both building mathematical discourse structures as well as building the listeners, connectors and reflectors needed in a mathematical community. During Number Talks, students listen to each others’ explanations and justifications and then also use mathematical language to communicate their own mathematical arguments. Before orally sharing their explanations to the whole group, students are often given the opportunity to turn and talk, or think in their head to formulate and rehearse their explanations.

In the book Teaching Mathematical Thinking, author Marian Small (2017) suggests the language that develops during mathematical argumentation and discourse may sound like this:

“I agree with ______ because _______.”

“I didn’t understand why you __________.”

“I disagree with ___________ because ____________.”

“I wonder why you _____________.”

“What if you had _____________.”

Small (2017) provides some examples of open question that nurture mathematical argumentation. For example, for grades 3-5 students:

Liz says that when you multiply two numbers, the answer is more likely to be even than odd.

Do you agree or not? Why?

And for grades 6-8:

A store employee noticed that an item’s price had been reduced by 30% and realized it was a mistake. So she added 30% back to the reduced price. Avery said the price is the same as it used to be but Zahra disagreed.

With whom do you agree? Why?

What tasks like these are we presenting to students to intentionally nurture and practice the development of explaining and justifying mathematical ideas and decision-making?

Mathematician Dan Finkel shares the importance of conjectures and counterexamples in his playful instructional approach. More information can be found on his website mathforlove.com

In the following example from Dan, a student made a conjecture that if you multiply both factors by two, the product will stay the same. Can you think of a counterexample that disproves this?

In their book But Why Does It Work? Mathematical Argumentation in the Elementary Classroom (2017), authors Susan Jo Russell et al share an efficient teaching model focused on mathematical argument for developing the ability of students to justify their thinking and engage with the reasoning of others. Their model supports students in:

noticing relationships across sets of problems, expressions or equations
articulating a claim about what they notice
investigating their claim through representations such as manipulatives, diagrams, or story contexts
using their representation to demonstrate and explain why their claim must be true or not
extending their thinking from one operation to another

In their book Teaching with Mathematical Argument (2018), authors Stylianou and Blanton suggest that a focus on justification and explanation of thinking can celebrate the diversity of thinking within our classrooms. From their book:

“How can argumentation be a goal and an expectation for all students? One strategy is to embrace students’ use of diverse strategies. This diversity can then be used to plan cognitively demanding instruction that includes argumentation and that allows all learners to build from their own thinking and access their peers’ thinking to develop their understanding of new concepts. Rich, open tasks that invite argumentation are challenging because of their open nature. However, their openness also allows access to students who struggle in mathematics. Being open implies having more than one entry point, which makes such tasks accessible to students who often struggle to follow one particular procedure.”

By honouring the diverse thinking of the learners in our classrooms, we are also nurturing the important idea that there isn’t “one right way” to do or think about mathematics. Creating entry points for all students to explain and justify mathematical ideas is part of creating a safe mathematical community for all.

Some questions to consider as you plan for learning opportunities to develop the competency of explaining and justifying mathematical ideas and decisions:

How do we support students and families in understanding that explaining and justifying your answers and processes is an important part of mathematics?

What problems and tasks are we presenting to students to intentionally nurture and practice the development of explaining and justifying mathematical ideas and decision-making?

What visual and language supports might support students as they engage in mathematical discourse and argumentation?

What opportunities do students have to notice patterns and relationships, make conjectures and generalizations across mathematical concepts? What ways could they share and explain their mathematical ideas by using materials, pictures or diagrams, stories or contexts or numbers and symbols?

How might technology provide access for students or transform the way they are able to explain and justify their mathematical ideas and decisions?

