During this post-spring break phase of the school year, we are providing continuity of educational opportunities and learning experiences for our students. We are planning these opportunities through the lenses of learning priorities, equity, access and compassion. Every student’s context will be unique and we are responding with choices and options that are manageable for families at this time. A collection of resources to support the teaching and learning of mathematics and numeracy during this time have been created and curated on a page on this blog, which can be found above.
Who could have predicted when we left for spring break on Friday, March 13, that we would not return to school as we have known it, for the rest of the school year. This spring has brought announcements, updates, change of plans, curveballs and new information and expectations on a regular basis. A global pandemic has brought changes to our lives, and to teaching and learning.
I never expected to have a YouTube channel, to be Zooming multiple times a day or to be doing live online math studio sessions but that’s what happened!
A highlight of each week was Thursday mornings when I took our math studio experiences online via Zoom. I hosted a primary session that usually had 30-40 students join in, and then an intermediate session that grew to about 15 students. I bought a special arm to hold my phone to use as a document camera so that I could do demonstrations for the students.
Some of their favourite projects were mazes, origami, cardboard shape structures and using the digital microscope.
The children in the Zoom sessions found ways to connect with each other – waving, calling out and commenting in the chat box. I loved hearing their little voices calling out, “Ms Novakowski, I need help…” as they worked on a project, holding it up to the screen for me to see, with a look that suggested that maybe I could reach through the screen to help them. These Zoom sessions highlighted the importance of the need for interaction during this time.
I also was fortunate to continue my learning with the grades 5&6&7 class an their teachers at Quilchena through Zoom math chats and numeracy tasks. More information can be found HERE.
I had regular weekly or bi-weekly Zoom chats with several small groups of educators throughout the term. Sometimes we were just checking in with each other but other times were time for planning together, sharing ideas and collaborating.
I also spent more time focused on content creation this spring than I have in a long time – from K-7 weekly math plans, interdisciplinary projects, math game resources and at-home learning ideas for families. It was an opportunity for me to think about connecting the dots across the grades as well as across curricular areas. Most these new resources are curated on our district portal, as well as on a page on this blog here:
Every Wednesday at 2pm, about twenty Lower Mainland educators in similar roles as mine met via Zoom to share ideas and resources around math education during this time. As events and protests here in North America amplified the important discussions around anti-racist practices in education, Shaheen and I were asked to sharing some of the work we have been doing in the district around re-humanizing mathematics through culturally responsive pedagogies and investigating social issues. This focus re-framed much of the discussion within this group and our planning for professional learning opportunities for next year. Some reading and resources can be found HERE.
At this point, as we come to the end of the school year, it is still unknown what September will bring. We have learned to much and developed so many new skills over the last three months and we will adapt again in September. For now, I am going to let go of some of my wonderings – wondering how The Studio and its focus on materials might look in the fall and wondering what format my district role and responsibilities will take on.
I’m looking forward to a summer of rest and rejuvenation through spending time with my family, my backyard, reading, creating, learning new things and enjoying the outdoors (and spending less time on Zoom).
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As the province moved to remote learning from home due the COVID-19 pandemic, the Quilchena teachers and I met via Zoom to plan numeracy experiences for the students that were connected to our current context. I joined in on the class’ Zoom meetings for Math Chats where we did routines like number talks and WODBs and also built content knowledge to support projects and numeracy tasks.
Two the at-home numeracy tasks the students engaged in this spring were Acts of Kindness and Garden Design projects.
In response to the pandemic and in-school instruction being suspended, we thought about ways for the students to connect to each other and the community. They were asked to participation Acts of Kindness. Some students painted rocks to leave around the neighbourhood while others created signs to put in the front windows of their homes. We also asked the students reach out to their classmates through phone calls. We asked the students to consider the “ripple effect” of their acts and to create a visual model to show the impact. The following are some of the students’ visuals which some also connected to ways to prevent the spread of the COVID-19 virus.
Another numeracy task the students did was a plan and design task, creating garden beds, boxes or containers. During our math chats, we learned about different kinds of polygons, how to calculate area and perimeter and then volume. Students were also asked to research and budget for how much soil they would need.
The following is the final task criteria:
And some examples of student submissions:
I am looking forward to continuing this numeracy project with this class next year. With thanks to teachers Jen Yager, Sam Davis and Christine Gerencser.
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On February 25, on what would be our last face to face time together, I spent the morning with the grades 5&6&7 class at Quilchena. At that time, I was still thinking I was going to Reggio Emilia, Italy for a study group on spring break and I shared a project from that community with the students to connect to their class’ Agents of Change and Human Rights project. In Reggio Emilia, the community has organized a Flags 4 Rights project where local children, as well as children from around the world, have submitted artwork sharing their thinking about children’s rights. The artwork was then transferred to large flags that were hung throughout the community.
