Archive for the ‘primary’ Category

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

Posted on: May 16th, 2018 by jnovakowski No Comments

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.

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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.

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

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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.

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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.

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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.

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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.

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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.

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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.

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~Janice

2017-18 primary teachers study group: session 5

Posted on: May 13th, 2018 by jnovakowski No Comments

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.

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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.

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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 No Comments

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.

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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:

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Number Talks

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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 No Comments

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:

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

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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

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

Elem Focus Day Jan 2018 Rich Investigations

2018 Elem Math Focus Visual patterns

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

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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?

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~Janice

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

Posted on: May 11th, 2018 by jnovakowski No Comments

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.

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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 4

Posted on: May 10th, 2018 by jnovakowski No Comments

On March 1, the primary teachers study group met at the Richmond Nature Park. We shared resources for learning about local living things and discussed the different services the Nature Park provides to schools and the community. The Nature Park is situated on a bog which is a very unique ecosystem.

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We visited different areas of the park, watching the birds come and go from the feeders, walking along the trails and boardwalk area.

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How does looking closely at a found object help you think about its story? What is the story of this (skeleton) leaf?

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There was still snow on the ground in some of the more shaded areas of the park and we used the snow as a story context. How could we use the snow as a background for map-making? We used found natural materials to create a map of a special place to inspire memories and story.

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The Nature House has lots of interactive displays. living things (including a functioning bee hive), and lots of information about species of plants and animals living in Richmond. Brochures are available listing local plants, birds and insects as well as brochures with self-guided tours of the park. We were all keen to continue to build our own knowledge of local species to be able to weave this knowledge into the outdoor learning experiences we are creating for our students.

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The Nature Park Society’s website can be found here: Richmond Nature Park Society

The City of Richmond’s Nature Park web page can be found here: City of Richmond – Nature Park

~Janice

2017-18 primary teachers study group: session 3

Posted on: May 10th, 2018 by jnovakowski No Comments

On January 18, Cori and Jen hosted the primary teachers study group at Diefenbaker Elementary. Teachers shared the different storytelling experiences they have been engaging in with their students.

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We went outside to a small stand of trees near the school and used natural clay from Deserres to create story trees with found, natural materials.

How might the shape, texture, crevices, branches or bark of a tree inspire a story?

What different parts of a tree could be the site for a story setting?

How can we transform clay to create characters for our stories? What can we add to clay? How can we spread and mold the clay? How might water transform the clay and our stories?

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One of our young guests created a dinosaur and was happily telling stories while the adults also played!

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As we left the traces of our stories behind, we wondered what families would think and wonder as they encountered them on their walk to school the next morning and what new stories might be inspired.

~Janice

February thinking together: How can we rehumanize mathematics?

Posted on: March 1st, 2018 by jnovakowski No Comments

For February, let’s consider how can we rehumanize mathematics?

I was able to attend and present at the NCTM Regional Conference in Chicago this past November/December.

Words that came up over and over again throughout the conference were: EQUITY, ACCESS, EMPOWERMENT, POWER, AUTHORITY, PRIVILEGE, IDENTITY and AGENCY.

These may not be the words you may initially think of when you think about major themes at a mathematics education conference but there is a definite shift in how the role of mathematics within a society is viewed, and who is being included and what voices are being heard.

The conference opened with a panel of speakers addressing issues of access, equity and empowerment.

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The link to the archived Facebook live video form the opening session of the NCTM Regional Conference in Chicago on November 29 2017 is HERE

Kassia Omohundro Wedekind shared her thoughts on “hands down, speak out” practices, disrupting the traditional practice of having students putting their hands up to respond to questions, which in classrooms often reflects the inequities in society at large. She encourages teachers to create conversation maps of the mathematical discourse in their classrooms and to encourage all students to see themselves as mathematicians and contributors to the discourse.

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Dr. Tyrone Howard discussed the issues of inequity in classrooms with regards to race. He affirmed the importance of context and that students’ issues of identity need to be addressed.

Annie Perkins shared practices from her own secondary classroom that support all her students in seeing themselves as mathematicians. She developed “The Mathematicians Project” with a focus on introducing students to mathematicians that are “not just white dudes”.

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Dr. Rochelle Gutierrez is a well recognized researcher and author in the area of equity in mathematics. Over the last few years, her papers and presentations have focused on the idea of re-humanizing mathematics. Photos of some of her slides provide a beginning glimpse into her work. What stands out for you? What are curious about learning more about?

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Another presentation from Dr. Rochelle Gutierrez that might be of interest and would be great to share with during a pro-d day to open up discussion around equity, access and culturally responsive pedagogies for all students:

NCTM 2016 ShadowCon: Stand up for Students 

Dina Williams closed the opening panel with stories from her classroom and her version of a powerful song –  A Change is Gonna Come.

