2015 February Archive - Mathematics and Science in SD#38 (Richmond)

Archive for February, 2015

investigating communication and mathematics at Westwind

Posted on: February 28th, 2015 by jnovakowski

The early primary teachers at Westwind are focusing on an Innovation Grant project around developing the competency of communication in the area of mathematics. For my visit to the school last week, we focused on having the students communicate their mathematical thinking and understanding through materials, pictures, numbers and words.

In Dee-Ann Wozney’s kindergarten class, I did a demo lesson during which the other kindergarten teachers observed. After talking to Dee-Ann about what her students had been learning about, we did a short number talk involving ten frames and then I pulled the book Frog in the Bog out my bag and went with that. As I have with other classes this term, we asked the students to figure out how many critters were in the frog’s tummy. I had double ten frame mats available for the students, tubs of Unifix cubes and the students also had their math journals. We had the iPad cart in the classroom and I quickly showed an app that was familiar to the students – DoodleBuddy and how they could use that to draw to solve the problem. I introduced the ShowMe app and how they could use their voices to record how they solved the problem, accompanied by a drawing. The students made their choices and set off to solve the problem or prove their answer.

Interestingly, none of the students chose to use the blocks to model the problem. Many children chose to use the ten frames, using a different colour for each animal as I had modelled when I demonstrated how they could use DoodleBuddy. Several children drew a picture using DoodleBuddy – often of the frogs tummy with dots for the critters inside. Many children used ShowMe, with a few changing to another way to represent. It is difficult to be thinking about how to use a new app and solve a problem at the same time! One student drew ten frames as a model in her math journal and then recorded the number sentence for adding up the number of critters using numbers and symbols. Such range and variety in one kindergarten class!

We came together to show and share our mathematical thinking and the students were proud to show their different representations. What the teachers noticed is that most of the students had difficulty sharing their thinking orally. After a few students had shared, we stopped and asked the students to turn and talk to a partner so that they had a chance to orally rehearse what they would share. In our debrief after the lesson, the teachers felt the students might need some thinking frames modelled and practiced such as “I used….because” and “This helped me to think about the problem by…” to focus on process and metacognition. By having students share the different ways they solved the problem and thought about the mathematics also helps the class as a community build a repertoire of problem solving strategies, models and approaches.

————

In Erin Stapleton’s grade 1 class, I did a demo lesson on linear measurement, with a focus on communication. Another grade 1 teacher was able to also be in the class. I spent several minutes at the beginning of our time together looking at some of the illustrations from the picture book Actual Size by Steve Jenkins. We compared our eyes to the squid’s eye and our hands to the gorilla’s hand. The focus of this group time together was language development. I introduced terms like baseline, comparing, difference and the different terms we use when comparing horizontal length (long, short) versus vertical height (tall, short). The term difference was difficult for the students. When looking at the gorilla’s hand in comparison to the classroom special helper’s hand, I posed the question – how could we figure out the difference in size? A few of the students shared ideas about ways to measure the two hands but didn’t quite get at how to compare those measurements. We would re-visit that concept later in a more hands-on way.

To begin our measuring, I brought along a tub of “snakes” and a nesting set of owl dolls. I used them to line up along a baseline with other objects to compare which were longer, shorter, taller, etc. The students then chose and object and were tasked with finding something longer or taller and something shorter. The students use the iPads to take photographs and then the app PicCollage to compile and label their photographs.

As the students completed their PicCollage and put the iPads away, the next task they focused on was going back to two of their objects and finding the difference in their lengths/heights. The students recorded their observations using pictures and words with some starting to use numbers related to measuring as well.

Part way through the “finding the difference” challenge, the teachers and I realized the students were just developing an understanding of this concept so we paused and I used one student’s objects to coach the students through how they might find the difference. By measuring the height of the water bottle and owl doll with Unifix cubes, we could then line up the two towers of Unifix cubes side by side and see what the difference was, or how many more cubes taller the water bottle was than the owl.

The students were then able to continue on with this challenging task. We came together at the end of our two blocks of time together to show and share our findings. The students shared how they used drawings, often labelled, and words to show the measurements. Some of the students began to construct written sentences, using the language of measurement that we had been orally practicing during the lesson.

In both classes, the students were engaged in mathematical thinking during complex tasks for their ages and had many opportunities for talking about mathematics and showing and sharing their thinking and understanding.

