Archive for October, 2014

what we know about patterning at grades 5&6

Posted on: October 31st, 2014 by jnovakowski

On Thursday morning, I visited Gillian Ewart’s grades 5&6 class at McNeely to work with the students around sharing their learning with technology. The class has moved on to investigating patterns. I explained that I had just been in a Kindergarten class where the students had been learning about repeating patterns. I asked Gillian’s students to explain to me what they meant by patterns. Students mentioned the terms input/output, expressions and “plus-ing numbers” with an example of a pattern rule of “starting at 2 plus 4″ with the number sequence of 2, 6, 10, 14, 18… and were able to use the terms increasing and decreasing patterns.

The students knew about t-charts and terms and what “n” stood for in an expression so I wrote the expression 2n + 1 on the whiteboard and asked the students to represent that expression using materials.

The different representations the students created reflected the materials they used. Some students wanted to replicate a t-chart and label the terms of their patterns, often using the materials to do so, like the photo on the right below.

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The photo on the left above shows how one student showed the “plus one” in each term but turning over the two-sided counter to show the yellow side. After sharing his example, we introduced the term constant. A growing vocabulary of mathematics language is associated with this topic of study.

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The students took a gallery walk around the class to see how other students represented the expression and thinking about “how is this the same as my representation? how is it different?” Next, the students were asked to think of an expression that they wanted to represent, choose their materials and represent the first four or five terms. Some students chose whiteboards or paper to create t-charts to solve for their expressions to support them as they built their representations. The students then took a photo with their iPads, labelled the photo using the Skitch app and then explained their pattern using ShowMe, submitting their screencasts to the class account.

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Some examples of their screencasts follow. These were their first attempts at orally sharing their understanding around number patterns and we asked the students to include as much of the specific math vocabulary as they could. We are considering these screencasts “first drafts” as most of the students just focused one part of a bigger explanation about their patterns. (please note that the sd38blogs platform is having difficulties with links to videos or embedding videos…here are the URLs for now until we get things sorted out)

http://www.showme.com/sh/?h=9nIZow4

http://www.showme.com/sh/?h=24I61w0

http://www.showme.com/sh/?h=z7KHnXc

For many students at this age, they become self-conscious sharing their thinking in large group discussions. Today we noticed the students were comfortable during the gallery walk where their models spoke for themselves and that the students are growing more comfortable recording their voices on the iPads. As a follow-up, some students will share their screencasts using the projector in the class and there will be another gallery walk where students need to figure out their classmates’ expressions, as expressed in their representations.

~Janice

 

Reggio-inspired mathematics: patterning kit

Posted on: October 30th, 2014 by jnovakowski

Over the summer we applied for a grant from the Vancouver Reggio Consortium Society to extend our professional Reggio-Inspired Mathematics inquiry project from last year to reach more teachers. Money from the grant has gone to build “kits” that will be used in many kindergarten and primary classrooms this year. Experiences with the materials in classrooms will be documented and added to our draft resource.

The first of the four kits to be ready and to go out to a classroom is the patterning kit. It looks like this when it is all packed up….

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and then like this when displayed as an invitation or provocation.

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The first class to use this kit is Marissa Kishi and her kindergarten students at Whiteside. We found a space to set up the materials in the classroom and the children were very curious!

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We gathered the students on the carpet area and after introducing myself, I let them know that their teacher had told me they had been learning about patterns. In the spirit of guided inquiry, I asked, “What is a pattern?” The students were able to provide many examples of patterns. Hands shot up and as I repeated my question, “What is a pattern?” students responded with:

“Yellow, blue, yellow, blue, yellow, blue”

and

“Green, yellow, green, yellow, green yellow”

and

“Blue, red, blue, red, blue red”

Some students used their hands to gesture and point as they described their patterns. Some students seemed to be “seeing” the pattern in their minds as they described them.

Marissa and I noted that all the examples involved colour and were AB repeating patterns. I asked the students to think of my question again and rephrased it, “What makes a pattern a pattern?” “What is it that’s special about it?”