Change has been a long time coming.

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So to think about…

Do all of your students see themselves as mathematicians?

What mathematicians do you talk about in your class? Do you provide “mirrors and windows” for your students to see themselves in the curriculum and in others?

What types of mathematics do we privilege?

What is culturally responsive pedagogy in mathematics education?

How is mathematics necessary for engaging with ideas of social justice?

How can we broaden our understanding of math to de-center what is typically viewed as “school mathematics”?

How do we create mathematics experiences in our schools that are inclusive for all learners?

~Janice

December thinking together: What is spatial reasoning?

Posted on: December 21st, 2017 by jnovakowski

This school year I am going to share a monthly focus as a way for educators in our district (and beyond, of course!) to think together, collaborate and share ideas around K-12 mathematics education. On the list are number sense, estimation, reasoning, spatial awareness…it is a list in progress so suggestions are welcome.

My intentions are to begin each month with a blog post highlighting a focus area in our BC mathematics curriculum and connecting it to the broader field of mathematics education. I plan to share links to websites and resources, share books that I have found helpful and provide examples of mathematical tasks from Richmond classrooms. During each month, I will also tweet out related links, ideas, blog posts and photographs from classrooms.

 

For December let’s consider what is spatial reasoning?

Spatial reasoning is based in dynamic processes with a focus on mental understanding and physical transformation. It is comprised of many elements and the current research in this area is looking at the interaction of these elements. Some “math verbs” associated with the elements of spatial reasoning include:

de/re/composing     re/arranging     relating       mapping      symmetrizing     visualizing    perspective-taking     locating

intersecting     transforming    scaling     folding    sliding      rotating    reflecting    balancing    imagining    comparing

One of our five mathematical big ideas in our BC mathematics curriculum focuses on spatial relationships. The K-9 “meta” big idea is: We can describe, measure, and compare spatial relationships. At each grade level, there is a specific big idea around geometry and measurement concepts that connects to the curricular content for that grade level such as thinking about composing and decomposing two and three-dimensional shapes. Connected to this are the curricular competencies of visualize to explore mathematical concepts and represent mathematical ideas in concrete, pictorial and symbolic forms.

Spatial reasoning in young children is an indicator of future overall school success, as well as more specifically, literacy and numeracy (multiple research studies across disciplines including Duncan et al, 2007 – cited in Davis, 2015). It is not a pre-determined trait but is something that is malleable and can be learned. Spatial reasoning and geometry are foundational to disciplines such as astronomy, architecture, art, geography, biology and geology and are an essential part of STEM/STEAM education and future careers.

Many elementary teachers in our district have been inspired by the Canadian book Taking Shape: Activities to Develop Geometric and Spatial Thinking.  In Taking Shape, the Canadian authors offer five key areas as their focus for spatial reasoning:

  • symmetry
  • transforming
  • composing and decomposing 2D images and 3D objects
  • locating, orienting, mapping and coding
  • perspective-taking

Math mentor teacher Michelle Hikida from Diefenbaker Elementary has used rich tasks from this book with her grades 2&3 students and shared this work at our elementary math focus afternoon. Students are engaged in creative and critical thinking as well as communicating and collaborating while thinking through these tasks.

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As there is a heightened focus on computational thinking and coding, we can see strong connections between spatial awareness and reasoning as students think about creating programs and commands to move objects through pathways and around obstacles such as when programming a Spher0 or using a coding program like Scratch.

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Spatial thinking and reasoning also are an important aspect in linking models to abstract phenomenon such as in calculus. Graphing calculators such as desmos support connection-making between visual-spatial models and abstract expressions.

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How could you nurture the development of spatial reasoning with your students?

What math to math connections are you making?

What connections to your students’ interests and other curricular disciplines are you making?

~Janice

 

References

Taking Shape: Activities to Support Geometric and Spatial Thinking K-2 by Joan Moss et al

Five Compelling Reasons for Teaching Spatial Reasoning to Young Children:

https://ww2.kqed.org/mindshift/2017/01/20/five-compelling-reasons-to-teach-spatial-reasoning-to-young-children/

Paying Attention to Spatial Reasoning: K-12 Support Document for Paying Attention to Mathematics Education, Ontario Ministry of Education, 2014 (available as a pdf online)

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

Understanding Geometry by Kathy Richardson

Learning and Teaching Early Math: The Learning Trajectories Approach by Douglas Clements & Julie Sarama

Open Questions for the Three-Part Lesson: Geometry and Spatial Sense K-3, 4-8 by Marian Small & Ryan Tackaberry