big mathematical ideas for K-2 2018

Posted on: December 19th, 2018 by jnovakowski

This fall we hosted a three-part after school professional learning series focusing on the big mathematical ideas in Kindergarten thru Grade 2. We have been doing this series for grades 3-5 teachers for the last five years and this year have added series for K-2 and grades 6-9 teachers. The focus of the series is to look at the foundational math concepts within the grade band and consider ways to develop those concepts and related curricular competencies. Other curricular elements such as core competencies, First Peoples Principles of Learning, use of technology and assessment are woven into the series.

September 27

We discussed three instructional routines focused on counting: choral counting, count around the circle and counting collections. The following are the professional resources that were recommended and every teacher attending was provided with a copy of Christopher Danielson’s new book How Many? and the accompanying teachers guide.

We shared the idea of unit chats which is the essence of the book How Many? What could we count? What else could we count? How does the quantity change as we change the unit we are counting?

We also introduced Dan Finkel’s website and his section of photographs that can be used for unit chats HERE.

Between the first and second sessions, teachers were asked to try one of the counting routines, read parts of the How Many? teacher guide, try a unit chat with their classes and do the performance task with one of their students.

October 25

We spent the first part of our session together sharing with each other about a counting routine they did with their class, how their students responded to unit chats and their findings from the performance task. Teachers brought video, photos and student work to share and discuss.

We discussed the importance of research-based learning trajectories/progressions to inform our instructional and assessment practices. The BC Numeracy Network has collated several learning trajectories/progressions HERE (scroll down to the bottom of this page).

We introduced the draft of the new SD38 Early Numeracy Assessment Tool which is intended to use with students from the end of Kindergarten through grade 2 to create class learning profiles and well as help identify specific learning goals for students. It can also be used by schools to monitor student progress over time. The assessment tool focuses on key areas of number sense and the tasks are drawn from the BC Early Numeracy Project and the work from the Numerical Cognition Lab at Western University. Teachers were asked to complete the assessment with one student they were curious about learning more about.

November 22

We began our session sharing how it went with the new K-2 assessment tool. The teachers had lots of good feedback and suggested edits which will now be taken back to the district committee for final revisions.

We shared some different materials and experiences to support the development of K-2 students’ number sense, connecting the ideas of counting, subitizing, connecting quantities and symbols and ordering/sequencing. One of our favourite materials is Tiny Polka Dot, which I personally believe should be in every K-2 classroom (available in Canada through amazon.ca HERE).

We also went over the ten frame games and tasks that can be used in K-2 classrooms for purposeful practice during math workshop or small group instructional time.

Teachers and their students took photographs to contribute to our own digital How Many? book and it is a work in progress but the collection we have so far can be found here (best viewed via Chrome):

How Many? digital book

Look for information and  next steps for our SD38 K-2 Numeracy Assessment Tool in the new year!

~Janice

creating spaces for playful inquiry: encounters with charcoal

Posted on: December 14th, 2018 by jnovakowski

To launch the 2018-19 season of our ongoing professional learning series, Creating Spaces for Playful Inquiry, we created opportunities for educators to have encounters with charcoal and make connections to teaching and learning across the BC curriculum. Inspired by our learning from Opal School in Portland to use different materials to explore ideas and emotions through an aesthetic dimension, we chose charcoal specifically as we believed it was a material that educators might need some support with, in understanding the material in new ways.

We shared a blog post from the Opal School Blog: Thinking with Charcoal

and shared the Canadian books The Art of Land-Based Early Learning (volumes 1 and 2) that can be found HERE.

I actually experimented with making my own charcoal. I trimmed some willow branches from my backyard, tightly wrapped them in cheesecloth and then aluminum foil (to eliminate any oxygen inside) and put them in our fire pit. I didn’t have enough wood to maintain a high enough heat for long enough (researched needing about an hour) so I “finished” the packages the barbecue. They worked out quite well but next time, I will strip the bark off the twigs first.

We curated a collection of charcoal and related materials from DeSerres and Phoenix Art Studio

and invited educators to engage with materials, ideas and concepts.

