geometry tiles

Posted on: January 5th, 2017 by jnovakowski No Comments

Inspired by a post on Christopher Danielson’s (yes, the author of the book and teacher resource Which One Doesn’t Belong?) blog called Talking Math With Your Kids, I created a set of geometry tiles. Always up to a crafty challenge, I thought…hmmm, I could make those! Christopher has created a one-pager of instructions as part of his Math on a Stick project for the Minnesota State Fair.

I found some balsa slats at Michael’s (teachers get a discount with a teacher card, just ask) and cut them to a 2 to 1 ratio which fortunately, gave me a set of smaller tiles of the same proportions.

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I painted front and back sides and edges with diluted acrylic paint although they could also be left plain. I marked the midpoint of one long side with a sharpie and used regular adhesive tape to tape off from the midpoint to each corner.

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I used black acrylic paint to paint in the triangles creating by the taping.

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And when the tiles were dry, I played around with what I could create with them. So much composing and decomposing of shapes!

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I used these geometry tiles as part of our mathematical tablescape at our Provincial Numeracy Project meetings to oohs and aahs.

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I’m looking forward to seeing how some students investigate these tiles!

~Janice

 

 

 

looking for math outdoors

Posted on: January 4th, 2017 by jnovakowski No Comments

During my last visit of the year to the Kindergarten classes at General Currie Elementary, it was a snowy and icy day so we decided to venture outdoors with some iPads to capture images of things that inspired our mathematical thinking. We had a quick talk with the students about how to look for math outdoors – looking up, looking down, looking all around. We talked about what math might look like outdoors – the counting of items, the shape of things, patterns in the environment, as well as sources of inspiration for thinking about math.

One of the first mathematical ideas we played with was shadows – how does your position affect your shadow? what determines the height of your shadow? what do we need to think about if we wanted to put our shadows in height order?

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As with the case of all our school sites…there is a story that lives there. General Currie was one of the first one room school houses on what was originally called Lulu Island. We stopped briefly at the historic building that is still on the new school’s site and talked about the time elapsed – what school might have been like, what the neighbourhood might have looked like, etc.

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We ventured on to the field and took photos as we walking along noticing nests in trees, tracks in the snow, all sorts of ice and frozen leaves.

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The ice was a source of fascination and many questions for the students. They were also very interested in some footprints they found and wondered about the size of different footprints or tracks.

We came back into the classroom and the students used the app Skitch with one of the photographs they took. They labelled, circled or used arrows to show where they noticed math or what inspired a mathematical problem or question.

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Classroom teacher Kelly Shuto then showed some of the students “skitches” to the class to inspire further questions.

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The following week Kelly tweeted out about the class photo book they had created, based on the idea “What math lives here?”

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In this crisp wintery weather, what will your students notice outdoors? What math lives in the frozen puddles and tracks through the snow? How far do animals need to travel to find food? What might your students wonder about?

~Janice

extending counting collections

Posted on: January 3rd, 2017 by jnovakowski No Comments

Counting collections has become a regular mathematics routines in many of our classrooms in Richmond. One of the important aspects of a routine is that students have opportunities to revisit and extend their mathematical thinking experienced through the routine over time. Although counting collections are kept “fresh” for the students over the year by introducing new materials to count, teachers have been asking me for ideas for other ways to use the counting collections they have accumulated. Inspired by a tweet about a blog post by Tracy Johnston Zager and a personal passion around the importance of problem-posing, I want to encourage teachers to create opportunities for students to pose mathematical problems, inspired by counting collections.

img_9163 I visited the grades 1&2 class at Garden City Elementary again at the end of November. Since my last visit, the class had continued to engage with counting collections and I talked to Cheryl Burian, the classroom teacher, about extending counting collections with problem posing. I read the book Cookie Fiasco with the class (from a  great new series of Elephant and Piggie books) in which some animal friends find different ways to share some cookies. During the story, we paused and considered what new problem emerged and the students discussed different ways to solve the problem. I explained that this sharing context was one type of math problem that could be considered with a collection of some sort.

The students counted some collections and recorded their counts on a math graffiti board or chart. During our debrief, we spent some time analyzing the counts.

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The students then chose one of their collections to inspire a math problem to be solved by their classmates. The gold pirate coins were a common source of inspiration and many students also drew upon the sharing context from the story to inspire their problems.