~Janice

playful storytelling at Tomsett

Posted on: February 21st, 2015 by jnovakowski

Salima Parvez, kindergarten teacher at Tomsett Elementary, received an Innovation Grant this year to investigate playful storytelling through the First Peoples Principles of learning. Drawing from our experience with the Quality Teaching and Learning project (QTL), we have planned some story retelling and story creation experiences for her students. Salima is using some of the TTOC release time provided through the grant to visit Diefenbaker and Steves classrooms that are involved in the QTL project.

Salima has read The Little Hummingbird with the students and they have enjoyed retelling and re-enacting the story. During my visit last week, we talked with the students about Richmond might have looked like thousands of years ago (before Costco, Superstores, cars and roads etc) and how the land and river was shared by Aboriginal peoples for fishing as well as food and plant gathering. I read them several pages from the book Sharing Our World, which explains the significance of many animals important to Aboriginal culture of the Pacific Northwest. The students were then asked to think of a story involving the animals and to create a scene or setting for their story.

As the children created their scenes and chose their animal characters, Salima and I sat alongside the students, listening to and documenting their stories. We took photographs, video clips, used the notes app to scribe students’ stories or the SodaSnap app to capture a photograph and short story. The focus of the project is to focus on oral storytelling and finding ways to capture the students’ stories is an important part of the process, so that we can see how the students’ sense of story and use of language is developing.

Here is a link to a short video of some of of the students’ stories HERE.

~Janice

recording our measuring

Posted on: February 19th, 2015 by jnovakowski

In Lauren MacLean’s Kindergarten and Grade One class at Blair, the students have been investigating measuring. For this visit, I introduced the concept of baseline, as an important idea when we are comparing lengths or heights of objects.

The students lined up lengths of ribbons from shortest to longest and enjoyed investigating the matyroshka dolls and ordering them from shortest to tallest.

What we noticed beginning to happen, with just the invitation of leaving small clipboards available to the students, that many students chose to start recording their different measurements.

Some students already have a developed understanding of measuring using standard units, even including “cm” in their recordings and these students expertly used rulers to measure, paying attention to the baseline or zero marking. Other students used numbers to record relative lengths or heights or drew/traced other “units” (like paperclips) to indicate the length or height. One student used labels (small and big) to describe her measurements. We had the students share the different ways they used to communicate their measurements.

A short Animoto video of the students’ measuring investigations can be found HERE.

~Janice

what stories do shapes tell?

Posted on: February 19th, 2015 by jnovakowski

I visited Marissa Kishi’s kindergarten class at Whiteside, this time to investigate the Reggio-inspired shapes kit with them.

One of the choices for the students was to PicCollage on the iPads and choose a shape and take photographs of examples of that shape around the classroom. The students then created a labelled collage of their shapes, creating awareness of shapes in the environment and how shapes combine to create design, structures, etc for different purposes.

The students enjoyed creating shapes and combining shapes using the shape sticks.

I also brought an Osmo along for the students to try creating shape pictures with the Tangram game.

Two interactions during my time with these students stood out to me.

One student who has not been very verbal with me spent several minutes engaged with two triangular blocks, moving them around in different ways to combine them to make new shapes. I watched him for awhile, noticing his perseverance and ability to flip and rotate the triangles. When I asked him to tell me about what he was investigating, he said simply, “triangle.” Powerful.

Another student kept pulling me over to where she was engaged with materials to tell me all about what she noticed. She held up a semi-circle and pretended to eat it like a piece of watermelon. She stacked several shapes with a triangle on top and pretended to blow it out like a candle. She made flowers and ants. She made many connections to the world as she investigated the shapes and she saw stories in the shapes.

The two students engaged with shapes and language in very different ways but both highlighted to me the power of materials to support students mathematical thinking. What stories do shapes tell? What shapes live within shapes? So much to explore!

A short Animoto video of our shapes investigation can be viewed HERE.

~Janice

problem solving with A Frog in the Bog

Posted on: February 17th, 2015 by jnovakowski

Last week I read A Frog in the Bog by Karma Wilson to three classes – the grades 1&2 class at Grauer and then the grades 1 and 1&2 classes at Blair. The focus of the math lesson for all three classes was the same – figuring out how many critters the frog swallowed and were having a bit of a party in his tummy. (fyi, one tick, two fleas, three flies oh my, four slugs and five snails)

In all three classes, there were a few students who were quickly able to mentally figure this out, or who had kept track while I was reading the story and they were eager to share their answers.

I then asked those students to find a way to “prove” their answer by using materials, picture, numbers or words. Other students engaged in solving the problem using the same criteria.

