Archive for the ‘early learning’ Category

2019-2020 primary teachers study group: session one

Posted on: October 16th, 2019 by jnovakowski No Comments

This year’s primary teachers study group has chosen the focus of trans-disciplinary learning in outdoor settings, connecting to the land and to place. For our first session of the year we met at McNeely Elementary on October 3, hosted by Anna and Shannon. Teachers were able to choose a focus book from four selections that we will draw upon over our time together this year.

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Jess Eguia framed our focus around thinking about planning through big ideas and concepts and shared some planning frameworks to support our work together.

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Concept and planning handouts from Jess Eguia:

Change Concept Handout

Conceptual Teacher Tool

Anna and Shannon shared the planning they have been doing with Jess and the three questions that are framing their year of learning with their students.

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We moved outside to the wooded area near McNeely. Teachers were asked to think about how the land inspired them to think about concepts. Some of us began with a concept and looked for where we made connections to that concept.

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With thanks to Jessica Szeto of Anderson Elementary for sharing her knowledge of local mushroom species. “For Richmond/Vancouver specific mushrooms that are more urban, the ones in the list are the ones that come to mind. There are also some other mushrooms that have been spotted in Richmond, but they look quite similar to each other (ie. russulas, cone caps) and need some closer looks at the gills and spores to identify. But the ones above are the most memorable and easy to identify!”

Mushrroom pictures and list: Mushroom PDF

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Our study group is in its seventeenth year and has endured because of the teachers involved and the participatory nature and the valued contributions within our group.

Looking forward to our next session together in November and how we might share our thinking.

~Janice

 

September thinking together: mathematics curricular content

Posted on: September 30th, 2019 by jnovakowski No Comments

For the 2019-20 school year, the “thinking together” series of blog posts will focus on the curricular content in the mathematics curriculum.  The “thinking together” series is meant to support professional learning and provoke discussion and thinking. This month will provide an overview of the curricular curricular content and then each month we will zoom in and focus on one curricular content area with examples from K-12 classrooms in Richmond.

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The curricular content is the “know” part of the know-do-understand (KDU) model of learning from BC’s redesigned curriculum.

The curricular content develops and builds over time. Each grade level has core curricular content knowledge and these are reflected in the big ideas for each grade level. There are five big ideas that reflect five strands of curricular content – number and number operations, computational fluency, geometry and measurement, patterning and algebraic relationships and data analysis and probability. A sixth content area in mathematics, financial literacy,  is new this curriculum.

Many areas of curricular content in mathematics are applied in other disciplines such as science, physical education and ADST.

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The curricular content along with the curricular competencies  comprise the legally mandated part of the curriculum, now called learning standards. This means that both curricular content and curricular competencies are required to be taught, assessed and proficiency/learning achievement is communicated to students and parents/guardians.

As we begin a new school year and are thinking about year plans and overviews we might consider the following questions:

  • What opportunities do students have to learn about what math is? How can we expand students’ thinking about all the areas of mathematics reflected in our curriculum? What do you think your students would say if you asked them: What is math?
  • What would you identify as core or foundational concepts or mathematical ideas at the grade level/s you tech?
  • How can we make the connections between curricular content and curricular competencies in mathematics visible in our classrooms and schools?
  • As we are planning for instruction and assessment, how are we being intentional about weaving together both curricular content and competencies What curricular content areas complement and are linked to specific curricular competencies?
  • How do you plan for opportunities for students to make math-to-math connections over the school year? For example, what connections are there between number and geometry or patterning and data analysis?

~Janice

professional learning from the summer of 2019

Posted on: September 2nd, 2019 by jnovakowski No Comments

Hi there,

It was a full and fun summer. I had lots of time to work on projects, read books, spend time with family and friends, tend to the garden, learn some new things and enjoy being outside where we live. I was also fortunate to travel a bit for work and build in some exploration time in the places I visited. All things that I like and bring my joy.

I receive and purchase a LOT of professional books. Books are a weakness for me and I often don’t have the time to read every new professional book I get. Because I often am asked to recommend books to schools, districts, etc my reading process is that I read the summary on the back cover or inside, I read through the tables of contents and then I skim through the whole book to get a sense of the flow of the book and to see how images, infographics etc are used. Finally, I choose one section or chapter of interest to read through completely. I feel okay about recommending books based on this process. Over the summer, I enjoy taking the time to read a selection of professional books cover to cover, usually about one a week in combination with my other reading for enjoyment. I received a new work iPads in June with an Apple pencil and my commitment this summer was to practice sketchnoting. The following are the sketch notes summarizing the professional books I read this summer.

