## 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...

## The Four Roles of the Numerate Learner

Effective teaching and assessment strategies to help students think differently about mathematics Mary Fiore and Maria Luisa Lebar If one were to ask whether language literacy and mathematical literacy were alike, I would predict that the beliefs of the majority would be that they are very different. In The Four Roles of the Numerate Learner, authors Mary Fiore and Maria Luisa Lebar use the fi...

## Making Number Talks Matter

Developing Mathematical Practices and Deepening Understanding, Grades 4-10 Cathy Humphreys and Ruth Parker Mathematics Professional Reading In my district, Number Talks: Helping Children Build Mental Math and Computation Strategies, Grades K-5 by Sherry Parrish has been a major resource for our primary and junior teachers to promote proficiency and fluency in number sense and numeration for t...

## Becoming the Math Teacher You Wish You Had

By: Tracy Johnston Zager Mathematics Professional Reading I just recently had the opportunity to read Tracy Johnston Zager's new book, Becoming the Math Teacher You Wish You Had and I'm so glad I did. The Foreword begins with a reference to the author, Tracy Zager’s quote that “Good math teaching begins with us” and tells us that the book will take us on a journey through a number of differen...

## 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...

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