Finding Elegance in Equivalence

Over the past week, we have been piloting diagnostic questions with students to get an idea of their understanding of equivalence. We gave students a series of questions, all having to do with the understanding of what the equal sign represents.

One question, though, really challenged my idea of what "higher order" strategies we were hoping to see in our students.

Here's the question:

If 4x + 8 = 52, what is 2x + 4?
Take a moment to figure it out.
What is your answer?
How did you come to that answer?

If you're like my colleagues and myself (and most of the students of whom we asked the question), your instinct might have been to solve for x using the first expression,

...and then substitute that value for x in the second expression:

So in this case, 2x + 4 = 26.

As students advance to higher order strategies when learning math, we often nudge them toward more efficient methods: generalized procedural strategies (as opposed to guess and check, or building concrete mode…

Blended PD - Reaching ALL Audiences

This past week, I took part in a discussion on Twitter about how to best curate and provide math resources for teachers. The Mathtastic PD series I wrote about in response garnered a little bit of interest, partially because it was delivered in a blended style - each session was designed around engaging participants both in-person, as well as remotely, at the same time.

In the original post, I mentioned how it was important to us to create GOOD, effective, remote PD. 

As someone who lives in a somewhat rural part of the province, and a two-hour drive from my board office, I have been on the receiving end of a lot of virtual presentations. And there's nothing worse than a fuzzy, poorly-mic'ed presenter whose slides aren't legible because of the camera angle. Well, maybe that one time I joined in the conversation via my Google Hangout connection and spooked the facilitator, because it was forgotten that I was even "there."

So, at the risk of just stating common sense,…

Beginning a New PD Adventure

This year, in response to feedback we had received from grade 7-12 math teachers that they would be interested in after-school professional development opportunities, we launched our Mathtastic PD series

Our goal was to offer quality professional development to teachers on a voluntary basis, on topics chosen by our math teachers. A quick poll of educators at the beginning of the year gave us an idea of the top five most-wanted PD topics:

1) Digital tools for teaching math
2) Coding in math
3) Triangulating assessment; Addressing needs of students with LD in learning math (tie)
4) Creating visuals to support learning mathematics
5) Spiralling math curriculum

While our initial goal was to have one session per month throughout the second semester, due to changes in schedules we were only able to have three afternoon sessions between February and the end of May

The three workshops we were able to offer this year were:

Introduction to Digital Tools in the Math ClassroomMath Strategies to Support…

Thinking and Re-thinking about Fractions

Last month, I was passing through the hallway one of our high schools, when I overheard a teacher delivering a lesson. He was discussing equations of some sort, where a fraction was multiplied by a variable. 

In this particular case, he was asking about 2/3 x 6. He checked the class for understanding: "Do we all know how to multiply a fraction by a whole number?" 

Think about that for a second. What is your go-to method for solving 2/3 x 6?

Thinking about fractionsPrior to this year, if someone asked how to multiply a fraction by a whole number, I would have given them the “algorithmic“ method of doing so: create a fraction out of the whole number by placing a numerator of six over a denominator of one. 

Then multiply my 6/1 fraction by 2/3: multiplying the numerators together and then multiplying the denominators together. This would give me 12/3, which could then be reduced to 4. 

Rethinking about fractionsFor the first time as a math teacher myself, as I walked by that classro…

Making Meaning of the Learning

We just finished another three great days meeting as the Mathematics Leadership Network (MLN) - a group of educators from boards of education across Northeastern Ontario, looking to further our development as mathematics learners and leaders.

Part of the learning in this latest round was centred on Michael Fullan's book, Indelible Leadership. In it, he discusses six big tensions when it comes to deep leadership. Two of those tensions - Lead & Learn in Equal Measure, and Feed & Be Fed by the System - really resonated with me.

Both of these tensions underscore the importance of reflection in one's practice. When learning (a fundamental part of leading), Fullan quotes John Malloy in saying: "...there has to be...vehicles, protocols, processes to actually reflect upon the learning, to make meaning out of what is emerging from the learning and then articulate from that." In order to give new learning meaning, we need to take the time to consolidate what we learn, po…

Digging Deep into Proportional Reasoning

This past fall, we continued a series of cross-panel co-teaching days with some of our grade 7/8/9 math teachers. In addition to co-designing and co-teaching a lesson in a grade 9 classroom, we also spent part of the day dedicated to digging a little deeper into a continuum of concept development for proportional reasoning.

Ahead of time, we asked each teacher to give the following task to their students. Calculators and manipulatives were allowed, and the question could be read to the students, but no instruction or guidance was allocated.

The point of the task was two-fold. First, we wanted to introduce teachers to the idea of how students develop proportional thinking. In upper elementary grades and in secondary math courses, we often jump right into the more advanced concepts, without looking back to see how students learned the basics (or even if they have learned the basics).

Second, we wanted to give teachers a chance to see how their students would fare on a question with no coac…

One Word 2018

It's that time of year again - a time for reflection and contemplation on the past year, and a time for setting new goals for a new year.

The past few Decembers, I've participated in the #onewordONT community, choosing a single word that summarizes my outlook and goals for the next year as I move forward in my professional practice.

For 2015, my word was JUMP - jumping into new adventures and taking risks to try new things.
For 2016, my word was REFLECTION - working more reflection into my practice as a teacher, but also helping my students reflect on their learning.
For 2017, my word was PATIENCE - practicing patience with both myself in learning a new role, and with the process of implementing change. It won't happen overnight.

PATIENCE was a good focus for me this past year as I work my way toward deeper understanding. Coming out of the classroom, I've been involved in many learning opportunities in my new-ish role as a math co-ordinator. The learning curve has been hu…