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IMG_4733In July I was invited to contribute to the updating of FNESC’s First Peoples Mathematics teaching resource. The existing resource was focused on grades 8&9 and can be found on the FNESC website here. The updated resource will focus on grades 5-9 and include adaptations for senior grades and K-5. It will be sent out to teachers to review this fall and will likely be ready spring 2020.

 

 

I attended a conference about early mathematics research in Portland, Oregon. The conference focused on current research and sessions were led be researchers and educators from across the USA. I learned about the DREME network from Stanford and the resources they offer and I was also fortunate to attend a session led by educators from the Boulder Journey School.

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My husband rode his bike down to Portland and met me there so we made a little holiday out of it. It was my first time attending this conference and I hope to go again next year. More info can be found here.

 

I had less then 12 hours at home from our trip to Portland before I flew off to Chicago. I was honoured to be invite to a Public Math Gathering organized by the Public Math group. More info about their initiatives can be found here. There were educators from Minnesota, Wisconsin, Washington and Chicago as well as artists and museum folk from the Chicago area. We participated in a neighbourhood event on the Friday evening and then visited the “famous” Mr. Bubble laundromat where we observed how math initiatives (form the group as well as provided by the Chelsea Clinton Foundation) were being used by families in the space. We then spent the afternoon designing and prototyping new math installations for the laundromat. We went back to the laundromat Sunday morning to observe how our installations engaged the public. It was such an inspiriting experience to work with such a diverse group of people around math.

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The summer always gifts me some sustained time to devote to writing projects. For many summers it was my academic writing but the last few summer I have been working on a book with a colleague, Misty Paterson. We finished off our edits in early July and sent things off to the printers. We held a book launch for Pop-Up Studio in Vancouver on August 28 – so great to be able to finally hold a book that took on a life of its own. More information about the book can by found on MIsty’s website here.

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I am one of the members of the BC Numeracy Network (if you aren’t familiar, the website is here) and a subgroup of us met this summer to begin work on a resource to support professional learning in mathematics teaching and learning. It is always great to be able to work with colleagues that have become good friends. Look for our project coming out this fall!

IMG_5733And my final writing project of the summer was the first issue of our BC Reggio-Inspired Mathematics Project magazine. The first issue is called Thinking About Mathematics through materials. Teachers from eight Coast Metro districts contributed to this magazine which captures our collaborative professional inquiry focus from the last school year. More information about the magazine, including ordering information, can be found on our website HERE.

 

 

For the last couple of years my curiosity has been piqued by images I have seen of beautiful geometry art shared on twitter. With some investigation I found an online Islamic Geometry course that many math teachers on twitter have taken and I signed up with a commitment to do the first introductory/basic course this summer. I learned a lot, made lots of connections (was excited to visit the Islamic Art wing in The Art Institute of Chicago) and am inspired to find ways to embed my new learning in math studio experiences.  Information about the course I took can be found here. Thank you to Samira Mian for her detailed explanations and lovely videos.

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Another highlight of a very mathy summer was visiting the Numbers in Nature  exhibit at Science World where I got some great ideas for projects and having our district’s Math Play Space at Richmond’s annual Garlic Festival. You can read more about that here.

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Wishing you all a wonderful September,

Janice

world tessellation day 2019

Posted on: July 4th, 2019 by jnovakowski

World Tessellation Day is celebrated on June 17 in honour of M.C. Escher’s birthday and was created by author Emily Grosvenor of Oregon. More information can be found HERE. Emily Grosvenor wrote a book about a little girl named Tessa who saw shapes, patterns and designs in the world around here. The book Tessalation was launched on Kickstarter and I was happy to support it. In celebration of the book launch, the author asked some of the supporters to do blog posts about the book and be part of a blog tour. The blog post I did can be found HERE.

World Tessellation Day was promoted in our district with connections made to our BC mathematics curriculum and it was great to watch social media posts appear highlighting tessellations! You can find some of these posts by following the hashtag #WorldTessellationDay – I have shared some posts from Richmond teachers below.

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This year, the Thursday before World Tessellation Day, I invited students to explore tessellations through materials in The Studio at Grauer after we looked at some of the pages of the book Tessalation. The investigation prompt was What can you find out about tessellations? Noticing the materials I put out, I need to remember to use some non-regular polygons as well.

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On June 17, our district’s Math Play Space featured materials that tessellate and we set up tables at the Brighouse Public Library during after school hours. Many children and families visited to investigate with the materials.

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I’m looking forward to making World Tessellation an annual public event not just in our schools but also in other places in our community!

~Janice

 

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.