~Janice

References:

But Why Does It Work? Mathematical Argument in the Elementary Classroom

by Susan Jo Russell, Deborah Schifter, Virginia Bastable, Traci Higgins, Reva Kasman

Heinemann Publishers, 2017

Teaching with Mathematical Argument: Strategies for Supporting Everyday Instruction

by Despina Stylianou and Maria Blanton

Heinemann Publishers, 2018

Teaching Mathematical Thinking: Tasks and Questions to Strengthen Practices and Processes

by Marian Small

Teachers College Press/Nelson, 2017

Promoting Mathematical Argumentation by C. Ramsey and W. Langrall (2016). Teaching Children Mathematics (volume 22), number 7, pages 412-419.

April thinking together: communicate mathematical thinking in many ways

Posted on: April 30th, 2019 by jnovakowski

This month’s curricular competency focus is communicate mathematical thinking in many ways. This curricular competency is the same across grades K-9 and is included in the Grades 10-12 courses as “explain and justify mathematical ideas and decisions in many ways“.

This competency falls under the organizer of “Communicating and Representing” which includes the following related competencies:

Elaborations are suggestions for educators to consider as they plan for developing this curricular competency:

communicate using concrete, pictorial and symbolic forms
use spoken or written language to express, describe, explain, justify and apply mathematical ideas
use technology for communication purposes such as screencasting and digital photography and videography

There are clear connections between the Core Competency of Communication with this grouping of curricular competencies. A one-page table showing the language of both types of competencies can be downloaded here:

SD38 K-5 Math Communication_Avenir

An important part of communicating mathematical thinking in many ways is to be able to use different forms such as concrete (materials or math manipulatives), pictorial (drawings, diagrams, tallies) or symbolic forms (numerals and symbols).

An example from primary classrooms of how students may move from concrete to symbolic notations is with the use of materials such as base ten blocks. Students may communicate their understanding of numbers by creating that number with materials and then recording the symbolic notation. The following are some examples from a grades 2&3 classroom at Cook Elementary that show how children used concrete, pictorial and symbolic forms to help them solve and communicate their solutions for mathematical problems.

As students begin to understand a concept, such as multiplication, they usually construct a representation with materials to build understanding. These representation may then be recorded pictorially and then labels are added using symbolic notation. This fluency between forms is important and the connections between representations is essential to conceptual understanding. A student may be presented with a symbolic form (such as an equation) and asked to show a concrete form or pictorial form that “matches”. The following are examples from a grades 2&3 classroom at Tomsett Elementary.

For our intermediate and secondary students, it is still important to be using concrete materials, especially when students are developing their understanding of a new concept such as fractions, decimals, or integers. The following are examples from a grades 4&5 classroom at Homma Elementary

and also more fraction investigations with a grades 4&5 class at Steves.

In our curriculum, the terms “concrete, pictorial and symbolic” are used in ways for students to think about concepts but also to communicate and represent their thinking. In some other jurisdictions around the world, the term CRA is used to reference an instructional approach to concept development, standing for Concrete, Representational and Abstract. More information can be found HERE. There is some overlap between the the CRA framework and how our curriculum focuses on concrete, pictorial and symbolic communication of mathematical thinking and understanding.

Another area of focus in our district is using iPad technology for students to communicate their thinking and learning. One of the most common uses of the devices in math is to use screen casting apps such as doceri, ShowMe, Explain Everything or 30Hands. When students screencast, they can take a photograph or video of what they are doing and then annotate with arrows, words etc and then orally describe their problem-solving process or thinking. For example, in a grade 8 class at Hugh Boyd Secondary, students took images of number balances they used to develop their understanding of equivalence in algebraic equations and then communicated their thinking by orally explaining their understanding.

Some questions to consider as you plan for learning opportunities to develop the competency of communicating mathematical thinking in many ways:

How is the core competency of communication noticed, named and nurtured during the teaching and learning of mathematics?

What different materials are students learning to use, think through and represent with? What materials are mathematically structured and what other types of materials might we offer to students?

What opportunities are we providing for students to share their thinking in different ways? Are students provided with choices and is there a balance in the different ways students can communicate their mathematical thinking?

How might technology provide access for students or transform the way they are able to communicate their mathematical thinking?

