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

Archive for the ‘inquiry’ Category

intermediate numeracy project: what is numeracy?

Posted on: November 19th, 2019 by jnovakowski

Numeracy is a K-12 focus in our school district. Numeracy and literacy are considered the two pillars of the BC curriculum and new Graduation Assessments in both Numeracy and Literacy are now in place in our province. With teachers, students and families that I work with, I explain the distinction between mathematics and numeracy. Mathematics is the discipline, the body of knowledge, content and processes/competencies. Numeracy is using mathematics to interpret and understand issues or solve contextual problems. Our goal is to develop both numerate citizens that use mathematics to make sense of the world around them.

One particular area of focus in our district is developing numeracy and related tasks with teachers and students in grades 6-9 as a way to bridge elementary and secondary learning experiences. One clsss that I am spending time with on a year-long focus around numeracy is the grades 5&6&7 class at Quilchena with teachers Samantha Davis and Jen Yager.

I visited the class at the end of September to introduce what numeracy is. We used the definition of numeracy from the BC Ministry of Education site and shared it with students and used the “exploding the sentence” strategy as a way for them to understand the meaning of numeracy.

The teachers had told me one of the current interests of the students was the climate strike. This was connected to their class focus on investigating youth who are agents of change and following the work of Greta Thunberg. I introduced the use of infographics to convey information and shared the following two images with the students. We discussed what we needed to know and do in order to be able to interpret the images and how different visuals can convey the same information but have different impacts on how we connect to the data and information.

At our next time together in October, we will think together through a numeracy task.

~Janice

2019-2020 primary teachers study group: session one

Posted on: October 16th, 2019 by jnovakowski

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.

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

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.

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.

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

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

outdoor classroom day: November 1 2018 and May 23 2019

Posted on: July 3rd, 2019 by jnovakowski

Outdoor Classroom Day is an international initiative to promote the importance of children experiencing the outdoors. The event began in London, England in 2012, grew internationally in 2015 and became a global project in 2016 with the support of educators, environmentalists, play experts, NGOs, Project Dirt and Unilever. The organization supports and shares research around the benefits of playing and learning outdoors. More information can be found on the website HERE.

We participated in our first Outdoor Classroom Day on November 1 with three classes at Grauer. Each class began with some time in The Studio where we shared ideas about where and how we might see and experience mathematics outdoors. I shared a different book of images with each class to inspire their mathematical thinking.

It was pouring rain most of the day, but being the day after Hallowe’en it was actually a good day to be outside and moving.

Each class took on different tasks with the grades 1&2 classes looking for and thinking about estimating, counting, size (measuring) and shape.

The grades 3&4 class worked in small groups with a task card prompting them to search for things outside involving mathematical ideas such as symmetry, fractions and measurement.

As we were coming inside, one of the grade 2 students said, “This was the best math day ever!”

The next Outdoor Classroom Day for this school year was May 23. The grades 3 and older classes at Grauer were at the district track meet, so the three K-2 classes spent the day outside together. We took our new Outdoor Studio Wagon with us outside and it was filled with materials, tools and resources to support and inspire our mathematical thinking.

We began our morning by finding out own counting collections outdoors and then recorded our counts in different ways. Some students gathered leaves, twigs or pieces of park to group and count while others found multiples in plants such as buttercups (counting the flowers by 1s and the petals by 5s) and clover (counting the leaves by groups of 3s).

After recess, we considered different types of branding and growing patterns that we noticed in the growth of trees, plants, leaves, flowers and roots and captured these patterns with clay prints and plant prints using rubber mallets.

Here are the contents in the Outdoor Studio Wagon:

SD38_Outdoor_Studio_Wagon_list

The next Outdoor Classroom Day is November 7 2019. You can sign up HERE.

~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.

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

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

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

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

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

~Janice

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.

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).

Thank you to Homma for hosting!

~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

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.

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

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

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

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

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

Have a lovely spring break!

~Janice

2018-19 primary teachers study group: session 3

Posted on: March 11th, 2019 by jnovakowski

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

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

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

How can mathematics help us to understand this issue?

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

What information could be collected?

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

What actions could we take?

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

~Janice

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:

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

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

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.

The 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

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.

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

Osmo 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?):

WODB_AR (movie file)

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.

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

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

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

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

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

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

playful_inquiry_charcoal_2018

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

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

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

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

~Janice, on behalf of the playful inquiry mentors