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Another way to play with the idea of counting collections is to see the “units” counted in different ways. The grades 3&4 class at Grauer Elementary counted some new collections the day before the holidays (which was also pyjama day at the school – just to explain some of the photographs!). The class has been learning about multiplication and thinking about different ways to represent the concept of multiplication such as in grouping and arrays. Although the students used the term “skip counting”, I introduced the term multiples to them. The question I asked them to focus on as they engaged in counting collections was: “What is the connection between counting and multiplication?”

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One pair of students decided to practice their 7x tables (their words…) and so grouped their glitter balls in groups of 7 on paper plates. As they began to count, they  noticed since they had organized their plates in two rows that they could visually see a ten-frame and decomposed their total number of plates into a group of ten and then a four. The video below has them explaining their thinking.

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Counting by 7s

Some of the collections I brought to the class were specifically curated to inspire students to think about multiples. I had bought several strands of holiday beaded garland and cut them into groups of 2, 3, 4, 5 etc beads. I anticipated that the students would either count them by 1s (each strand) or by multiples (the number of beads in each strand).

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Here are two videos of students’ counting of the collections:

Counting by 5s

 Counting by 10s

Other pre-grouped collections that could be used are items like packages of crayons (I have seen them in 8s and 12s) or geometric shapes where the number of sides could be counted as multiples. In both cases, the item (or shape) can be counted as a singular unit or a multiple unit, creating different entry points for students as they engage in counting collections.

Richmond teachers (and others!) – if you give one of these ways to extend counting collections a try with your students, let me know and send some photos and insights along!

~Janice

primary teachers study group: second session

Posted on: December 7th, 2016 by jnovakowski

A summary of our first primary teachers study group session and goals for the year can be found HERE.

For our second session of the school year, the primary teachers study group met at the Richmond Nature Park. We read and discussed the story of this place and learned about the formation of the bog environment and the uniqueness of this ecosystem. We connected this to the video of the formation of the delta from the online Musqueam teachers resource developed by the MOA and the Musqueam Nation which can be found HERE.

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We visited different parts of the Nature Park, thinking about how we could engage students in different spaces. The Nature Park has a covered area with picnic benches for eating or journalling as well as other seating areas.

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Another favourite spot is the bird watching area where there are many bird feeders set up that are visited by a variety of birds and squirrels. Makes for excellent observing and a chance look closely at animal behaviour! I like to take video to share with students after a trip to “re-live” and discuss what they noticed.

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We walked through along the board walk and took a short trail loop to notice and talk about the variety of trees and plants in the park and ways to engage students. We also bounced on the bog!

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One of the plants we looked closely at was Labrador Tea, a common local bog plant, turning the leaves over to help identify it. Traditional local indigenous uses for this plant include making a tea infusion to treat colds and sore throats.

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We looked at the variety of bat and bird houses and discussed these as a great ADST project for students to consider and design based on the needs of their local environment. “Bug hotels” or pollinator houses are another design option as well for school garden spaces.

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As it got dark, we visited the Nature House where one of the staff members shared some interesting information about local snakes with us.

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Teachers who have brought classes to the Nature Park shared some of their experiences and the Blair team shared how they were doing a self-guided trip with three classes the following week and were doing three different inquiry-based stations during their trip.

We will be meeting again in January, registration is still open on the Richmond Professional Learning Events site.

I am curious what sort of questions our students are having about the impact of the snow and cold on the living things around their schools?

~Janice

playful storytelling opening session

Posted on: November 30th, 2016 by jnovakowski

Marie Thom and I hosted our opening session for our Playful Storytelling through the First Peoples Principles of Learning series. We are in the fourth year of this project in our district, involving ten elementary schools over the years.

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Many of the storytelling experiences we have engaged in so far have involved local plants and animals, the use of natural materials to create local settings, retelling of stories by indigenous authors and illustrators and the use of animal characters, story stones, puppets and “peg doll” characters for the students to create their own stories. We have attended professional learning opportunities at the Musqueam Cultural Centre to consider how culture, language and place could inspire our project.

After an acknowledgement of territory, a welcome, introductions, and an overview of the history of this project, as we sat in a circle, we asked each teacher to consider and then share what First Peoples Principle of Learning they identified with and why and to share what they were curious about in terms of this project for this school year.