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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

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

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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

2018-2019 primary teachers study group: session five

Posted on: June 5th, 2019 by jnovakowski

Our fifth session of the year was hosted by Sarah Regan at Homma Elementary o April 11. Teachers shared how they had been using the book Flow Spin Grow and our French Immersion teachers were happy to have the French version now available! Teachers shared how they took photographs of the types of patterns they found outdoors and used them for inspiration in the classroom for creating patterns with materials, doing looking closely observations for science, inspiring artistic creations, etc.

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After our professional sharing, the group visited the Homma Gardens and outdoor classroom and shared ideas around how mathematics can be experienced in the garden at this time of year such as building trellises  (shape, design, symmetry, measurement) and reading seed packages (time, duration, elapsed time, measuring time, measuring depth, measuring distance apart, estimating height).

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Thank you to Homma for hosting!

~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“.

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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

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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.

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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

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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?

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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:

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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

 

 

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Teaching with Mathematical Argument: Strategies for Supporting Everyday Instruction

by Despina Stylianou and Maria Blanton

Heinemann Publishers,  2018

 

 

Screen Shot 2019-05-26 at 7.58.18 PMTeaching 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:

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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

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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

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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.

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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.

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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

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

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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.

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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

March thinking together: engage in problem-solving experiences connected with place, story and cultural practices and perspectives

Posted on: March 14th, 2019 by jnovakowski

This month’s curricular competency focus is engage in problem-solving experiences that are connected to place, story, cultural practices and perspectives relevant to local First Peoples communities, the local community, and other other cultures. This curricular competency is the same across grades K-12 and courses and falls under the organizer of “Understanding and Solving” which suggest the focus of using contextual and meaningful experiences to support mathematical understanding.

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

  • in daily activities, local and traditional practices, the environment, popular media and news events cross-curricular integration
  • have students pose and solve problems or ask questions connected to place, stories and cultural practices

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The focus and thinking behind this curricular competency are the ideas of authenticity, meaningfulness, engagement and connectedness. Not all mathematics learning needs be contextualized or connected to “real life” but for many students who may see math as something that they do at school between 9 and 10am and don’t yet see the relevance of the math they are learning, providing tasks and problems that connect to place, community and culture may support their mathematical thinking and learning and broaden their understanding and appreciation for what math is and how it can be experienced. Experiential and holistic learning are foundational to the First Peoples Principles of Learning and these are considerations for all learners. The First Peoples Principles of Learning also remind of us of the importance of connecting learning through place and story, working with others and developing a self of self, family, community and culture. This curricular competency is aligned with the Personal and Social Core Competency – positive personal and cultural identity, personal awareness and responsibility and social responsibility.

Some resources to consider:

Messy Maths by Juliet Robertson (elementary resource for taking math learning outdoors)

Tluuwaay ‘Waadluxan Mathematical Adventures edited by Dr. Cynthia Nicol and Joanne Yovanovich (mathematical adventures from Haida Gwaii developed by community members, elders and educators)

BC Numeracy Network – Connecting Community, Culture and Place

First Peoples Mathematics 8&9 developed by FNESC - this teacher-created resource is being revised to reflect the current BC mathematics curriculum and provide more learning experiences across grades and disciplines.

 

Blog posts from this site with related information:

Place-Based Mathematics

Place-Based Mathematical Inquiry

Primary Study Group 2018-2019 – Outdoors Math

Indigenous Content and Perspectives in Math

 

Some questions to consider as you plan for learning opportunities to develop the competency of engaging in problem-solving experiences connected to place, story and cultural practices and perspectives:

How does place/land/environment inspire mathematical thinking? What potential numeracy or problem-solving tasks emerge when we think about local land-based contexts?

What problems or issues are facing the local community? How might mathematics help us to think about and understand these problems or issues? What information or data might be collected and shared? How can we use different tools to communicate mathematical information to create an opportunity for discussion and engaging in a problem-solving process?

How does Indigenous knowledge connect, intersect and support the curricular competencies and content in our mathematics curriculum? Who is a knowledge holder in your local First Nations community that you could learn from and with? 

What are authentic resources? What stories and cultural practices are public and able to be shared? What doe it mean to use authentic resources, stories, and elements of culture in our mathematics teaching? How are resources specific to a local context? Who can we go to to find out more information and learn about local protocols?

What cultural practices in your community have mathematics embedded in them? How might we use the structure of “notice, name and nurture” to expand awareness of what mathematics is and how it can be experienced?

How can stories help us think about the passage of time, relationships, connections and mathematical structures, actions and models?

~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.

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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.

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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.

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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.

IMG_8871Our 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.

IMG_8882 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