~Janice

2018-19 primary teachers study group: session 4

Posted on: March 11th, 2019 by jnovakowski

Our fourth session was held at Blair Elementary, hosted by Karen and Tanyia. They shared the development of their outdoor learning space and how it and the gardens are being used by teachers and students in the school.

We walked around the school grounds, looking for inspiration for mathematical thinking. At this time of year, you can really see the structure of the deciduous trees and it is an opportunity to notice lines, shapes and angles. With moss and lichen growing on some trees and on fences, there are lots of math-inspired questions that can be investigated around the life cycle, size and growth of these unique living things.

We noticed many trees with some interesting growth patterns and markings (some caused by pruning according to our master gardener Megan). What stories live in these trees? What might a timeline of a tree’s life look like? Seasons, years, decades – such an interesting lens to explore concepts of time through.

Sarah Regan and Megan Zeni were awarded this year’s June Chiba Sabbatical and used their release time to visit several outdoor/nature focused schools across southern BC. We were happy to host them and have them share some of their experiences.

Our next study group book is the Canadian children’s book Flow Spin Grow: Looking for Patterns in Nature. It connects really well with our focus this year of finding and investigating mathematics outdoors. After sharing our focus on twitter, the author shared his website where he has curated some resources to complement the book HERE.

I know my eyes will be open for all sorts of patterns – branching, spiralling, spinning – as spring emerges around us.

Have a lovely spring break!

~Janice

2018-19 primary teachers study group: session 3

Posted on: March 11th, 2019 by jnovakowski

Our third session was hosted by Jessica, Lisa, Laura and Sasha at Anderson Elementary. A couple of the teachers are particularly knowledgable about mushrooms and shared information about the fungi in the neighbourhood.

We walked through Garden City Park and the Anderson teachers shared how they use the space over the school year to observe and document seasonal changes. The students were also very observant of how the windstorms this fall/winter affected the park and the changes created by the storms. The City of Richmond has created an arboretum area on the west side of the park, with plaques identifying and describing the trees. There is also the opportunity to observe birds and other urban wildlife in the park.

A focus of some of the teachers has been on the human impact on the local environment. Some questions for teachers and students to consider:

How can mathematics help us to understand this issue?

What data/information could be collected and how could it be shared?

What information could be collected?

How might different ways of sharing information have an impact on understanding of the issue?

What actions could we take?

Looking forward to seeing how different schools and classes make connections between mathematics and their outdoor environment.

~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

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

Handouts from Fred Harwood’s sessions can be downloaded here:

Elem Focus Day Jan 2018 Rich Investigations

2018 Elem Math Focus Visual patterns

Thanks to Tracy Weeks of the Canadian Federation for Economic Education (CFEE) for coming and sharing information about financial literacy with Richmond educators.

As educators gathered back in the gym for an end of afternoon prize draw of math resources, they were left with a reminder to consider the mathematical story that is being told in their classrooms and schools. What story do we want our students to tell about their mathematical experience here in our district?

~Janice

creating spaces for playful inquiry: thinking about reflection – January 2018

Posted on: May 11th, 2018 by jnovakowski

On January 25, Richmond educators gathered at Grauer for our second dinner session of our Creating Spaces for Playful Inquiry professional learning series. This month our focus was on reflection and time. Educators shared their experiences engaging in playful inquiry with their students and considering the role of reflection in documentation and making both students’ and our professional learning visible.

After dinner together, teachers participated in interest groups facilitated by our playful inquiry mentors.

A handout with curricular connections to the idea of reflection can be found here: Reflections_Provocations_Jan25_2018

~Janice

2017-18 primary teachers study group: session 2

Posted on: May 10th, 2018 by jnovakowski

On December 7, Anne-Marie Fenn hosted our primary teachers study group at Woodward Elementary. We went outside and Anne-Marie shared the vision and plans for their new outdoor learning space.