With this prompting, one student explained that a pattern was something that repeats over and over. Repeating patterns are the type of patterns that are specified in the Kindergarten and Grade 1 math curriculum and although there are many types of patterns, I was happy we had moved towards a definition that made sense to these students.

We shared the different materials and spread them out on the tables in the classroom and asked the children “What different patterns can you make?” and asked them to keep thinking about “What is a pattern?”

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With pirate voices, a group of girls enjoyed creating patterns with buttons they discovered in a treasure chest. “red, black, red, black, red, black”

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Some hardware intrigued a small group of boys. Some students laid out the pieces in patterns while others tinkered away with them, figuring out how they worked together and then created patterns. Because the materials were all the same colour, the students needed to think about how to create and describe patterns in a different way. The pattern above was described as “up, down, up, down, up down”. In the photo below, the little guy I talked to pointed out all his patterns which were really little “stems” or “excerpts” of patterns that he embedded in one big continuous string of nuts and bolts and such. We had a great conversation but when I pressed him a bit on isolating the patterns and showing me which parts repeated, he didn’t want to go there. He was happy to continue investigating and laying out the materials.

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In the photo above, a student found a great solution for some coloured wooden beads that kept rolling away!

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In Kindergarten, students need to demonstrate their understanding of patterns with two or three elements. Since many of these kindergarten students seemed “stuck” on working with just two colours (and often in AB patterns), by providing them with three colours to work to with, we hoped they might branch out a little with their patterning and they did!

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I am looking forward to visiting this class again mid-November and seeing and hearing about what the students have uncovered as the investigate patterns.

~Janice

introducing playful storytelling at Steves

Posted on: October 29th, 2014 by jnovakowski

We are continuing our work with the Quality Teaching and Learning project with early primary classes and teachers this year. Our district’s inquiry is looking at the role of playful storytelling experiences in students’ oral literacy development.

Information about our work in the QTL project last school year can be found here:

Grades 1&2 Storytelling

 An introduction to QTL

Kidd, Diefenbaker, Blair and Blundell are continuing their work in the project and Steves, Ferris and Cook are joining the project this year.

Last week, I visited the Kindergarten and Grades 1&2 classes at Steves. Before my visit the teachers, Kathleen Paiger and Ellen Reid had taken the students outside to forage for materials for story settings/animal habitats.

good-morning-world-by-paul-windsor-640I shared some of the animals I had brought with me and their significance to local Aboriginal cultures and read the students Good Morning World. The students then chose their materials to create a setting for their story and then chose animals.

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What happened next in both classes was pretty special. A calm overtook the classes and the students were engaged with their materials and stories.

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Some students focused on building and creating while others enjoyed having their animals talk back and forth to each other. Some students were happy with a limited supply of materials and animals while others amassed quite the collection in front of them. Students naturally merged their materials and stories together. For some students, sharing their stories with an adult seemed very important, especially if it was captured on video.

Here are two short video clips of some kindergarten stories:

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These classes had collected rocks, twigs, leaves and acorns on their school grounds. As the students began to build their settings for their stories, one student in the grades 1&2 class was holding a twig with attached leaves in his hands, standing it up like a tree. I asked him if he could think of a way to make the twig stand up on its own…he thought of play dough. His teacher had plasticine in the class and he used that to stick his twig in and voila…a tree was standing. Other students noticed this and we had forests popping up all over the classroom.

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The synergy that emerges is one of my favourite parts of this project. The students collaborate, build on each others ideas  and co-create their stories…and forests.

-Janice

popsicle stick ten frame tutorial

Posted on: October 26th, 2014 by jnovakowski

I have created a photo tutorial of how to make the popsicle ten frames that we have been using as part of our Reggio-Inspired Mathematics Inquiry Project here in Richmond. After the ten frames have popped up in photos in presentations I have done at the NCTM conference in New Orleans and the BCAMT conference in Surrey, I have had many requests for info on how to make them.