A primary class from Grauer created artwork that was sent to Reggio Emilia. The following is just one example:
We invited the intermediate students at Quilchena to engage in a plan and design numeracy task, considering creating flags for their school, what size they would, where they would be hung and what their budget would be.
The students measured, estimated, visualized and drew their plans to think about about where they would hang the flags and what size they could be.
The students shared and compared their plans. It would have been great to have been able to follow through on this task and think about what students could design and create for their school after spring break but alas, that was not to be!
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On January 29, I spent the morning with the grades 5&6&7 class at Quilchena thinking about numbers in the news. We connecting this idea to our study of infographics and how numbers can be used to inform, persuade or evoke emotion in us. We wondered how headlines might use numbers to pull us into a news article and how we can use numbers to make sense of the world around us.
We began by asking the students what their sources of news were. Many replied hearing it on the radio when they were driving with their parents. We shared sources of both local and national/international news.
We then shared some different current headlines with the students and asked them to analyze them with the following questions:
We then invited students to choose a current event that they were interested in, either local or global, and to find a news article about it that included the use of numbers, whether it be quantities, measurements or percentages.
The students investigated their news articles individually or in pairs or triads. The events of most interest to the students included the wildfires in Australia and the recent plane crash involving Kobe Bryant.
The students shared their findings at the end of their time together and compared data from different sources.
The COVID-19 virus outbreak was just beginning to be a focus in the news and some students were interested in learning more and chose this as their current news. Who could have ever predicted at the end of January what this would have meant for us here in Richmond and all the mathematical modelling that has been involved with our public health guidelines in the province?
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The Richmond School District’s Math Play Space popped up at several school and community events this school year.
In the fall we were at Blundell Elementary for their Meet the Teacher Night/Open House:
We visited Kingswood Elementary during one of their afternoons of parent-teacher conferences:
Gilmore Elementary invited us to their school during an afternoon of conferences with families:
We set up in the school gym at Diefenbaker Elementary during an afternoon of conferences with families. We set up earlier in the afternoon so some of the classes could come by for a Math Play Space experience as well.
Our last school visit of the year was at Walter Lee Elementary where the Math Play Space was set up in one of their wings during an afternoon of student-led conferences:
We also set up on the main floor of the Brighouse branch of the Richmond Public Library for two afternoons:
February 13 – What different ways can you make a heart with the materials? (and other playful creations)
A public blog with an events calendar and information for parents related to the Math Play Space can be found HERE.
Unfortunately due to the COVID-19 pandemic, our events needed to be cancelled in the spring. We look forward to re-imagining how the Math Play Space might be experienced as we move forward with new health and safety protocols.
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Just before spring break, I was fortunate to collaborate with secondary colleagues from our department, Shaheen Musani and Baren Tsui on a professional learning series for secondary school teams. The series is called Math for Action and looks at the intersection of mathematics and social issues with a focus on student agency. A goal of the series is to elevate the importance of numeracy across curricular areas.
A variety of resources were shared. A book list that supports this series can be downloaded here:
We looked at this Social Justice Lens, as created by the BCTF’s Social Justice committee.
It felt like we just got started with this thinking together and then in-school instruction was suspended. We look forward to continuing this series in some format when we return to school in the fall.
Although I believe nothing replaces the physical and sensory interaction with materials such as math manipulatives, in this time of COVID-19 and its many health and safety precautions and protocols, we are turning to the use of virtual manipulatives or e-manipulatives more then ever. Students can use them on their computers or devices at home or in-school so that students do not need to physically share and use materials that would need to be regularly sanitized.
The use of widely-used commercial mathematically structured manipulatives originated with the design and creation of Cuisenaire Rods in the early 1950s , although many other math materials, such as Froebel’s gifts and some Montessori math materials had been in use before this. Unifix Cubes were developed soon after this in 1953, by a family of educational suppliers who had worked with both Froebel and Montessori. Over time there have been “overhead projector” and magnetic versions of these manipulatives and since the 1990s virtual manipulatives have been developed using flash or java apps or applets.
One of the first collections of virtual manipulatives was the National Library of Virtual Manipulatives hosted by Utah State University, launched in 1999. You can find manipulatives sorted by math topic and grade band. The site can be accessed HERE.
A book sharing ways to teach mathematics with the manipulatives from the NLVM was published in 2010. I found it still available for purchases HERE.