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Kathleen Paiger and Ellen Reid, who taught together at Steves Elementary last year and are going into their third year of the project (Ellen is teaching at Blair this year), shared their story of their experience and their students’ experience in this project.

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Leanne McColl, one of our district’s teacher consultants shared the draft goals of our new Aboriginal Education Enhancement Agreement with the Musqueam community and we considered how this continues to inspire and give meaning to our project.

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Leanne also shared information about the new Musqueam teaching resource and kit that was co-created with UBC’s Museum of Anthropology and the Musqueam Nation. The link to the online resources to support the Musqueam teaching kit developed by the Museum of Anthrop0logy and the Musqueam community is HERE.

To extend the story experiences we have been engaging in so far, we focused on the idea of creating story landscapes by weaving in more sensory experiences to our storytelling experiences- sounds, movement, textures and scents. I shared a video I had taken at Garry Point as an idea to use video of as a background or backdrop for storytelling experiences, inspired by the “forest room” created by the educators at Hilltop School in Seattle. The video can be viewed HERE.

Marie presented several storytelling provocations to inspire new layers and dimensions we could add to our storytelling experiences with students.

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img_8946To honour the importance of the learning through the oral tradition, at the beginning of our time together, we asked Michelle Hikida, who has been a part of this project since the first year, to listen during the session and to synthesize and summarize the key learnings at the end of the session. Michelle chose to use pictorial symbols to help her remember the four learnings she wanted to share with the group.

 

In their reflections at the end of the session, many teachers commented that they wanted to try more storytelling experiences outdoors as well as adding more sensory layers. We are looking forward to lots of inspiring and creative stories created by our students this year!

~Janice

introducing clothesline to the kindergarten students at General Currie

Posted on: November 29th, 2016 by jnovakowski 1 Comment

Last Tuesday, I made another visit to the kindergarten classrooms at General Currie Elementary. During each visit I introduce a new mathematical “routine” to the students and teachers and then extend the routine with some related learning experiences.

I introduced the “clothesline” introduced to me via Twitter by Andrew Stadel last year. There is a website dedicated to sharing information about clothesline math HERE. Most of the work I have seen done with the clothesline is at the middle school level and I can see great uses for it in exploring equivalent fractions, decimal fractions and percentages with our intermediate students. In looking at the kindergarten mathematics curriculum  for BC, sequencing and representing numbers from 0-10 is an important learning standard and connects to the use of the clothesline, a form of interactive numberline.

We began with just the numeral cards and the students came up on a a time (in random order) to place their cards on the clothesline. They were asked to state their reasoning for why they put their cards where they did.

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After the 0-10 cards were in place, we took them off and then I shuffled them with the ten frame and tally cards and handed one card out to each student. Again, the students came up one or two or three at a time and placed their cards, explaining their reasoning. When there was an equivalent representation already in place, they just placed the card on top of the other.

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The tent cards I created can be downloaded here:

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When I asked the first class of kindergarten students one way of showing “seven”, one little guy held up seven fingers. I hope to take some photos of the students finger combinations next week when I visit to include these on a set of cards.

I can also see great potential for the clothesline to look at multiple representations of numbers in grades 2-5 to help students think about place value.

After each class worked with the clothesline, the students could choose from several related learning experiences, all that focused on sequencing numbers or representing quantities to 10.

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The students were highly engaged with the materials and were able to share their thinking about why it was important to know how to order numbers –  ”to count, to be organized”. In one of the kindergarten classes we looked around the classroom for ways that numbers in order or sequence were used. The students found the 100-chart, the calendar and the clock.

Next week, we are going to do some number talks with dot cards and ten frame  cards and investigate the idea of parts-whole relationships in numbers by decomposing and composing quantities.

~Janice

what does it mean to be a “low” math student?

Posted on: November 23rd, 2016 by jnovakowski 2 Comments

So typically on this blog I share stories of what is happening in Richmond classrooms and about professional learning experiences for Richmond educators. This post takes a different tone…one that I hope will provoke thinking and discussions about the intersection of language and students and math.

