why do we do this anyways?

I have never had a student ask me this in such forthright manner before...Why do we do this anyways?  We are never going to use this in our jobs.

Wow. From grade seven. I wonder what she will have to say as the mathematics she does at school becomes more abstract and seemingly disconnected from "real life".  Good for her to say how she feels and ask the tough questions. Although I wasn't expecting this today, I was prepared, am always prepared for how I might respond to this question.

Let me provide the context of this interaction...
I was at Quilchena Elementary for my monthly visit with the intermediate teachers. Today we focused on the role math materials/manipulatives can play in students' communication of their mathematical understanding and thinking.

We began our day in Una's grades 4 & 5 classroom working on using arrays to model multiplication and moving to using base ten blocks to model two-digit by two-digit multiplication with a focus on the place value language that "matched" the materials. This was hard work for these students. Many students were able to calculate the answers to the questions mentally and then modelled the answer with the base ten blocks. When re-directed to explain how this model showed the process of multiplication (which was the intention of the lesson), they were befuddled. The students needed some modelling and we used an approach to multiplication that could be described as distributed or parts-based and then connected this to the models that could be created with base ten blocks. There were some aha moments from students for sure but also, more work still to be done. Here are some examples of how the students worked through 12X23 and how some of the students represented the process in their math journals using pictures, numbers and words.

I moved on to Andrew's grade 7 class and worked through a similar process with the intention of moving to multiplication with decimal numbers. This is where the student's question came up as I moved from table to table. I took a few seconds to pause and calmly answered.

You probably won't use base ten blocks in any future job you have. You probably won't have to show your boss how you can multiply large numbers but...you will probably be asked to think, to problem-solve, to reason, to make sense of data and information. When we do things like this, it is to help you make meaning and create connections, to help you understand the mathematics more deeply, to be a thinker.

The principal takes all the intermediate classes for choir on the days that I visit so the teachers and I can meet together and discuss emerging issues in our collaborative inquiry. Today, we discussed students' notions of what math is, brain development, and why we teach math. Math isn't just for our students' future jobs. Being numerate is part of being an educated citizen who will make meaning of the world, ask questions and think critically. We talked about what mathematicians do...math is not about doing things quickly. Mathematicians spend long periods of time on one problem or proof, thinking, analyzing, synthesizing, generalizing, making conjectures, reasoning, creating models, etc. I think that sometimes we forget this in school mathematics which can often seem rushed and hurried to students.

After our collaborative time, I visited Tanya's grades 5 & 6 class that has been working on area and perimeter. With the resource teacher, I worked with a group of students on connecting arrays, area, perimeter, multiplication and division using colour tiles. Lots of oral explanations and mathematical vocabulary were used during our discussions.

For a performance-based task, the students in this class were designing their own apartments having to consider the total area and the area and perimeter of the rooms within. As I chatted with one student who had grandiose design ideas for her apartment, she said she liked doing this because it was real math, that she would use when she was grown-up. 

Made me think...sometimes the contexts and applications we provide in math classrooms help students to see the relevance of the math they are learning. Sometimes, it's not so clear and that's okay. We learn and think about math because it is developing us as thinkers and problem-solvers and nurtures the habits of mind that are going to help us in "real life" regardless of what job we might have.

~Janice

playground design and minecraft

Last week I had the pleasure of visiting Blair Elementary, the school I was a teacher-librarian and resource teacher at for the last three years. The parents are fundraising to build a new playground and April Chan, the teacher-librarian and resource  teacher invited members of the PAC, the school's principal and Chris Loat and I to attend a presentation from a group of students that she has been working with.

This group of students comes together once a week to do personalized inquiry projects. This term, the group embraced the idea of designing a new playground for their school. They interviewed and surveyed students to see what would be important to have in a playground and brainstormed ideas in their inquiry notebooks. The students worked in small groups to design a model playground, gathering lists of ideas and materials needed.

 The students then created scale models, many of which were developed directly from "blue prints" the students created.

The students presented their playground models, explaining why they chose certain elements or themes and described the process they went through in designing and creating their models.

Members of two of the groups also then used the tech phenomenon of Minecraft to build their playgrounds. The students navigated us through three-dimensional models of their playgrounds up on the big screen.


Here is a shot of the Minecraft model of a playground followed by the other model the students created.

I jumped on the Minecraft bandwagon when my sons became quite passionate about it. I watched and asked lots of questions and could see the potential for it in the classroom, if used with guidance and parameters. Last year, I was fortunate to work with this same group of students at Blair. For one of our inquiry projects we looked at innovation and students created Rube Goldberg type contraptions. Three of the students created and presented their work using Minecraft and were tremendously engaged.

If you are interested in the history and development of Minecraft, I recommend this book. Really interesting read.  For more information on Minecraft in Education, check out this site.

Lots of curriculum connections can be found in mathematics and science but more importantly, the process of inquiry, problem-solving, design-thinking and collaboration are competencies we know we want all students to develop while they are in school and these were all core to this project.

Chris Loat also did a post on our visit and it can be found HERE.

~Janice

what we know about coins

The Grade 1 students in Jenna Loewen's class at Garden City Elementary have been happily singing away to the classic song "Canada in my Pocket" by Michael Mitchell as they have been learning about the Canadian coins.

When I visited their class on Thursday, they could tell me all about the values of the coins, what colours they were and what animals or boats were on them. One student was also happy to share all that he had learned about the caribou...

We had small collections of pennies, nickels, dimes and quarters. The students enjoyed examining each coin and feeling the difference in their textures. They looked closely at the numbers, words and pictures on the coins. Each team of students took turns taking photographs of the coins using the iPads.

