Making Mathineers: Transformational Math Experiences That Build Conceptual Thinking for Both the Teacher and the Student

Endorsements

As someone who was highly challenged with Math in school and declared herself as not good at math, this book is THE answer to our students no longer saying that! The nuggets of genius that Jonily has included in this book should be in every classroom. Every. Single. One.

—LaVonna Roth, Chief Illuminator,

Author & Speaker for Ignite Your S.H.I.N.E®

Jonily is all about Making Mathineers. Her stories are relatable, and her passion is infectious. She shows us that every student has their own mathematical story within them. This ground-breaking book will change the way we know and do math.

—Kary Oberbrunner Author of Elixir Project and

Day Job to Dream Job

Making Mathineers

Transformational Math Experiences That Build Conceptual Thinking for Both the Teacher and the Student.

Jonily Zupancic

With April Tribe Giauque

Making Mathineers

Copyright © 2020 by Jonily Zupancic with April Tribe Giauque.

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—for example, electronic, photo-copy, recording—without the prior written permission of the publisher, Author Academy Elite. Mindsonmath.com

Paperback: 978-1-64746-492-9

Hardback: 978-1-64746-493-6

Ebook: 978-1-64746-494-3

Library of Congress Control Number: 2020917112

Foreword

Welcome fellow educators! My name is Pat Quinn and for the past two decades I have been helping create school environments where all students can be successful. As a classroom teacher with years of experience at the elementary, middle, and high school levels, I have seen many programs come and go through my district, my school, and my classroom. Like many of you, I often shake my head when the names of the programs change, but the results do not. Year in and year out there are students who struggle to learn, survive, and succeed.

As the author of two bestselling books about creating classrooms where all students can thrive, I spend time traveling the country helping teachers and schools design better learning environments. About ten years ago I started to hear one name mentioned at multiple schools in which I worked. Her name was attached to words like common sense, teacher-friendly, and realistic. When I asked who they were talking about, the answer was always, Jonily!

I knew if there was this much grassroots support from teachers for someone who was sharing their craft, this must be good. So I made the trip to Ohio to check Jonily out. I was not disappointed.

Jonily Zupancic is a force to be reckoned with. She is truly a classroom teacher. She has the ability to communicate how teaching techniques she is using can easily be replicated by any educator. I have personally witnessed first-year teachers and 30-year veterans both using Jonily’s strategies in the same school! Across different curriculum, standards, states, and systems, her methods have been tried and tested and have proven to work for all students!

The world of improving math instruction is filled with researchers who study techniques in sterile settings that do not survive the transition to the chaos of a real classroom. These well-meaning academics have the luxury of controlling the variables that a classroom teacher simply does not.

Schools around the country are also dotted with superstar math teachers who have some sort of magic that makes their students succeed while other students do not. Unfortunately, either this cult-like personality is impossible to duplicate by other teachers, or the superstars themselves are unable to communicate what they are doing in a way that is meaningful to other teachers.

Jonily is the exception to both rules. Certainly, she is a superstar teacher, but not due to any magic not accessible to other teachers, (unless you count her smile)! Her techniques are proven to work in actual classrooms with lively students and real chaos that happens every day.

Because of this, Jonily Zupancic is uniquely qualified to write this book, Making Mathineers. This book is one of the few I would recommend to any teacher serious about reaching all students.

Math is a gateway to high-paying jobs and a future filled with opportunities and options. To deny this opportunity to a portion of our students because of a lack of time, resources or willingness to change is not acceptable. In a world where the advice coming from experts is often unrealistic or untested, Jonily fills these pages with simple strategies and techniques that open up the world of math to all students in all our classrooms. Jonily’s focus to make every student a Mathineer is the power of this book.

I cannot wait to get started!

—Pat Quinn

Author and Speaker at PatQuinn.com

Dedication

To my mom, dad, and Ryan for your unconditional support and for always cheering me on. To my kids, Anden and Baylor. You have been the driving force of making me the Mathineer I am today. Not only do I see math differently because of you, I see the world differently because of your perspective. You are the inspiration for my work. And finally, to the teachers and students I have had the opportunity to learn from over the past 20 years. Thank you for the wealth of mathematical knowledge I now have!

Table of Contents

Stories: Through Language, Stories Draw Us in. Math Stories are no Different.

CH1: Quadrant & Language: A Quick History

CH 2: Students—Math Ability and Number Sense

CH 3: Teachers—Can Be Taught

CH 4: Rebekkah—Where it all Started

Symptoms: My student struggles with ________. Teachers, Feel Free to Fill in the Blank.