Here goes…

I am often engaged in conversations about mathematics teaching and learning where I hear from teachers, “I have so many low students,” and it makes me wonder what is meant by “low”. I am sure I have used the term myself in the past but I have been increasingly more aware of the impact of labels and language on not just the professional conversations we have but also on how this impacts our relationships with our students. I have begun to challenge teachers on their use of this term and stop them as they say it…”What exactly do you mean when you say ‘low’?” I don’t mean to put teachers on the spot or to to make them feel uncomfortable in our conversations but I think the language we use in conversations about students is really important and we need to be mindful about this.

My prickliness about how we talk about children was amplified when I had my own children, both of whom have their own personal strengths and stretches. I can’t imagine how I would feel, or how my sons would feel, if they were ever described as “low”. What impact does this language of  ”low” have on our students as learners and on ourselves in our role of teacher? How does this thinking affect our mindset about learning?

So what does it mean to be a “low” math student…

Does it mean that the student does not have an understanding of foundational concepts in mathematics? Did the student not have access to teaching at his or her just right level? Was the student absent from school or ill for extended periods of time? Was the student not assessed thoroughly to inform instruction? How can the student be supported to gain foundational concepts and confidence in mathematics? What structures are in place in your class and in your school to support core foundational understanding in mathematics?

Does it mean that the student has difficulty learning math because of memory, health, attention, behaviour or learning difficulties? When in class, does the student have difficulty paying attention, focusing, sitting? Does the student seem unable to retain information the way it is being provided? Does the student have behaviours that are affecting his or her learning and engagement? What practices, materials and structures are in place in your classroom or school that provide choices and adaptations in time/pacing, materials, place/learning environment, quantity of work output expected and depth of content knowledge?

Does it mean that the student has a different story than his or her classmates? Has the student had breakfast? slept? Is the student living in a safe home environment? Does the student have to care for siblings or parents? Does the student need to work to add to the family income? Does the student have regular absences? Why is that?  What might be affecting his or her image of self as a learner and as community member in your classroom? As teachers, are we acknowledging and checking our place of privilege and power and how this might be affecting our students? What is the student’s story and how might this be affecting his or her learning of mathematics? What supports does this student in your classroom and school need to be successful?

Does it mean that the student does not have access to resources to support learning and success at school? Does the student have the tools and resources (human and physical) he or she needs at home to support learning? Are assignments and studying accessible and equitable for all students regardless of their home or financial situations? What supports can the teacher and school provide so all students have equitable access to the resources needed to support their learning? Afterschool homework clubs or peer tutoring? Choices in assignment and homework formats?

Does it mean that the student’s written work, homework and quiz and test scores do not indicate achievement of learning standards? Is written work or practice not completed during class time? Are homework assignments not turned in or completed, or attempted? Does the student seem to understand the mathematics during performance tasks and class discussions but is not successful on quizzes and tests? What different opportunities are students provided to communicate their thinking and learning? (It does not have to be written down to “count”!)

In all of the above scenarios, it may seem that I suggest that it is the teachers’ and schools’ responsibility to ensure student success in mathematics. Well, it mostly is – that is our job. Of course we need to have students and parents as part of this story, but when they may not seem to be, we, as a system, need to think about how to bring them alongside instead of using fixed terms such as “low” as an excuse, and explanation or a dismissal of responsibility.

How can we re-frame how we talk about our students and how we talk about learning mathematics?  There is a strong movement in mathematics education coming from various voices including Dr. Jo Boaler of Stanford University. This movement is based on the belief and conviction that ALL children can learn mathematics. Dr. Boaler’s work around mathematical mindsets is shifting how educators, parents and students think about the learning of mathematics. More information can be found here.

I attended a Learning Forward dinner event at the end of April and one of the question prompts the secondary teachers from Surrey gave us to provoke discussion was:

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This issue of deficit language resonates with me and I think by re-framing the language we use will re-frame how we see ourselves as educators and how we see the students in our classrooms.

Inspired by Linda Kaser and Judy Halbert and the four fundamental questions of the NOII, I wonder how many of our students feel that their math teachers believe that they can learn? We know its important that teachers convey that they care for their students and that they believe they can be successful. How does our language need to be re-framed in our classrooms so our students believe this to be true?

Instead of describing our students as “low”, what different language could we use? Learning. Developing. Growing. Competent. Full of promise and potential. How does using strength-based language shift our conversations and interactions with our students and with each other as professionals?