As the sun was going down, we played with the elements of light and shadow and considered ways we could include these ideas into our outdoor (or indoor) storytelling experiences, thinking about how these ideas might enhance or add new problems to students’ stories.

After coming back in to Anne-Marie’s classroom as it started to get dark, teachers shared different outdoor storytelling experiences they had tried with their students.

Thanks for hosting us Anne-Marie!

~Janice

creating spaces for playful inquiry: thinking about relationships – September 2017

Posted on: October 5th, 2017 by jnovakowski 1 Comment

Inspired by our staff’s visits to the Opal School in Portland, we continue this year with our Creating Spaces for Playful Inquiry Series. Sixty Richmond educators registered for this three-part dinner series, with a growing waiting list of educators wanting to be part of this series. This continued interest in this work speaks to the ripple effect that our playful inquiry community is having in schools and in our district. Many new teachers have heard about playful inquiry and how it aligns with goals and aspects of BC’s redesigned curriculum. A goal for the series is for teachers to consider: How can we create new possibilities for joy, wonder and inspiration?

So what is playful inquiry? Playful inquiry is not a new term and much has been written about it as a pedagogical stance. In Richmond, we have drawn upon our experiences and relationship with the Opal School in Portland and made connections to our BC context and curriculum. At our last study tour to Portland in March, the following explanation of playful inquiry was provided:

In this explanation of playful inquiry words such as community, collaboration, citizen and uncertainty pop out. The term “learning alive” resonates with the spirit of inquiry we are hopeful of nurturing in our classrooms. Why playful inquiry? The above definition suggests an approach that will support students in thinking through the uncertainty in the world around them and nurture student agency in seeing themselves as contributing citizens in their community. So we can work together towards the goals and vision of what playful inquiry can bring to our classrooms and schools.

So how do we enact playful inquiry in our classrooms? For planning purposes, we often use the framework of –

playing with materials
playing with language
playing with ideas

to help us consider different ways to engage our students and ourselves with playful inquiry.

Playful inquiry creates opportunities for deeper engagement with concepts and idea, choice in ways students may pursue uncovering the curriculum, personalization and meaning-making as well as providing openings for connection-making, seeking relationships – both with self, each other and with ideas.

*****

As teachers arrived at Grauer Elementary, they were provided with provocations created by our playful inquiry mentors. These provocations were either pedagogical – meant to experience through the lens of an educator and to reflect on practice or, were those that students engaged with in Richmond classrooms.

After a welcome, introductions and an overview of the series, teachers shared and discussed questions such as:

What is a provocation? How is a provocation alike and different from an invitation or a rich open task?

Some conditions for provocations were shared:

responsive
provokes thinking
connects to a big idea, concept or theme
is ongoing, lingering, extends

We talked about the theme of relationships for this session and how relationships were an inherent part of teaching and learning – social and emotional relationships but also relationships with and between curricular ideas. Some of the provocations shared and how the concept of relationships is embedded throughout our BC curriculum were provided to participants here:

SD38_Relationships_Provocations_Sept28_2017

Other big ideas and themes that we have engaged with as a playful inquiry community were shared:

Three of our playful inquiry mentors shared stories from their classrooms. Michelle Hikida from Diefenbaker shared how her and grades 2-4 group planning team are focusing on the big idea of stories this year and how they collaborate together to plan provocations based on students’ interests an questions. Laurie David-Harel from Whiteside shared the movie trailer she created for her school’s parent evening to share how the Kindergarten students in her class engage in playful learning. Karen Choo from Blair shared how sharing circles and using clay as a metaphor supports relationship building in her grades 4&5 classroom.

After dinner together, teachers met in interest groups with conversations and sharing facilitated by our playful inquiry mentors.

Many of the interest-based inquiry groups will continue their conversations with schools visits, online collaboration or other forms of sharing before our next whole group session together in January.

Participants were asked to consider what “one thing” they will play with, try , take risks with…what might be your one thing?

Blog posts from previous years can be found HERE

More information about the Opal School can be found HERE

~Janice