We then used the app Haiku Deck (like powerpoint for the iPad) and the students created captions describing each coin.

Here is an example of a group project created in Haiku Deck:


Created with Haiku Deck, the free presentation app

Our redesigned curriculum in mathematics has re-introduced aspects of financial literacy beginning at the grade one level. Learning to identify and describe Canadian coins will be one of the curricular content pieces at the grade one level and this is an example of a task that will support student learning in this area.
~Janice

showing what we know in math...first time using iPads

On Thursday, I introduced iPads in the classroom to Tina Grigoriadis' grades 3 & 4 students.  Garden City has 8 iPads (with more on the way) and the students were very excited to use them for math. They worked so well in groups of three, collaborating and sharing.

The class has been learning about multiplication and has just begun to learn about division and its connection to multiplication, specifically looking at arrays. Tina had many visual supports up in the classroom to support students with their mathematical understanding.

We introduced the students to the MathTappers iPhone app called Multiples. It has options for working with different levels of factors and practicing both multiplication and division, with ten frames and hundred charts as visual supports.

 The students then worked together, creating three different arrays using math materials. They learned how to take photographs with the iPads and then import these photographs into an app.

We then taught the students how to use the doceri app to use photographs, diagrams and the students' voices to represent and share their understanding of multiplication and division through the use of arrays.

 Some students preferred preparing a script that they could read as they recorded their voices on the iPad.

Here are some examples of the students' screencasts:

These screencasts reveal a "first-timers" use of the app - figuring it out, seeing what it can do. Most of the students described multiplication and division equations for the array they had photographed. A further extension (maybe for second-timers) would be to further explain their thinking about the connection between multiplication and division and how an array supports their understanding.

When we asked the students what they liked about using the iPads, one student commented that he was having fun but then he realized he was learning at the same time. As educators, we know that engagement leads to higher rates of learning and retention of information and these kinds of experiences that are hands-on, minds-on and collaborative are highly engaging for students.

~Janice

water cycle simulation in grades 2&3

The McNeely grades 2 & 3 teachers continue to explore ways of using iPad technology to capture students' learning in science. On Monday in Anna Nachbar's class, we discussed the water cycle - precipitation, collection, evaporation, condensation. We had lots of recent examples of precipitation to refer to - rain, sleet and snow.

We simulated the water cycle using the classic boiling kettle and cold cookie sheet demonstration. We poured the water into the kettle (collection), turned the kettle on and boiled the water, watching the steam come out (evaporation) and then watched as water droplets formed on the bottom of the cold cookie sheets (condensation) to the point that the poured down the cookie sheet and onto the desktop (precipitation).

The students worked in pairs and took photographs of each stage of the demonstration. Some students also took photographs outside as it was a very rainy day and there were good examples of collection (puddles), precipitation (rain) and condensation (clouds).

 The grades 2 and 3 students then were introduced to the app PicCollage and the students included four photographs, one for each stage of the water cycle. They added text to label or explain the stages.

With PicCollage it is easy for students to email their project as a jpg file and the following are some examples of the students' work:

Two students did some "app smashing" and used the image they had created in the PicCollage app and used it in the ShowMe app to further explain the stages of the water cycle:

 In Deanna Mayotte's class, we did the same simulation but this time, the students used the screencasting app ShowMe to document and explain the four stages of the water cycle.

And I liked how these two students connected each stage of the water cycle to what was happening in the real world outside!

During this professional inquiry, the teachers and I have talked a lot about the value of having the students develop a repertoire of apps that they can use to represent and share their science learning. After spring break, we intend to introduce another app or two and then maybe decide on a science task we can do and have the students choose the app they would like to use to share their learning.

~Janice

creating double bar graphs to compare winter olympics medal counts

The grades 5 and 6 class at Garden City has been learning about bar graphs. As part of a collaborative inquiry amongst a small group of teachers at the school, we have been looking at how iPad technology can enhance mathematical communication and engagement.

This week we provided the students with the medal counts charts from the 2010 and 2014 Winter Olympics. The students were welcome to use another data set or quickly create their own survey to collect some data, but the focus was on the creation of graphs using the iPads so I think all of the students just used the medal counts for their data set.

The students used the screencasting app doceri to create the graphs, after a short discussion about when and why you would use a double bar graphs. We reviewed the parts of a graph and then students worked in small groups to create their graphs. There was some frustration in labelling the axes and the students wished there was a typing/text feature that was easy to use.

The students' explanations in the following screencasts reveal a few things - misuse of mathematical vocabulary in labelling axes, understanding of the components of a graph to convey information clearly and a hint at the purpose of bar graphs. We didn't provide specific criteria about what the screencasts needed to have and if we had, we might have received more consistent information included in all the screencasts. The students seemed to have a good sense about what information they should try and convey though, without our explicit guidance.

And yes, the students could have just as easily created these graphs using paper and written out their analyses instead of using a screencasting app. After introducing apps like doceri, they become part of a student's repertoire and hopefully, they will be given choices in how they might represent and share their learning, and those who want to use paper and pencil can and those who want to use a screencasting app can do so or there might also be an option 3!

When we are assessing mathematical understanding, does it matter how students show us what they know? I don't think so. I think our role as teachers is to make sure students have many opportunities to show what they know about something, in ways that work for them. We want all our students to be successful and screencasting apps like doceri allow students who may have difficulties writing their thinking down on paper a way to show what they know, using visual supports and diagrams to enhance their explanations.
~Janice