Our resource document about charcoal, including the questions provided to provoke educators’ thinking can be found here:

playful_inquiry_charcoal_2018

Some educators commented that it was their very first time using charcoal themselves and they reflected on what it meant to explore a material for the first time, how that made them feel both curious and vulnerable and also sparked many connections and ideas for using charcoal with their students.

Two of our playful inquiry mentors, Sharon and Christy, shared experiences and stories from their classrooms

and then after dinner together, we broke off into mentor group to share ideas and think together about ways to engage with playful inquiry this school year.

We have been growing our playful inquiry community in our district for several years now with both our own initiatives and projects as well as continuing to nurture our relationship with Opal School and it is exciting to continue to welcome teachers into our conversations. Our next district event will be an open studio at the district conference on February 15 and a playful inquiry symposium on the afternoon of the district pro-d day on May 17.

~Janice, on behalf of the playful inquiry mentors

2018-19 primary teachers study group: session 2

Posted on: December 12th, 2018 by jnovakowski

Our second session of this year’s primary teachers study group was hosted by Anna and Shannon at McNeely Elementary. Anna shared the book about mushrooms that her students researched and wrote after finding and investigating the mushrooms they found in their mini-forest near the school.

The class was also inspired by one of our study group books, Anywhere Artist, and went out into their mini-forest to create art with found materials.

The land art of UK artist James Brunt (on twitter at @RFJamesUK) also inspired us to take on the #100LeavesChallenge.

Anna and Shannon toured us through McNeely’s new outdoor learning space and through their mini-forest, adjacent to the school.

Together we shared ideas for how different plants, trees and animals could inspire mathematical thinking or questions to investigate.

Thank you to Anna and Shannon for hosting us!

~Janice

2018-19 primary teachers study group: session 1

Posted on: December 12th, 2018 by jnovakowski

Beginning our sixteenth year, the Richmond Primary Teachers Study Group met for the first time this school year on October 11 at Diefenbaker Elementary. As agreed upon by study group participants, this year’s focus is on the teaching and learning of mathematics in places and spaces outdoors, considering both how to take mathematics outdoors but also how the outdoors can inspire mathematical thinking.

Our three study groups books that we are going to draw inspiration from this year are:

Messy Maths by Juliet Robertson

50 Fantastic Ideas for Maths Outdoors by Kristine Beeley

Anywhere Artist by Nikki Slade Robinson

There are so many books and resources available to support our professional inquiry together this year.

We spent some time exploring the Diefenbaker garden, playground and new outdoor learning area and considering what math we could find in these spaces.

One of the tasks we did was using materials or referents to estimate and create the length of one metre. We followed this up by each making our own “Sammy the Snake” – a one metre length of rope (idea from the Messy Maths book). This length of rope can be part of a “go bag” to take outside for measuring lengths, perimeter, circumference of trees and to think about fractions (by folding the length of rope). It is a flexible tool to support students’ developing understanding of comparing, ordering and constructing concepts of measurement and number.

Thanks to the Diefenbaker team for hosting us!

~Janice

December thinking together: visualize to explore mathematical concepts

Posted on: December 11th, 2018 by jnovakowski

This month’s focus is on the curricular competency: visualize to explore mathematical concepts.

In the 2007 WNCP mathematics curriculum, visualization is defined as involving “thinking in pictures and images, and the ability to perceive, transform and recreate different aspects of the visual-spatial world”. Concepts such as number, spatial relationships, linear relationships, measurement, and functions and relations can be explored and developed through visualization.

In the new BC grades 10-12 courses, the elaborations for this curricular competency are:

• create and use mental images to support understanding
• visualization can be supported using dynamic materials (e.g., graphical relationships and simulations), concrete materials, drawings, and diagrams

Visualization and spatial reasoning involve the relationship between 2D and 3D shapes as well as dynamic imagery such as different perspectives, movement, rotations and reflections. Visualizing involves an interplay between internal imagery and external representations  (Crapo cited in NRICH article below). Students need experience with concrete and visual representations/pictures/models as well as being able to visualize something in their minds, often referred to as the “mind’s eye”.