My hope is that we can describe our students as curious and engaged mathematical thinkers and learners – what is the story that needs to unfold in our classrooms if this is our goal?

Math matters. Language matters.

~Janice

With thanks to Faye Brownlie, Shelley Moore, Jane MacMillan, Lisa Schwartz and Sarah Loat for their feedback and contributions to my thinking for this post.

uncovering thinking about addition and subtraction in grades 1&2 at McNeely

Posted on: November 3rd, 2016 by jnovakowski

I am doing a series of visits to the early primary classrooms at McNeely Elementary to work with the teachers around inclusive practices that support students’ mathematical thinking and understanding. Meeting the first class of grades 1 & 2, I began with a number talk to see what strategies the students were able to use and to see how the students engaged in mathematical discourse. We named strategies and introduced terms like justify and reason into the students’s math talk.

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To follow this, I had designed several provocations for students to engage with around the concepts of addition and subtraction. I connected some of the provocations to the K-2 big ideas about computational fluency – relationships between addition and subtraction and building on an understanding of five and ten. After the number talk, I adjusted some of the provocations I had planned, being responsive to what the students had demonstrated during the number talk.

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I provided a brief overview of each provocation set out on a table, reading the question and showing the materials. I explained to the students that they would choose what ideas they wanted to investigate or questions they wanted to engage with and they could stay with one provocation the whole time or move to different tables. This was the first time the students has worked in this way during their mathematics time but for the most part, the students made good choices and stayed engaged with the ideas we were thinking about.

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The SumBlox blocks were presented on a table for students to explore. This was the first time these students had seen these blocks so I wanted to give them to time to explore and investigate the blocks without a specific question to guide their play.

While students were engaged with the materials and ideas, the classroom teacher, the learning resource teacher and I were able to spend time alongside students, listening and noticing. There were opportunities to prompt and provoke and to invite students to explain what they were thinking about or practicing.

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We brought the students to a meeting at the end of our time together, after they had put away all the materials we had been using. The students are beginning to learn how to talk about their mathematical thinking and shared what they did, what they liked and some students were able to share what they learned. With time, the intention is that students will share their findings and questions and make connections with each other during this closing discourse or “congress” time.

At lunchtime, the teachers and I were able to meet and discuss what they had noticed, what questions they had and what assessment information was able to be collected during the practices of a number talk and provocations. A starting point for professional discussion was sharing some of the video I had captured of students explaining their thinking. Based on what we noticed, the classroom teacher and learning resource teacher set some goals as to what they were going to work on with the students before my next visit – developing strategies focused on making ten and developing the language of “decomposing by place value” when explaining their mental math strategies.

These big concepts of addition and subtraction will be explored and investigated in many different ways all year – they are foundational concepts at these grade levels.

~Janice

inclusive practices in mathematics for grades 6-9

Posted on: October 30th, 2016 by jnovakowski

Building on interest from an ILC (Inclusive Learning Community) project Shelley Moore and I facilitated with grade 8 teachers at Boyd Secondary, we held an after school session in October looking at inclusive practices in mathematics for grades 6-9 teachers. These practices are particularly mindful of the personal, social, intellectual and physical needs of students in the middle school age range.

Shelley began the session by sharing Richmond’s history with inclusive education and sharing some frameworks she has developed for thinking about inclusion (bowling pins, Fisher-Price stacker toy, planning pyramid, etc). She refers to inclusions lenses – personal, social and intellectual as well as places – different classrooms and places in the school as well as out of the school.

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In using the planning pyramid, Shelley considers goals, tasks and questions for all students, some students and a few students, starting where ALL students can access the unit or lesson. And here’s Shelley doing the tree pose – using the analogy that everyone/all could start this yoga pose by using the wall for support!

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Shelley shared the two year project with the grade 8 teachers and students at Boyd, with the first year addressing the Shape and Space curriculum and the second year examining the linear equations part of the curriculum. One example of a planning framework for an initial lesson on geometry looks like this:

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We shared photographs and video from the Boyd ILC project to share how the project unfolded with the students. Blog posts about the project and be found HERE and HERE.

I shared some of the practices and structures that we considered during the ILC project at Boyd and that can be used as a guide for planning mathematics lessons and units with inclusion in mind.

