## 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

## 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

## science and tech – show and share

Posted on: December 8th, 2014 by jnovakowski

On Wednesday after school, we held a “show and share” to share some new science and tech learning materials available in our district. All of these materials promote creative thinking and links were made to the creative thinking competency in our redesigned curriculum.

Teachers had time to try out the different materials, sign up for borrowing kits from DRC and for some hot chocolate, tea and cookies.

Osmo

The Osmo is a new device for the iPad that uses reflective artificial intelligence to use the camera within the iPad and a reflector to create a play area in front of the iPad. The kit comes with the device, a tangram set and a set of alphabet tiles and it now available at Apple stories as well as online. The three apps that work with the device are free through the iTunes store – Tangram, Words and Newton. The Osmo creates an interactive collaborative experience.

littleBits

littleBits are magnetic electronic components that can be connected to create circuits. The bits have different functions and allow students to make things that can do things just as make noise, light up, have a fan, etc. We piloted these materials in primary, intermediate and secondary classrooms last year with high engagement for students.

Squishy Circuits

Squishy Circuits are electrical circuits created with a battery pack, wires, LED lights and other components such as buzzers. Conductive and insulating playdoughs allow students to easily and safely create circuits.

Three Osmos are available to borrow from DRC as are three littleBits  kits – the pilot project kit, the workshop kit and the space kit. Squishy Circuits are on order and will be available soon.

~Janice

Posted on: November 27th, 2014 by jnovakowski 3 Comments

The students in Gillian Ewart’s grades 5 & 6 class have been beginning to learn about factors and multiples through creating arrays. Last week we decided to play around with the concept of “halving and doubling” as a strategy and how it could help us think about factors. I asked the students to created an array for 8 x 6. This task brought up language around columns and rows and what 8 x 6 would look like.

We then took the students through modelling halving and doubling with their arrays. Halving the numbers of rows and then sliding one half of the rows up to double the amount in each new row.

The big idea here is that the product (48) stays the same and that there is a relationship between halving and doubling. The students began to anticipate what their arrays were going to look like, realizing they were going to need to be creative in order to create their arrays after halving and doubling their 2 x 24 arrays!

As the students built and photographed their arrays, we recorded the corresponding equations on the whiteboard.

We also looked at all the factors we found for 48, beginning to look at factorization and “factor trees”.

As students were halving and doubling, they documented each stage by taking a photograph with the iPad and then labelled their photos using the Skitch app. We asked the students to focus on communicating what they had learned about factors by using arrays. The students then either used PicCollage or ShowMe on the iPads to compile their photographs and share what they had learned.

Here are some examples of the PicCollages the students created:

As students completed their documentation as a way to share their learning, they were asked to choose a new multiplication equation and play around with the idea of halving and doubling their arrays. This is something that the class was going to continue investigating after I left. We could have begun our investigation this way, with students creating different arrays, halving and doubling and seeing if they could generalize what might happen. For this context, we decided that a guided approach to start would provide the students with the language and understanding they needed to be successful when they investigated their own arrays.

This was my last scheduled visit to McNeely and our goal was to introduce a variety of iPad apps to the students so that they would have different ways to communicate their mathematical thinking and learning. I’m looking forward to hearing from the classroom teacher and students as to how this journey continues for them.

~Janice

Posted on: November 20th, 2014 by jnovakowski

Last week during my visit to Gillian Ewart’s grades 5 and 6 class, we played around with the big idea of equivalence. The focus of our time together was coming to an understanding that the = symbol is a sign of equivalence or balance.

I began by reading the first few pages of the picture book One is a Snail, Ten is a Crab, pausing a few times to check in with students to see if they were “getting it”.

I wrote the equation 9 = 2D + 1 on the whiteboard, intentionally choosing the order in which I presented the equation. I asked students to talk to a partner about what I had written. They shared their thinking and they realized the D was for dog (D is 4 legs) and that the +1 was the “constant” of the snail, as expressed in the book. I asked if there was another way I could have made 9 and they shared that a S + 1 would also work (S is the eight legs of a spider).

As a whole class we played around a bit with the idea of the balance scale and balancing both sides of the equation. So I added another dog to the right side and asked what I need to do to the left side to keep the equation balanced….D + 9 = 3D +1.