Canadian and International research has shown that there are links between strong abilities to visualize and success in mathematics. One widely used psychological assessment for visualization involves “The Paper Folding Test”  in which a paper is folded and a hole is placed through a specific location and the participant is asked to visualize what the paper will look like when it is unfolded, utilizing the ability to generate, maintain and manipulate a mental image, (Lohman, 1996 cited in Moss et al 2016). A recent study also found a link between the ability to visualize and success with solving mathematical word problems, citing the ability to mentally visualize and make sense of the problem contributed to success in diagramming and solving problems (Boonen et al 2013 cited in Moss et al 2016). The Canadian work of (Moss et al 2016 ) and their Math for Young Children research project focuses on spatial reasoning and the importance of developing students’ flexible use of visualization skills and strategies.

Instructional Resources

The book Taking Shape (referenced below) provides several visualization tasks on pages 30-35 but visualization is an important component of most of the spatial reasoning tasks in the book.

Quick Images is an instructional routine that supports the visualization of quantities and shapes. Dot patterns and composition of shapes are often used as quick images. More information and videos can be found on the TEDD website HERE.

A short article from the NCTM explaining the connection between visualization and subitizing can be found here:

NCTM_quickimages_tcm2016-12-320a

Fawn Nguyen has compiled a collection of visual patterns HERE. Visual patterns provide the first three steps of the pattern and then students are asked to visualize the next steps, which involves both arithmetic, algebraic and geometric thinking.

Desmos in an online graphing calculator that allows for students to predict,

visualize and graph linear relationships and functions and relations.

So what does it mean to be proficient with visualizing?

As we begin to work with the new proficiency scale across BC, we need to consider what it means to be proficient with visualizing to explore mathematical concepts in relation to the grade level curricular content. As more teachers across the provinces the the scale, we will have examples of student proficiency that demonstrates initial, partial, complete and sophisticated understanding of the concepts and competencies involved.

For example, a grade six student at the end of the year would be considered proficient with visualizing geometric transformations if they were able to follow directions to mentally translate, rotate and reflect a 2D shape and show or describe the resulting orientation/position.

Some questions to consider as you plan for learning opportunities to develop the competency of visualizing:

How is the core competency of communication developed through the process of visualization? What different ways can students show and explain what they are visualizing – using materials, pictures or words?

How do the competencies of estimating and visualizing complement each other to support reasoning and analyzing in mathematics? How can using visual referents support estimating?

How can we help students understand the purpose and usefulness of developing visualization skills and strategies? What examples can we share of scientists and inventors that used visualization to develop theories and ideas?

What opportunities are we creating for students to practice and use visualization skills and strategies across different mathematical content areas such as geometry, measurement, number, algebra and functions?

~Janice

References

Thinking Through and By Visualizing (NRICH)

The Power of Visualization in Math by Jeremiah Ruesch

Spatial Reasoning in the Early Years: Principles, Assertions, and Speculations by Brent Davis and the Spatial Reasoning Study Group, 2015

Taking Shape: Activities to Develop Geometric and Spatial Thinking by Joan Moss, Catherine D. Bruce, Tara Flynn and Zachary Hawes, 2016

number glass gems

Posted on: September 18th, 2018 by jnovakowski

One of the elements of The Studio at Grauer that teachers often notice is the collection of numerals we have in baskets and trays on our shelves. I have collected these over the years and find them in craft and scrapbooking stores, thrift stores, Habitat for Humanity ReStore, and Urban Source on Main Street in Vancouver. I am always on the lookout for numerals. Students use them in their play and investigations, ordering them, using them to label/represent their collections or sets of materials or to use as purposeful numbers in their creations (addresses, phone numbers, parts of a story, etc).

Just to clarify some terms…

Digit – A digit is a single symbol used to make numerals. 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are the ten digits we use in our number system to make numerals.

Numeral – A numeral is a symbol that stands for a number.

Number – A number is a count or measurement that represents an idea in our mind about a quantity.    Numerals are often used to represent a number.

It is how these materials are used that leads to them becoming called numbers – they are used to connect meaning to the symbols by matching the symbol to a set or quantity or are put in order/sequence which gives meaning to the symbols. They can also be used to represent the number in an expression or equation.

I chose to make my most recent set of glass gems using the digits 0-9. This way students can put them together to create different numerals/numbers to label their representations/sets/quantities.