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Some of the choices that students were provided were what types of materials they might use. For example, during our lesson together about the volume of prisms, some students built prisms with cubes, some students used centimetre graph paper to create nets for their prisms and other drew 3D drawings that represented the measurements they were working with. Another choice was the range within the concept being addressed – for example, in the geometry lessons, identification of basic 2D shapes (faces) was an access point for all while some students investigated a range of 3D prisms. In the study of linear equations, choices of equations to investigate and represent with balances and other materials were provided, increasing in complexity or number of operations. Students were also provided with choices in how they processed or representing their thinking, for example, iPad technology was available and students could use the camera to take video or photos and then use a choice of screencasting apps to provide evidence of their understanding of the concept. Non-permanent vertical surfaces (NPVS) aka whiteboards or windows provide another choice for students who may not want to sit and work at a desk or table or use paper and pencil. The research-based practice of using NPVS has been shown to increase engagement and mathematical discourse, particularly at the middle-school age range.

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I shared the idea of mathematical routines such as number talks as inclusive practices with starting points for all and a way to build an inclusive mathematical community in the classroom. These routines also focus on the nurturing and development of the curricular competencies which are the same for grades 6-9. One of the routines shared was WODB (Which One Doesn’t Belong?). This routine has become very popular in Richmond classrooms as it provides an opportunity for the clear connection between curricular competencies and content. Four items are presented and they all belong to a set/group of some sort – integers, polygons, etc but each item is unique is some way. The goal of the routine is for the students to analyze and use reasoning to justify or defend which one they think doesn’t belong in the set and why. WODBs for geometry, number, graphs, etc are available at WODB.CA  - a site curated by an Ontario secondary math teacher.

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Shelley has posted a pdf version of our slides from the session on her blog. They can be found HERE.

Because of interest, we will be facilitating a repeat of this session on December 6 from 3:30-5:00pm at IDC – register on our district’s event page with further follow-up sessions planned in the new year.

~Janice

introducing WODB in Kindergarten

Posted on: October 30th, 2016 by jnovakowski

I was back visiting the kindergarten classes at General Currie last week. After being introduced to Counting Collections, the students and teachers were interested in being introduced to a new math routine. Because I had noticed they had been exploring gourds the week before when I visited, I used gourds to introduce the idea and thinking behind a WODB (which one doesn’t belong?). As is the case with most young students, the students stayed quite focused on one of the objects being “the” right one and we needed some prompting to look at  various attributes – colour/s, shape, size, “bumpiness” – to think about why each gourd was unique within this set of gourds (how they are alike…all gourds, all have some orange). The students began to use language layering attributes together to describe uniqueness – “this one is the bumpiest and mostly all orange”.

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After looking at the gourds together and talking through “justifying” their choices, I showed them a WODB from the website wodb.ca - one I often use when introducing WODBs to primary class. I asked the students to notice how the dice were the same and then how they were different and then to turn and talk to a math partner.

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The students then moved on to some table time, choosing from more WODB experiences or working with counting collections. I just used masking tape to add a WODB frame to a table top and added a basket of  fall leaves. The things the students noticed and their theories  - “this one doesn’t belong because it has holes, it has holes because an animal was hungry and munched it” were interesting to listen in on. Lots of opportunities for sharing thinking and reasoning along with oral language development.

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I also had copied some WODB grids for students to use with materials from the classroom. One of the kindergarten classes used a basket of blocks to create WODBs for each other. Some students began by making three items similar and one that was significantly different and then, as they played with the idea of  a WODB a bit more, the students were able to explain a reason for each of the blocks not belonging in some way.

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The routine of WODB emphasizes many of the curricular competencies in K-9 mathematics:

  • use reasoning to explore and make connections,
  • develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving,
  • communicate mathematical thinking in many ways,
  • use mathematical vocabulary and language to contribute to mathematical discussions,
  • explain and justify mathematical ideas and decisions.

Using WODBs as part of your math program provide opportunities to develop curricular competencies connected to curricular content.

wodb-student-book-coverBuilding on the exploration the students were doing with shapes, I left a copy of Christopher Danielson’s book Which One Doesn’t Belong? with the classes so they can continue thinking about shapes and WODBs!

I will be back to visit these classes in a few weeks and am looking forward to seeing and hearing how their mathematical reasoning and communication has developed!

 

~Janice