So here we go…

For each popsicle stick ten frame you need:

12 standard size popsicle sticks

strong scissors

Aleene’s tacky glue (others may work but this is my tried and true favourite)

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I usually work on wax or parchment paper so that I can easily peel off the ten frames once they are dry (some glue gets under them).

Using strong scissors, but just the tips off of three popsicle sticks.

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Next, cut about one-third off another three popsicle sticks. The length of the longer piece which you will be using for the ten frames should be about 7.5cm long.

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Glue the straight tips of the popsicle sticks together.

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Position the three long glued-together sticks equal distances apart, using a popsicle stick to use as a referent. (If you are mass producing the ten frames, you could draw a template under your wax or parchment paper.) Glue a popsicle stick on each end of your frame. I find putting a dot of glue on the three contact spots on the base the easiest way to make sure everything lines up.

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Glue a popsicle stick directly over the “joints” of your long three glued-together sticks. This helps to reinforce and stabilize your ten frame.

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Glue down the last three popsicle sticks to make your ten frame and let the glue dry…time will depend on the temperature and humidity. I am usually making them late at night and just leave them be overnight and they are good to go in the morning!

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Now, you could be all particular and measure this out exactly but I just kind of eyeball it. After all, I am making these homemade creations for students as tools, and I have never had a single student comment that the ten frames aren’t exactly straight or the spaces all equal!

Students can use loose parts, mathematics manipulatives or other items to represent numbers for both counting, developing number sense and as a tool for beginning computation.

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One of the nice features of these frames is that students can lift them up and the representation stays behind…another way to visualize. The ten frame can then be used over and over again to create number representations.

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And yes, these little mushrooms are my latest obsessions. I just painted the tops of small wooden drawer pulls. I also made a set of dotted red amanita mushrooms to help students think about subitizing.

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~Janice

 

looking closely: the power of observation in early science experiences

Posted on: October 24th, 2014 by jnovakowski

On Friday afternoon, as part of BC’s PSA day, I presented a session at the BCScTA conference at Cambie Secondary here in Richmond. I shared some inquiry projects we have been working on in Richmond primary classes focusing on “looking closely” and investigating science outdoors.

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The following is the handout shared at the session:

Looking Closely BCSCTA 2014

-Janice

using visual tools to support early numeracy

Posted on: October 24th, 2014 by jnovakowski

I had the pleasure on the BC PSA day on Friday to share some of the work we are doing in Richmond in the area of early numeracy at the BCAMT fall conference in Surrey. My presentation shared the ways visual tools support strong number sense, the foundation of computational fluency. Examples of using Reggio-inspired practices, number talks and the use of iPad technology were shared from Richmond classrooms.

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The handout with links and resources can be accessed through the following link:

BCAMT 2014 handout

Thanks to the many teachers attending my session for their contributions to our thinking and learning. Apologies to those of you who were crammed into the room, standing along the periphery or on the floor!

-Janice

thinking about decimal fractions in grades 5&6

Posted on: October 22nd, 2014 by jnovakowski

I have spent two Thursday mornings in Gillian Ewart’s grades 5 & 6 class working with the students as they learn about decimal numbers (tenths, hundredths, thousandths) and how to represent them. Students at this grade level need a strong understanding of tenths and hundredths and then should be able to generalize this understanding to thousandths, ten thousandths, etc. Taking the time to work with concrete materials and visual tools to represent these numbers helps to develop strong conceptual understanding and sense about these numbers that will support students when they begin to apply operations (adding, subtracting, multiplying and dividing) to these numbers.

The iPad app, Skitch, was introduced as a way for students to capture representations of decimal numbers. The students took photographs of hundred grids in the classroom and then used the drawing and text tools within the app. The students saved their images to the iPad’s photo album.

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The students were then introduced to the screencasting app, ShowMe, and students were asked to show what they knew about decimal fractions/numbers by using the images they created in Skitch and then annotating the images further as they narrated their screencasts. Gillian quickly set up a class account on showme.com so the students could log in and save their screencasts to a shared site.