I asked the students to create an equation and add different animals or amounts to keep it balanced. A student asked, “Do we have to write the equations like that? (pointing to the whiteboard) Backwards?” which led to a great discussion about equations and trying to really get at what the = sign means. Some of the students continued to refer to “5” in the example below as “the answer” which as teachers, gives us great information about the myth-busting we can work on together.

The students engaged in the balancing equations work in a range of ways. Some students got very creative and complex with their equations on their whiteboards, others modelled their equations with materials, some students were able to think about the big idea using less complex equations and with the support of an adult and others used patterns in their equations to build and extend.

I

As students created equations, they took photos with the iPads to document their experiences. I did a quick demonstration of the PicCollage app and asked students to combine some of their photographs with a statement of learning for our time together. This is a great assessment check-in as a teacher and helps students to focus on big ideas in mathematics and providing evidence of their learning.

~Janice

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.

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.

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.

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

## 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.

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

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.

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.

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.

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.

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

## introducing Osmo

Posted on: September 27th, 2014 by jnovakowski 1 Comment

After seeing some early investors post about Osmo on twitter, I jumped on board and pre-ordered one. Osmo is an interactive system for the iPad using the camera to create Reflective Artificial Intelligence. The three free apps work with a reflector and base to create an interactive play environment. The Osmo is recommended for children ages 6-12. Osmo has two tag lines:

Play on the iPad with real people and real objects.

Osmo promotes social intelligence and creative thinking.

I opened my box and found three boxes of components.

I loaded the apps from the iTunes story, put my iPad in the base (you have to take any cases or covers off your iPad) and slipped on the reflector over the camera.

and we were ready to go!

First up was Tangram. The puzzles have difficulty options – the pieces are shown in colour, or in black and grey or just outlines. As you place the pieces in front of the iPad, the game provides feedback as to when you have the piece in the correct place and orientation. Great feedback provided as you play and overall, just a great visual-spatial play experience.

Next we tried Words. A beautiful photograph comes up on the screen and you are prompted with the number of letters in the word and then have to choose the letter tiles to spell the word. The letter tiles don’t have to placed in correct spelling order, the app reads the letter and places the letter in the correct spot in the word. If you place a letter tile out that is not in the word, it fills a spot at the top of the screen to show you what letter you have used incorrectly. This game can be played by yourself or versus friends and gets progressively more difficult. A great game for word work.

The last game we tried was Newton. There are not any physical components to go with this app but I personally found this one the most creative and engaging. Visual-spatial problem solving, physics and pinball wizardry all play a part in this amazing interactive experience. You begin with a plain white piece of paper and the reflector reads whatever you draw or place on the paper. Balls start to drop from the top of the screen and you need to direct them to their targets. It is a little mind-boggling at first to see your hand appear on the iPad screen as a line drawing. I also placed my phone down and it “read” that and created an image – I used it to bounce balls off of like a pinball machine. All the adults around me were amazed by Newton – lots of great interactive fun and learning to be had here!

The current price is \$80 and a reflector and base would be needed for each iPad which makes Osmo a little pricey for classroom use but on the upside, it is such a social, interactive game that can be placed upright on a table so that a group of 4-6 children can easily stand around and play together.

I’m looking forward to seeing what new apps and play experiences this new company comes up with!

~Janice

## documenting the components of soil

Posted on: April 19th, 2014 by jnovakowski

I made my monthly visit to McNeely last Monday to work the grades 2/3 teachers on their collaborative inquiry in using iPad technology to enhance students’ learning in science.

As part of the classes’ study of air, water and soil, I led a discussion with the students about the four main components of soil – air, water, organic matter and inorganic matter. The students were able to give example of what they might find in the soil outside that is organic and inorganic. Then, we went outside and collected a soil sample from the school’s garden plot. The students had great fun digging in the soil, trying to find some interesting specimens to add to their sample.

Upon return to the classrooms, the students looked closely at their soil samples, using magnifying glasses and loupes and using the zoom feature of the iPad camera.

The students took some really interesting photographs with the iPads.

The students used the app PicCollage to document their observations, including examples of both organic and inorganic matter.

Pairs of students that were finished their PicCollage page then used the ShowMe app to explain the difference between organic and inorganic matter.

We are hoping to add a new app or two to the schools’ iPads in May so that we can add one more app to the students’ repertoire of apps they can use to document their learning.

~Janice