At Grauer in the grades 1 and 2 class…

this student described his cumulative adding strategy

this student combined numbers to make 5s and then counted by 5s to reach 15

this student used a ten frame to count out the animals and then recorded this in his math notebook

this student used cubes, a row for each type of animal, and noticed a pattern, and then he counted the cubes one by one to reach 15

this student explained that he looked for numbers to make 10 and then added on

this student used diagrams of the ten frames to combine the different groups of animals, and seeing the total as a ten and a five to make 15

At Blair…

this student used the ten frames to model the number of animals in the story using a different colour for each group of animal

then she snapped all the cubes together to show the increasing number pattern

this student counted out the cubes on the ten frame then stacked them in towers to show the numerical pattern

this student drew the frog’s tummy and all the critters in it and counted them up one by one

this student was exploring how to record what he did in his head which was combine 4 and 1 to make 5 and then 2 and 3 to make 5 – two fives are ten and then add five more to get 15

this student used tallies as he counted up the animals in his head

we used the large ten frames and magnets to help us visualize and describe our stategies

the students enjoyed drawing the critters in the tummy and then thinking of different ways to count them up

In all three classes we focused on the students’ communicating their mathematical thinking. For many of the students, they only tried one way to solve the problem so by sharing their different approaches at the end of the class, they were able to hear and see some different ways for solving problems.

~Janice

math sessions at the district convention 2015

Posted on: February 8th, 2015 by jnovakowski

This year’s district convention is on Friday, February 20 at Cambie Secondary. Three of our math mentor teachers are presenting sessions.

During the first session, Braunwyn Thompson is presenting a session for teachers of grades 3-7 about using technology to support student communication in math.

During the second session, I am presenting a session about Number Talks, focused on teachers of grades K-5.

During the third session, Michelle Hikida is presenting a session on mathematical inquiry for primary teachers.

Weily Lin is collaborating with Asha Padmanabhan to present a session focussing on big mathematical ideas, intended for teachers of grades 4-9.

We invite administrators, teachers and educational assistants to attend these sessions to support their professional learning in the area of mathematics teaching and learning.

~Janice

place-based learning at Diefenbaker

Posted on: February 7th, 2015 by jnovakowski

Diefenbaker was one of the four schools that began in the Ministry’s Quality Teaching and Learning project last year around our district focus of playful storytelling using natural materials and weaving in the First Peoples Principles of Learning. Three of the teachers and one new staff member are continuing in the project this year which is also meshing nicely with a school-wide professional learning focus on the First Peoples Principles of Learning, Aboriginal education and indigenous knowledge.

On Friday, I spent the morning at the school and a block of time in all four classes. A teacher from Tomsett joined me in the classroom visits as she is working on an Innovation Grant project based on the QTL project.

We began in Jaclyn Cruz’s kindergarten classroom where they are just beginning to engage in playful oral storytelling. Today, the students were focused on building and creating scenes for their stories. A variety of materials were provided for the students to choose from. The classroom teacher and ELL teacher both recorded students’ descriptions of their story scenes using their iPads.

This student explained, “The bears are going to go in the forest and eat things. Here are trees and water and this is a log with grass in case you fall off.”

We then visited Michelle Hikida’s grades 2&3 classroom where the students spent the fall learning about the Fraser River. This week, they have begun to consider the stories that the Fraser River has to tell. The students created their story scenes, incorporating their factual and historical knowledge of the Fraser River – its depth and speed, what animals would be living in and near the river, what plants and trees would be near the river and how people interact with the river.

The classroom teacher paused the students so that a student could share his story. The students gathered around and watched and listened as he told his story. His classmates had thoughtful comments noting his expressive voice and a learning message about forgiveness built into the story.

After recess we visited Margaret Choinski’s grades 2&3 classroom where the students have written stories based on story scenes they created using photograph backgrounds.

The class has read the story Yetsa’s Sweater by Sylvia Olsen and the students have learned about the history of the Cowichan sweater.

Margaret has shown them a video documentary about the process of making the sweaters and the students have become well aware of the social justice issues involved with how these sweaters created huge profits for owners of tourist stores, particularly on Vancouver Island. The video of The Story of the Coast Salish Knitters can be found HERE.