Materials needed: large glass gems (found at Michael’s and some dollar stores), foam paintbrush, Mod Podge and number stickers or cutouts

Instructions: Using the flat side of the glass gem, apply a light coat of Mod Podge and lay a numeral upside down, centred on the back of the gem. Press down and smooth surface so that the numeral adheres and there are not air bubbles between the surfaces. Let dry for a couple of minutes and then apply a coat of Mod Lodge to the entire surface of the flat side of the glass gem. Let dry for 20-30 minutes and then apply a second coat. Let dry and then they are ready to be used.

We have also created materials similar to this by adhering stickers to tree cookies/slices or to smooth stones. It’s just handy to have a collection of these and students find all sorts of ways to use them.

~Janice

school-based collaborative professional inquiry projects

Posted on: June 14th, 2018 by jnovakowski 1 Comment

One of the professional learning structures used in our district is collaborative professional inquiry based in schools. I collaborate with school teams that come together with a focused area of professional inquiry in the area of mathematical teaching and learning. I support the school teams through developing curricular and pedagogical content knowledge through mini-sessions and providing resources as well as planning together and engaging in adapted lesson study including time each visit to debrief and plan next steps. This year, all school teams involved included at least one teacher in the district’s mentoring program as we focus on supporting teachers new to our district and to the profession.

General Currie (term 1)

The three kindergarten teachers at Currie (two new to teaching K) chose to focus on core concepts and inclusive instructional routines related to these concepts. Inclusive routines are those that provide access points for all students in the class and are used regularly over time to develop mathematical thinking and ideas. The routines focus on developing the mathematical curricular competencies and content in our curriculum. Over several sessions in the kindergarten classrooms we engaged in routines such as counting collections, clothesline, decomposing and number provocations. The three teachers and their classes followed up this project with a field trip to The Studio at Grauer.

Garden City (terms 1 & 2)

Three small groups of kindergarten through Grade 5 teachers came together with a combined focus of “connecting the dots” of the redesigned curriculum – weaving together key elements such as inquiry, teaching and learning through big ideas, new content areas like financial literacy and a focus on First Peoples Principles of Learning and connecting math to place. I spent several sessions in classrooms co-teaching with teachers and having lunch hour meetings.

Tomsett (term 2)

A large group of kindergarten through grade 6 teachers chose to focus on supporting student learning of number concepts through a guided math approach. This approach to teaching math was new to all of the teachers involved. A guided math session (often done once or twice a week) has a focus of a core math concept as the focus. A whole group mini-lesson or routine begins the session followed by opportunities for students to practice in small groups or independently. This practice may involve working with materials, math games, an open task or problem or using an app with visual tools that support mathematical understanding. The teachers works with small groups of 2-5 students round this core math concept for about 5-8 minutes, designing and structuring a mini-lesson for them at their “just right” math level of understanding. The is an opportunity for the teacher to collect assessment evidence of students’ understanding. The end of the session involves connecting the dots between the practice opportunities and consolidating students’ thinking through sharing and discourse.

I spent several in-class sessions with student and teachers as well as lunch hour debriefs, sharing and planning with the teachers.  In between my visits, the teachers collaborated and shared resources and ideas amongst themselves. At the end of the term the grades 5&6 teacher reflected on how the project had transformed her teaching and commented that she will never go back to teaching math the way she used to. All of the teachers commented on how much better they knew each of the students’ mathematical understanding through this approach.

Steves (terms 2 &3)

A team of four grades 2-5 teachers chose to focus on structures that support differentiation in mathematics teaching and learning. In-class co-teaching sessions and lunch hour meetings focused on inclusive instructional routines, rich open tasks and providing choice with a lens to addressing the range of learners in each classroom. In the grades 2&3 class routines such as number talks and Which One Doesn’t Belong? and games were introduced and extended through work with materials. In the grades 3&4 and 4&5 classes, some of the structures we focused on were choice – choice of materials and choice of ways to represent thinking. We also used open questions and contextual problems that focused on big ideas and core concepts and considered how these tasks provided access points for all learners.

I always enjoy being immersed in classrooms and schools, learning together with teachers and students!

~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

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 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