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An example of one of the students first tries at a screencast is posted below:

http://www.showme.com/sh/?h=QDS4HHU

A mathematics-based app that students used to start up their mathematical thinking at the beginning of our second session was Math Tappers: Numberline (an iPhone app). Students chose a range of numbers they felt comfortable working with and a type of numberline (different types of reference points) and then had to place a decimal number where they thought it should go. The students receive feedback as they play. The whole series of Math Tappers apps is excellent and they were developed by University of Victoria professors so they are particularly well suited to our curriculum.

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Next, we introduced the app Number Pieces. The students had been working on representing decimal numbers using base ten blocks and this app has students work with base ten blocks as a virtual manipulative and label and annotate their representations. The students then either used the Number Pieces app or a photo of a concrete representation with base ten blocks to import an image into ShowMe. The students then created a short screencast (we gave them an upper limit of one minute this time) to share their understanding of representing decimal numbers.

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By doing some oral rehearsal before recording, the students are getting more comfortable in communicating their mathematical understanding. The classroom teacher, Gillian Ewart has commented on the insights she gets into her students’ understanding and misconceptions as she listens to and views the screencasts which provide valuable information to plan what comes next in planning her instruction.

~Janice

thinking about math in September

Posted on: October 6th, 2014 by jnovakowski

Last week I was in two upper primary classes working with the teachers as they began to think about their math programs for the year.

In a grades 2&3 class at Grauer, the classroom teacher read the students Wemberley Worried by Kevin Henkes and she had the students write on a post-it note the one thing they were most worried about. Many of the worries were about friendships and such but five of the students expressed that their main concern was dealing with “hard math”. I was saddened that students as young as this had somehow internalized such negativity and anxiety about math. Why is math viewed as being “hard”? I wanted to have a discussion with the students. My sense from our short discussion was that others had warned them about math getting harder…that they should be ready for harder math, etc. Everything can be hard when you are learning something new…reading, riding a bike, learning to ski. Thinking hard and working hard at learning in part of the process. I am hoping to help turn some of the students’ attitudes about math around this fall and help them experience the joy of learning math.

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In both Andrew Livingston’s grade 3 class at Quilchena and Gillian Partridge’s grades 2&3 class at Grauer, I led whole class number talks. Many elementary schools in our district are working with the Number Talks resource. It is a great structure for students to communicate their mathematical thinking and for teachers to weave in needed modelling of mental math strategies as they respond to students and where they are in their thinking. In both classes, we began with 8+5, focusing on using doubles and making 10 and then moving to 48+5 and then 48+35, with the intention that students will use the strategies that they used with single digit numbers and see how they can be used with two-digit numbers. Embedded within the Number Talks structure is a layer of metacogntion – helping students become aware of what strategies they know. Students are asked not to raise their hands right away. They are asked to quietly hold up their fingers in front of them to show how many “ways” they can figure the question out. This of course, also gives everyone a chance to think for themselves without giving up once some students start waving their hands. We also practice communicating clearly with math language as we do “think, pair, share”  for some of the questions so all of the students get opportunities to explain their thinking to someone else.

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In the grades 2&3 class at Grauer, I wanted the students to think more broadly about mathematics and asked them to use pictures, numbers and words to show what math is all about it. This goes back to our discussion about math being hard and when I asked for examples, the students mentioned multiplication and division. Math is of course, so much more than number operations and I wanted to acknowledge that with this class.

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In the grade 3 class at Quilchena, I asked the students to show as many different ways as they could to make 78 using pictures, numbers and words. A task like this gets at students’ general number sense as well as their fluency and flexibility in thinking about numbers. We saw lots of creativity emerge once the students got going. And then, they were very excited to do some math graffiti on the whiteboard to share some of their ideas!

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I am visiting both of these classes again this week, checking in to see where the students are and working on some specific mental mathematics strategies.

-Janice