On Friday, the students were creating border designs for a toque for one of the students’ new baby brother. Margaret is an expert knitter and is going to use of the student’s designs to create this special gift. Margaret shared knitting patterns she was able to find and provided the students with grid paper and some tips on creating a design that could be replicated. The students often chose elements from the artistic animal tiles that Margaret has in the classroom

Our last visit was to Kelly Hink’s kindergarten classroom. Here is the area in her classroom full of storytelling materials.

On each table was a plat of materials ready for students to select from.

The students had previously read the little book Raven and the Box from Strong Nations and retold that story. Today they were reading the little book I Spy Raven and retelling it, using their own choice of characters. Kelli modelled choosing characters and using the language from the book, demonstrated how to change the language to make sense for the characters they had chosen and the materials they had available. The students were paired together for their story creation and telling.

As in Michelle’ class, Kelli paused the class to listen to one pair’s story, to inspire students with their own stories.

Here is a link to two students sharing their story – HERE.

So much playing with language for five year olds!

~Janice

number talks

Posted on: February 7th, 2015 by jnovakowski

Last week I visited six classrooms in three schools to engage students in number talks and model this practice for teachers.

At Byng, in the two grades 4&5 classes we focused on multiplication strings beginning with the fact, 8 X 7. Most students were able to call out the answer (56) and then we focused on ways to fluently work with the numbers to help us understand multiplication. If you didn’t “know” the answer to 8 X 7, how could you figure it out? What do you know that could help you? A student shared that he could half the 8 and that he knew 4×7 was 28 and then he could just add 28 and 28 as that would be 8 7s. Another student said she would decompose 7 into 3 and 4 and do 3 7s and then 4 7s and then add them together. Since no students suggested it, I modelled decomposing the 7 into a 5 and 2 and asked if 5s and 2s were “easy” for their brains to work with and the students agreed that would be an efficient way to figure this question out. Students who are able to work fluently with multiplication like this demonstrate that they understand multiplication and have strong number sense which will help them out as they move to working with fractions, polynomials and higher level mathematics and making sense of numbers in their world.

In the grades 2&3 class at Byng, we focused on subtraction, building from two-digit subtracting one-digit numbers to two-digit subtracting two-digit number questions. The students demonstrated their fluency with the strategies of decomposing, counting back using a friendly number as a benchmark, using double and using known addition facts. The classroom teacher asked me to focus on the concept of adding up to subtract which requires an understanding of “difference” between two numbers. I find the open number line is the most accessible visual tool to support students’ understanding with this. As we proceeded with our number talks, I sensed the students’ growing understanding of this strategy and tool and for our last question, I called students up to the whiteboard to demonstrate their strategies themselves. The students added up by using tens and adding up to a benchmark/friendly number.

In the grades 1&2 class at Grauer, the students are beginning to use ten frames as a visual tool. We did a number talk using the ten frames, looking at decomposing numbers as they could see them visually in the ten frame. We played “flash it” and then “show it” where I flashed a ten frame card and then had to build and show it on their own ten frame. We then played “roll, build and see ten” to develop their understanding of complementary numbers to make ten. The students rolled one die, built their number on a ten frame and then visualized how many more to make 10 and had to say that number out loud. The game was extended for some students using a double ten frame mat to make 20. We then focused on the making 10 strategy as we did a number talk together not the board to figure out addition questions such as 8 + 5 and 9 + 6.

At Blair, in the grade 1 and the grades 1&2 classes, we did short number talks with ten frames, played some ten frame games like at Grauer and then did an addition number talk to focus on the strategies of counting on, making 10 and using doubles, having the magnetic ten frames available to students to use as a visual tool.

~Janice

Palmer Science Fair

Posted on: February 6th, 2015 by jnovakowski

Palmer held their annual science fair on Thursday, January 29th. Unfortunately, I was out of town at a conference so was unable to attend this year. Teacher Jason Chow provided some photographs to share here. As they did last year, the neighbouring elementary school classes were invited to attend during the afternoon. I am sure it was very inspiring for our younger scientists to attend.

A post on the Palmer website about the event can be found HERE. There are lots of great photos posted along with the results.

Thank you to Jason Chow for the photos!

a visit to Opal – January 2015: Hieu’s story

Posted on: February 4th, 2015 by jnovakowski 2 Comments

“Never doubt that a small group of thoughtful, committed, citizens can change the world. Indeed, it is the only thing that ever has.”

― Margaret Mead

Today, six days after our visit to Opal School in Portland, Oregon, I find my mind is still reflecting, questioning and creating meaning from the experience. Every moment of the conference gave me new insight to the practice of teaching.

