Archive for the ‘intermediate’ Category

January thinking together: use technology to explore mathematics

Posted on: January 31st, 2019 by jnovakowski

This month’s focus is on the curricular competency: use technology to explore mathematics.

This is the language that is used from K-5 with the accompanying elaborations:

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This is the language of the learning standard for grades 6-9:

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And this is the language of the learning standard in grades 10-12, with elaborations that are more course-specific:

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There are many questions that arise for educators and parents around the use of technology. In some contexts the use of personal devices becomes a management and liability concern for schools and in other contexts there are access and equity concerns around technology. In terms of pedagogy and appropriate use, there is always a professional judgement made as to the suitable use of technology and whether it is enhancing the learning experience in some way. Technology is not to be used just for the sake of using technology but instead, choices are made around technology use based on intention, context and purpose. In mathematics, there are many applications that allow for students to visualize and experience mathematics in ways they would not otherwise be able to (one example is the use of Desmos). Another aspect of using technology in mathematics teaching is as a tool to represent and share students’ learning. There are many accessibility features available on devices for students who may need different tools to support their communication or recording of ideas. Technology can be a powerful tool to support inclusive practices, choice and differentiation.

When we look at BC’s redesigned curriculum for information on the role of technology within a learning environment, the following is shared:

ICT-enabled learning environments

Students need opportunities to develop the competencies required to use current and emerging technologies effectively in all aspects of their learning and life. Technology can facilitate collaboration between students, educators, parents, and classrooms while also providing schools with rich online resources. Today’s technology enables classrooms, communities, and experts around the world to share digitally in a learning experience, wherever they may be.

source: https://curriculum.gov.bc.ca/curriculum/overview

E-Portfolios

Communication with families (and others) is an important part of our education system and in our district we are embracing e-portfolios and the use of technology to share and communicate student learning and progress with families. Students are able to take photographs or videos and upload them to their portfolios and annotate their posts with information or self-assessment about their learning. The teacher is also able to add descriptive feedback that is shared between teacher, student and family.

Screencasting

As a classroom and resource teacher and teacher-librarian, one of my favourite uses of technology was the use of screen casting apps. These apps allow students to take a photograph of the math they have been building, creating, diagramming or recording and then use annotation tools such as text labelling and arrows to explain their thinking as well as using audio tools to narrate their thinking. I found that many students were more confident and detailed in sharing their learning through these apps that what I might have found out about their understanding in other ways. There is also an honouring of students’ uniqueness in how they might see or think through the mathematics that can be shown through these types of apps. Some examples of screen casting apps we use in our district our: ShowMe, Educreations, Explain Everything, 30Hands and Doceri.

Math Apps

There are many apps that can support mathematics learning – some are mathematics specific and others are used to represent and share learning. A caution is the type of math apps that are essentially a worksheet and don’t include any sort of feedback to students, visual supports, problem-solving or mathematical thinking. Some locally produced apps include the TouchCounts from SFU that uses the research around gesturing to create an interactive app that focuses on counting and decomposition and composition of quantities. Another series of BC apps are the MathTappers apps developed through the University of Victoria. Each app has visual supports for students developing their understanding of a concept as well as symbolic or abstract notation. There are also choices as the number range that students can work with, allowing for differentiation. These apps are all on our district configured iPad devices. Some specific apps from this series include Find Sums, Multiples, and Equivalents.

Screen Shot 2019-01-31 at 11.10.00 AMThe apps from the Math Learning Centre are also on our district configured iPad devices and allow for content creation and capturing students’ process and thinking. These apps are in web-based and iOS and Android formats. More information can be found HERE.

 

 

There are also so many apps that allow for students to share their thinking such as ShowMe, Educreations, Book Creator, PicCollage, 30Hands and Doceri.

Tracy Zager shares her ideas on evaluating math content apps HERE. Her non-negotiable criteria are:

1) no time pressure

2) conceptual basis for operations

3) mistakes are handled productively

Read through her blog post for explanation and examples.

The following is a link to some recommended apps and blog posts about students using them from #summertech15 and HERE is a blog post about using iPad technology and specific apps to support all students in mathematics.

