## Redefining Mathematics Education Related Posts

## Why Japanese Multiplication Works

Japanese Multiplication? Chinese Multiplication? Line Multiplication? Whatever it's called, it's only a trick if you simply memorize without meaning Have you ever wondered why Japanese multiplication works? I've heard some call it Chinese multiplication, multiplication from India, Vedic multiplication, stick multiplication, line multiplication and many more. While many might argue as to the...

## Counting Principles – Counting and Cardinality

A Progression of Counting and Quantity As a former secondary math teacher and intermediate math coach, my new role as K-12 math consultant has led to a wealth of knowledge that I wish I had during my years spent in the classroom. My conversations about student learning needs with intermediate and senior math teachers always seems to come down to gaps in student understanding, however rarely wer...

## The Progression of Fractions

Exploring Fraction Constructs and Proportional Reasoning Fractions are a beast of a concept that causes struggles for many adults and students alike. While we all come to school with some intuition to help us with thinking fractionally and proportionally, the complexity quickly begins to increase as we move from concrete, to visual, to symbolic and from identifying, to comparing, to manipulatin...

## The Progression of Multiplication

Arrays and Area Models to The Standard Algorithm Did you know that the words "array" and "area model" appear in the Grade 1-8 Math Curriculum a combined 22 times? Not only do arrays and area models help to support the development of proportional reasoning when we formally introduce multiplication in primary, but they also help us understand how to develop strategies that lead to building numbe...

## The Progression of Proportional Reasoning From K-9

The Foundation and Development of Multiplicative Thinking Proportional Reasoning is a big idea that is connected in some way to all mathematical strands and stretches across many grades in the Ontario mathematics curriculum. While many focus on the importance of proportional reasoning for students in junior and intermediate grades, I believe that we can see the early development of proportional r...

## Talk Less, Listen More

Time flies, doesn't it? It is hard to believe that this is my first post of the 2016-17 School Year and it is the middle of October. After doing some travelling to present throughout the summer and spending the balance of my time with my family, the beginning of the school year came fast and furious and hasn't slowed down yet. There was definitely no "ease in" time for my new role as K-12 Math...

## [Updated Post] Does Memorizing Multiplication Tables Hurt More Than Help?

Post update: Saturday May 21st, 2016 This post was originally written two years ago and admittedly took an angle that downplayed the importance of automaticity of multiplication skills which was not the original intention. Please read on as I attempt to clarify the original intent of the article. Let's Promote Understanding to Build Automaticity Over Time As you may have heard in the Globe and...

## What Makes A 3 Act Math Task So Effective?

When delivering teacher workshops, I almost always include a 3 Act Math Task as a way to model the 4-part math lesson framework and for teachers to experience the power of introducing new concepts by leveraging curiosity. Although my workshops spend a significant amount of time exploring interesting lessons, teachers often want a formal description of what defines a 3 Act Math Task from any othe...

## #MTBoS Blogging Initiative Week 1: One Good Thing

Man. Time FLIES! I feel like it was just yesterday when I made a commitment to myself to do a "Week In Review" series that summarized what I had been up to in the classroom each week. I had all the momentum on my side up until week 6, but then I was off to Norway for the NORCAN Project for over a week. Talk about falling off the wagon hard! Then, we hit the busy "before Christmas Break" stretc...

## Grade 9 EQAO Math Practice Links for @Knowledgehook Gameshow!

Convenient & FREE Practice Options For Your Students A few folks were interested in the Free EQAO Practice via Knowledgehook’s Gameshow tool, but felt they didn’t have the time to experiment with a new tool during “crunch time” in the semester. I know the feeling! Now, Knowledgehook has made it easy for students to practice any Gameshow independently without any setup, registration, or other h...

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