On the first evening, my colleagues and I entered empty classrooms and observed the projects and environments that children were engaged in. As I wandered in and out of the six classrooms, I was taken aback by the aesthetic of the materials, the walls and the artwork produced by students as young as three to as old as 11. Some questions popped into my head. “How did the teachers come up with these ideas?” “How did the teachers know what they wanted children to learn?” “How could these students come up with such complex ideas and how did they learn to express their ideas in such sophisticated ways?”

“How might we use the wire to create a balanced composition that represents the idea of a community?”

However, it was not until the next day when we returned to observe teachers and children in action did I realize that nothing in the environment compared to the interactions and conversations I heard and saw. In every movement, every comment, every question, there was genuine care and respect. I saw students hugging each other, smiling at each other and displaying positive body language during whole group and small group conversations. In small groups, I heard only one voice at a time; children gave the speaker attention and responded truthfully and thoughtfully with their ideas. It did not seem as getting the “smartest” or “rightest” answer mattered, it was that each person had a voice. In this community of learning, competition did not take precedence and students and teachers felt they could take risks in areas where they felt most passionate and connected. Though I didn’t hear phrases such as “well done!” or “that’s a great comment,” I also didn’t see students seeking for teacher attention or affirmation. These students displayed a high level of self-awareness and self esteem at such a young age.

In the afternoon, at the Museum of Learning, we sat and listened to the teachers speak of their practice, I discovered that teaching was their life’s work and this place allowed them to share a core set of values. They spoke of teaching as a craft and as project in humanity. I realized their practice as individuals and as a collective is powerful because of their values. I reflect now on my own values. What do I believe education is? What do I see children as? What is authentic learning? Who sets the goals for learning? How is authentic learning measured? By measuring a child’s learning, what practice places judgment and what practice prepares the child for the step?

Each teacher that came up to speak spoke of the work they do as teacher-researchers. I have come to understand that this is a subtle but very significant shift in perspective when it comes to effective professional development. I asked teachers in a small group discussion what they did to harness their values and improve their practice. They said that they committed themselves to a reflective share in a circle space together once a week. Just as they planned circle time for students to share ideas as equals, they too, share their practice, their queries, and their need of help. From there, they work together to imagine and create possibilities for their students.

I learned the power of circle within my own practice from my colleague and friend, Lynn Wainwright. I was able to witness the affect of a commitment to deep listening of each other’s stories. It is through our collective stories that help us to reflect on ourselves and give us knowledge and courage to transform our practice for the sake of children’s learning. The teachers at Opal not only teach the process of inquiry, they also live it themselves.

At Blair, we value collaboration. We believe that an inquirer must have certain capacities, those capacities include the ability to reflect, communicate, and to think critically and creatively. But above all else, we know that a safe environment of community must be fostered before any depth of learning can occur. We are working to “walk the talk” through our own collective practice. This year, in my role of teacher-librarian, we have carved out blocks of collaboration time that can last for a full term of three or more months for interested teachers. The collaboration blocks allow students time to dive deeply into the big questions and enduring understandings; but, they also free teachers from time restraints so that we can reflect on patterns of our practice and develop our hunches and follow through with action learning (Halbert & Kaser, 2013). I am inspired by the collaboration I saw in Portland. I am wondering, “How can I open up spaces for teachers so all are invited to challenge their own practices?” “What are the structures we can use so that we focus more on the process of learning rather than the product of the weeks we have together?” “What do I need to do to improve my interaction as a collaborator to my colleagues?” To answer this latter question, I am reminded of two quotes I encountered in the past weeks.

“Listening is the simplest form of respect.” By Bryant H. McGill

and

“Attention is the rarest and purest form of generosity.” By Simone Weil

My personal take away from my days at Opal is to exercise restraint. In restraint, I can allow space for others to speak and feel. In restraint, I can allow myself to think carefully the language I will use to show respect and gratitude. In restraint, I will try to not react to my own emotions or my own assumptions. This is a goal for both my personal and professional relationships with children and adults.

I am deeply grateful for the opportunity to attend the Opal School Visitation Days. I truly felt that I saw the art of teaching before my eyes. I am eager to try the many other facets of inquiry learning that I witnessed there including the use of studio materials, the strategy of story workshop and many others. I believe that there is much that can be applied to our British Columbian context and also to our Richmond context. My learning journey is richer because of the teachers and students of the Opal School and because of the organization of The Centre for Children’s Learning.

Thank you, Hieu

Blair Elementary (teacher-librarian and resource/ELL teacher)