 

Calculators

Although BC does not yet have a specific statement on calculator use, there is no intent that students will use calculators to complete calculations instead of learning the concepts and practice involved with operations (addition, subtraction, multiplication, division). In some cases, students that have specific learning needs and plans may use calculators as an adaptation. In some cases, teachers may choose to provide the choice of calculators when the focus of the lesson or assessment is not on calculation but on another area of the math curriculum such as problem-solving and calculators can be used for the necessary calculations so that students can focus on the other aspects of the task. Calculators can also be used to investigate patterns and relationships, support student reasoning or justification.

The NCTM has a research brief on calculator use in the classroom which can be found HERE as well as a position paper on calculator use in elementary grades which can be found HERE.

Virtual Manipulatives

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The Math Learning Centre offers a variety of virtual manipulatives in web, iOS and Android formats. They can be accessed HERE.

 

 

 

desmos

Desmos is a free, online graphing calculator application that is used by teachers and students all over the world. There are both web-based and app platforms. Students are “able” to play with parameters in an equation and visually see how the graph changes as the parameters change.  The desmos staff and teachers across the world have developed lessons and tasks that are open source and shared through the desmos teacher website at no cost HERE. There is also an activity builder so that teachers can create their own tasks.

I attended a math conference a few years ago where Eli Luberoff, CEO of desmos, shared his passion for the teaching and learning enabled and enhanced by this tool. In particular, I was captivated by the marble slides task he shared and the authentic learning that we witnessed happening for students in the video he shared.

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More information about Desmos and access to many classroom activities can be found HERE.

Coding and Computational Thinking

There are many links between coding and computational thinking. Two new senior math courses – Computer Science 11 and 12 have been added to our BC curriculum framework and these courses focus on coding, programming and computational thinking.  I will be sharing a blog post specific to coding and math in the next few months.

Osmo

Screen Shot 2019-01-29 at 10.56.25 PMOsmo is an interactive accessory for iPad technology that uses the camera to create Reflective Artificial Intelligence. The red camera clip and white base are used with free apps and game materials that can be purchased online or at the Apple Store. Two of its earliest games focused on mathematics – the Tangram game focuses on spatial reasoning and the Numbers games focuses on decomposition and composition of numbers. Osmo is always developing new games including a Pizza game that focuses on financial literacy and a series of coding games.

More information about Osmo can be found in a blog post here and on their website here. The SD38 DRC has five Osmo kits available to borrow. Note that one iPad device is needed for each kit.

Augmented Reality (AR)

Augmented reality (AR) is an interactive experience of a real-world environment where the objects that reside in the real-world are “augmented” by computer-generated perceptual information, sometimes across multiple sensory modalities (from Wikipedia). There is an interplay in AR between digital and real-world environments whereas in Virtual Reality (VR) you engage with a simulated environment. A few years ago we had a Google Expeditions team visit Homma school and share their Google cardboard virtual reality devices with the students. A blog post about that experience can be found HERE. This was a first foray into thinking about ways this kind of technology could support teaching and learning. My first experience with AR was a few years ago when the colAR app created a special event to go along with Dot Day (inspired by the book by Peter Reynolds). The information about this can be found HERE and is a great starting point to use AR with students.

Our new technology integration teacher consultant Ellen Reid has been exploring AR with the iPad app AR Maker . We talked about the mathematical possibilities for using AR and along with the development of spatial reasoning, the following concepts came to mind: surface area, volume, transformational geometry, scale, proportion, ratio, 2D and 3D geometry, and composition and decomposition of shapes. The following are some photos Ellen captured as she created AR WODBs (Which One Doesn’t Belong?):

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For Richmond teachers, please also check out the Integrating Technology for Teachers page, curated by Chris Loat, on our district portal linked HERE.

 

Some questions to consider as you plan for learning opportunities to develop the competency of using technology to explore mathematics:

How can technology enhance students’ mathematical experience and see and think about mathematics in different ways?

What specific curricular content and competencies at your grade level could be explored and investigated through technology, including the use of calculators?

How can technology be used to support students’ collaboration and communication in mathematics?

What opportunities are we creating for sharing and communication with families through the use of technology?  How are we communicating with parents how forms of technology are being used in our schools to support learning in mathematics?

~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.

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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.

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

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

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

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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.

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

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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.

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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

 

 

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.

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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

Screen Shot 2018-12-11 at 4.11.50 PMThe 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 Screen Shot 2018-12-11 at 2.26.05 PMcomposition 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:

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Screen Shot 2018-12-11 at 2.28.51 PMFawn 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.

 

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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.