The following are suites of free, accessible virtual manipulatives:
(please note that all image below are screenshots from the websites and do not link to the apps/sites. there is a link for each website embedded in the description)
The Math Learning Center
The Math Learning Center provides a suite of virtual manipulatives that are available as web-based apps, iOS apps and are also available in the Chrome Store. The Math Learning Center iOS apps have been loaded to our district-configured sets of iPad devices. Some of the apps have a new sharing features that allows teachers to pose problems or design investigations specific to their class of students. The pages hosting the apps and more information about them can be found HERE. Some of the apps available are pictured below.
Didax Education has created virtual manipulatives of their widely used physical manipulatives such as Unifix Cubes. The manipulatives, instructions, learning activities, and ways to embed the manipulatives in online platforms can be found HERE. Some of the virtual manipulatives that can be found on the Didax site are pictured below.
Mathies Learning Tools have been developed in Ontario, including Canadian money manipulatives. Information is available in English and French and the tools are available for different platforms. The pages hosting their virtual manipulatives and other tools can be found HERE.
Mathigon hosts a “polypad” which is like a web-based whiteboard screen that their suite of virtual manipulatives can be used on. The page can be accessed HERE.
Toy Theater hosts a page of virtual manipulatives. The site also includes a range of number charts like 100 and 120 chart and Canadian money manipulatives. The page of virtual manipulatives can be found HERE.
The following suites of virtual manipulative are added from Twitter suggestions. With thanks to Karla Pearce, Alistair Carratt and Sean K for their suggestions.
Mathsbot hosts a page of virtual manipulatives within their site found HERE. There are standard math manipulatives like tangrams, pattern blocks and Cuisenaire rods but also tools like discs, dice, counters, a visual fraction wall, geoboards and many other visual supports for learning, doing and thinking about mathematics. It is the only suite that I have found that includes prime factor tiles, number frames and Hungarian frames.
Geogebra create a specific page to host tools to support remote learning, including an array of whiteboards (dots, grids, isometric, etc) as well as virtual manipulatives such as algebra tiles, protractors, fraction circles, prism creators, and many others that can be used across the grades. This page can be found HERE.
The Geogebra home page also takes you to several math apps, tasks, simulations, games and other classroom resources.
Some online resources on the research and use of virtual manipulatives:
As part of the NCTM 100 Days of Learning series, Chrissy Newell presented a webinar, sharing different ways to use virtual manipulatives. The recorded webinar can be accessed HERE. And the presentation slides can be downloaded here:
This year’s Big Math Ideas for Grades 3-5 series used Tracy Zager’s book, Being The Math Teacher you Wished You’d Had, as our core resource. Teachers read chapters between our sessions and we shared our highlights at the beginning of each session along with exploring some of the resources, websites and math tasks from the book.
The publisher’s companion website for the book, with supporting materials, can be found HERE.
In our first session, we explored the idea of what mathematicians do and shared some of the picture books that Tracy highlights in her book along with some others from my collection. We watched a video “How to Snakes” by mathematician/artist Vi Hart, in which she exemplifies the playful, curious nature of doing mathematics. You can find the video HERE.
Other areas of focus during the series included computational fluency and using math games for purposeful practice.
In our second session, we looked at the big idea of spatial relationships.
Much like our students, teachers learned “at-home” during term three, during our province’s continuity of learning during the global COVID-19 pandemic. We joined together on Zoom for our next scheduled session in April and the group decided it would like to continue to connect every two weeks.
We shared and collected resources to provide to families during this new way of teaching and learning and have posted some of them on a page at the top of this blog, called PTSG Outdoor Learning Opportunities. A direct link can be found HERE.
An area we focused on during our Zoom discussions with communication with families. We compiled the different ways teachers in the group were successfully communicating with students and their families.
In June, the teachers in the group completed an online survey to provide feedback on this year and to plan for next year. Areas of interest include teaching and learning through the First Peoples Principles of Learning, the core competencies, student agency and a continued focus on outdoor learning.
Take care and have a wonderful summer,
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For our fourth (and what turned out to be our final in-person time together) session, the primary teachers study group met at Anderson Elementary.
We began our time together by investigating the materials included in the Bog Ecology Kit, available through our district resource centre (DRC).
Inspired by some cards in the kit, the group decided it wanted to create plant cards on a ring that teachers could take outside with their students. Each teacher in the group will take on a local plant to photograph and research with their students.
The teachers from Anderson took us out to visit their outdoor learning area and garden and then we walked over to Garden City Park, where we used Anne-Marie Fenn’s nature finding list to observe the area.
Thank you to the Anderson teachers for hosting us!
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