#NotABookStudy - A 21st Century Professional Learning Opportunity

What a time to be an educator. Seriously, I mean that.

I feel so privileged to live in a time where we can conduct meaningful collaborative professional development from the comfort of our own couch, hundreds of kilometres away from some of our colleagues, learning at our own pace, on our own schedules, through whichever medium we prefer. Sounds pretty awesome, doesn't it?

As a part of this Northeastern Ontario Mathematics Leadership Network's (MLN) learning opportunity, we're embarking on a virtual learning journey, better known as #NotABookStudy, as we take a deeper dive into Cathy Fosnot's book, Young Mathematicians at Work: Constructing Multiplication and Division. 

While we have only packed our bags and begun this trek, so to speak, we've already had the opportunity to learn and share alongside some of Ontario's brilliant math leaders, not to mention, Cathy Fosnot herself, who shares her wisdom and experiences with us in a weekly live radio broadcast through VoicEd, as we unpack a new chapter each week. 

This style of PD is certainly something new for me, as the differentiated learning opportunities are only limited by your own imagination. Want to go deeper into a particular idea? Toss out a comment on Facebook and see who bites. Have a burning question related to a particular idea from the latest chapter? Tweet it out with the hashtag #notabookstudy and wait for the flood of reponses. Even if Twitter and Facebook aren't your thing, you've still got options, as there's always an avenue for you to enrich your experience. The weekly podcast alone, is enough to whet anyone's appetite for more, and if you can't catch it live, it's archived for listening at your own convenience (which may have been the case for me during Week 1, as I couldn't pass up my tickets to the Blue Jays home opener!)

Thus far, we've explored the first few chapters, which has only scratched the surface of the landscape of mathematical ideas, the role of context, and developing mathematical communities. At this point, that landscape still seems a bit fuzzy, and maybe even daunting, as it appears to be a long journey towards the horizon. But like all great adventures, with the right tools, resources, and companions, it will be an exhilarating ride to be sure.

As a mathematics leader in our system, I'm wondering about how we can create more opportunities such as this, as I know there would be a great deal of interest in this innovative style of professional learning. In the meantime, bring on chapter 3!

My First Three-Act Math Task

In recent months, our math team has been exploring rich math tasks, not only as an engaging way to teach math to students, but also as a tool to help educators understand the variety of strategies that students use to solve a problem. We can then place these strategies along a progression of inefficient to efficient. 

Lately, we have taken an interest in three-act math tasks, and in particular, tasks created by Graham Fletcher (a.k.a. GFletchy). If you aren't sure what a three-act math task is, you should check out this post from Dan Meyer, the inventor of the three-act task, among many other awesome things. I've been thinking about creating a task for a while now, and I finally got around to doing it. So, here's my first attempt. Enjoy!

DVD Dilemma

Ontario Curriculum: Grade 4

4m29–multiply to 9 x 9 and divide to 81 ÷ 9, using a variety of mental strategies 4m31–multiply whole numbers by 10, 100, and 1000, and divide whole numbers by 10 and 100, using mental strategies

4m34–use estimation when solving problems involving the addition, subtraction, and multiplication of whole numbers, to help judge the reasonableness of a solution

4m35–describe relationships that involve simple whole–number multiplication 4m36–determine and explain, through investigation, the relationship between fractions and decimals to tenths, using a variety of tools and strategies

4m37–demonstrate an understanding of simple multiplicative relationships involving unit rates, through investigation using concrete materials and drawings

Act 1:

1. How many DVDs will fit on the shelf?
2. What is your estimate?

Here is a link to GFletchy's three-act task recording sheet.

Act 2:

The width of one section of the shelf       The width of two DVDs

Act 3:

Click here to go to the Google Drive folder with all of the files. 

From Patterns to Algebra

For the past several weeks, our math team has been facilitating professional development sessions relating to the work of Dr. Ruth Beatty and Dr. Cathy Bruce, co-authors of From Patterns to Algebra, a truly amazing resource that showcases the progression of conceptual understanding of algebraic concepts.

We are extremely lucky to have Dr. Beatty so close to us, as she's literally just up the road at the Lakehead University Orillia Campus, and she's been kind enough to agree to work with our board to support our 7-10 cross panel inquiry work.

One of the most beautiful aspects of Beatty and Bruce's work, is how algebraic concepts are made so clear for students, through concrete representations using colour tiles. When students have the opportunity to mess around with algebraic concepts early in their elementary education, their transition to secondary school and formal algebraic instruction becomes much more fluid, as they already have all of this beautifully pre-constructed knowledge and understanding.

One of the things that From Patterns to Algebra explores is how very young students, even in Kindergarten, can begin to think about the relationship between the position number and the number of tiles, and use this understanding to make near, far, and very far predictions about a pattern. As an educator, it really is amazing to see that conceptual understanding unfold before your eyes.

One of my favourite activities that we've been exploring in our professional development sessions is the Secret Pattern Building Challenge, where students work in pairs to create the first three positions (or terms) of a given linear growing pattern using colour tiles.

An example of a Secret Pattern Building Challenge card

As a scaffold, students may use two different coloured tiles (one to represent the constant and the other to represent the multiplier), but as they develop their understanding, this scaffold may be removed, so only one colour tile is used. Once students have created the first three positions, they turn over their Secret Pattern Building Challenge card, and begin a gallery walk to see if they can guess the rules of the patterns created by their peers. This is a fun and engaging way to help students see concrete representations of algebraic expressions, while giving them the opportunity to get creative with their pattern in the process. Students may also begin to move away from simple array structures with the tiles, and start exploring other representations, including tile location and orientation.

Building the first three positions of the pattern

I've created a Secret Pattern Building Challenge Card google doc that can be found here, so you can try this activity out in your own classroom.

Of course, as previously mentioned, the beautiful thing about Beatty and Bruce's work is how well each of the concepts explored are scaffolded in a way that allows students to build on prior knowledge in a meaningful way. It really is powerful stuff, as it allows students to move away from recursive thinking to multiplicative thinking.

If you haven't had a chance to explore From Patterns to Algebra, I highly recommend finding yourself a copy. If you're an SCDSB teacher, I can guarantee there is at least one copy in your building! Otherwise, here's a link.

If you get a chance to try out some of the activities and document the experience, I'd love to hear about it!

Getting Started

During my first week as a math resource teacher, I thought about how great if would be if I made an effort to document the incredible learning experiences that lay ahead. Maybe I'll write a blog, I said to myself, I'll get started on that next week.

Well, almost three months in, I'm finally getting the wheels off the ground. Better late than never I guess.

My blogging experience has been limited to documenting a trip to Europe a few summers ago,  in an effort to not only provide our friends and family with daily updates of our adventures, but also to provide my wife and I with a personal and detailed artefact of our travels. While it seemed tedious at times, we cherish that snapshot of our trip, and we appreciate having such a dynamic collection of stories and pictures at our fingertips, and I found the reflective process almost meditative.

So here I am, trying to encapsulate my experience as a math IRT.  I have a love for doing math and for teaching math, but I recognize that there is a vast amount of mathematical ideas, content knowledge, and good pedagogy that awaits my discovery.

I can't say with any certainty how often I'll post, or even what I'll write about, but I owe it to myself to at least make an effort to make some sense out of the journey, and the lessons learned along the way.