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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

 

September thinking together: mathematics curricular competencies

Posted on: September 28th, 2018 by jnovakowski

For the 2018-19 school year, the “thinking together” series of blog posts will focus on the curricular competencies 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 competenecies and then each month we will zoom in and focus on one curricular competency and examine connections to K-12 curricular content, possible learning experiences and assessment.

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

The curricular competencies are intended to reflect the discipline of mathematics and highlight the practices, processes and competencies of mathematicians such as justifying, estimating, visualizing and explaining

The curricular competencies are connected the the Core Competencies of Communication, Thinking  and Personal & Social. More information about the Core Competencies can be found HERE.

 

Screen Shot 2018-09-28 at 9.45.26 PMThe curricular competencies along with the curricular content comprise the legally mandated part of the curriculum, now called learning standards. This means these competencies are required to be taught, assessed and learning achievement for these competencies is communicated to students and parents.

Something unique about the mathematics curricular competencies is that they are essentially the same from K-12. K-5 competencies are exactly the same with some slight additions in grades 6-9 and then building on what was created in K-9 for the grades 10-12 courses. Because they are the same at each grade level, to be assessed at “grade level” they need to be connected to curricular content. For example, one of the curricular competencies is “estimate reasonably” – for Kindergarten that will mean with quantities to 10, for grade 4 that could mean for quantities to 10 000 or for the measurement of perimeter using standard units and for grade 8 estimating reasonably could be practiced when operating with fractions or considering best buys when learning about financial literacy.

The new classroom assessment framework developed by BC teachers and the Ministry of Education focuses on assessing curricular competencies and can be found HERE.  A document outlining criteria categories, criteria and sample applications specific to K-9 Mathematics can be found HERE. The new four-point proficiency scale provides language to support teachers and students as they engage in classroom assessment.

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As we are 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 it means to be a mathematician and what mathematicians do?
  • What opportunities can be created over the school year for students to name, be aware of, practice, develop and reflect on the core and curricular competencies in mathematics?
  • How can we make the core competencies 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 competencies and content? What curricular content areas complement and are linking to specific curricular competencies?

~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.

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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.

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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.

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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.

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

~Janice

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

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

Screen Shot 2018-06-12 at 11.25.11 PMThe First Peoples Principles of Learning is a foundational document in the redesign of BC’s curriculum frameworks. The Principles were developed by FNESC (First Nations Education Steering Committee) and the poster in English can be found HERE and in French can be found HERE. As Jo Chrona would say, the FPPL are much more than the poster – they are principles that are inclusive of all children in BC while honouring Indigenous ways of being and knowing. FNESC has developed teaching resources such as the In Our Own Words resources for K-3 and the Math First Peoples resource for Grades 8&9 (currently being updated) but much of the information and ideas in the resource can be adapted for all grade levels.

 

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

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

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

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

Link to BCNN page here

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

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

To consider…

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

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

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

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

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

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

~Janice

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

Posted on: June 7th, 2018 by jnovakowski

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

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

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

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

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

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

SD38 K-5 Math Connections between Core and Curricular Competencies

SD38 6-9 Math Connections between Core and Curricular Competencies

SD38 K-5 Math Communication

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

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

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Here is one example of a recording form:

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

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

~Janice

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.

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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

Talk With Our Kids About Money 2018

Posted on: May 12th, 2018 by jnovakowski

As part of a national financial literacy month every April, the Richmond School District participates in Talk With Our Kids About Money Day (TWOKAM) the third Wednesday in April. Financial literacy is a new part of BC’s redesigned mathematics curriculum with a content learning standard at each grade level from K-grade 9.

To raise awareness of the resources available to teacher, local CFEE (Canadian Federation for Economic Education) representative Tracy Weeks shared materials and information at our Elementary Math Focus Afternoon in January.

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In April, an assembly was held at Burnett Secondary with CFEE president Gary Rabbior talking to students about financial literacy.  Tracy Weeks (CFEE) facilitated an information session for parents at Hamilton Elementary on April 9.

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On April 18 – national TWOKAM day – a finale event was held for parents and students at Brighouse Elementary. Student projects from Burnett Secondary were on display and guest speaker Paul Lermitte shared ideas with parents for developing financial literacy with their children at home. Thank you to Brighouse for hosting this well-attended event!

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We hope to continue to grow the idea of “Money Fairs” (think financial literacy fairs like science fairs) in our district as we continue to teach and learn about financial literacy in our classrooms.

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TWOKAM – CFEE website link

~Janice