CH 5: Positive-Positive—Quadrant I

CH 6: False-Negative—Quadrant IV

CH 7: Quadrant III—Negative-Negative

CH 8: False-Positive—Quadrant II

Strategies: It’s a Chicken and Egg Thing.

CH 9: Play, Say, See, Show, Know

CH 10: Target Questions—

CH 11: The Strategy of Making a Mathineer

11.1: The 120 Chart

11.2: Paper Folding

11.3: Making Rectangles

11.4: Subtraction is Distance

11.5: Division is Counting

CH 12: Change Behavior Before Belief

Success: Watching the Plots on the Quadrant Move!

CH 13: Look at my Plot, I Moved a Dot!

CH 14: Hey Teachers, Let’s Chat!

CH 15: Dallas—The Discovery

CH 16: Going Beyond Playing School

BACKADS

WORKS CITED

Introduction

Language is human communication through any of three methods that consist of the use of words in a structured way. These methods include spoken, written, and signed communication used by communities and countries. Without language, we would struggle to convey our needs and desires. In fact, we would lack the ability to learn from each other and teach our next generation.

Our stories are told through language, each person’s life is a story, compiled through experience and perspective. When you return home from a day of teaching, a family member may ask, How was your day? You might respond by sharing a story about a student, an incident on the playground, or something crazy that happened in math class. We are programmed to learn through stories.

Math loves stories. Our lives are replete with story and word problems, and if you are thinking that this book is full of all the tips and tricks on how to solve them, you’re wrong. We don’t need tips and tricks, vocabulary memorization strategies, or step by step linear approaches. There’s a new story to tell, designed to bring you a mathematical experience you won’t be able to forget.

Through the use of stories, you will experience Number Sense and what it truly is versus what you may perceive as Math Ability. Buckle up as we go through stories of the ups and downs of students and their teachers. I can’t wait for you to improve your own and your students’ Number Sense and Math Abilities! Experience the stories of students and teachers, discover symptoms, teach strategies and find success for all students! Are you Ready? Here we go!

Stories

Through Language, Stories Draw Us in. Math Stories are no Different.

1

Quadrant & Language: A Quick History

Language. What is it? It is human communication through speaking, writing, or signing that consists of the use of words in a structured way. It is a system of communication used by a community or a country. Without language, we can’t get our wants and needs met. We can’t share our desires with others, and we will struggle to learn anything. Language, in whatever form, allows us to express our wants and needs, and includes the discourse of math.

Many cultures provide people with an understanding of numbers through their language. They teach a word that represents each number, like one, two, three, four, five, and so forth to ten. Words that continue beyond ten are also represented in every language. There are structures and sets of rules in many languages that use the ten-rule, and also some that don’t.

In English, what comes after ten? Eleven, twelve, thirteen, fourteen, and so forth. However, there are many languages in the world that teach counting beyond ten using a consistent pattern of combining tens and ones, such as in Chinese and Russian. In these languages, eleven and twelve follow a pattern that helps learners visualize what occurs after 10—ten plus one. It’s different and easier to grasp than what occurs in English. Eleven and twelve are words that don’t follow a number structure.

In Chinese and Russian, the number for the English word eleven is a structure that includes the number ten: Ten plus 1, ten plus 2, ten plus 3; only in this context we get to leave out the word plus. The counting then becomes 1 ten 1, 1 ten 2 and so forth, until twenty, which is two tens plus zero, or 2 ten 0, and twenty-one, which is 2 ten 1. In German, as in English, the first two numbers following ten also don’t fit the pattern but everything from thirteen and up do. The numbers structured beyond the tens remain in that structure through hundreds, thousands, and so forth. It’s easier to think about what is being represented in this structure.

In Chinese, Russian, and German, children learn as tiny toddlers that there is place value and structure to numbers. Thankfully, it’s more than just memorizing or rote counting. They are learning to add one from the base to a set of ten each time you count up, and the language supports the structure because they repeat the word ten with each count. The language gives mathematics a sense of connection to the operation of number and value right from the start.

I had been teaching for a few years before my son, Anden, was born. I had a strong sense of numbering by this time. I wanted to make sure my son had this as well. When he was a toddler, I taught him how to count using the same structure as the Chinese do: 1 ten 1, 1 ten 2, etc. instead of eleven and twelve We did it every time we counted anything. The same rule applies for twenties: 2 ten 1, 2 ten 2; thirties: 3 ten 1, 3 ten 2 and so forth.

He took off with it and counted in this manner when we were in the car, at home, or out in the community. We did it forward and backward up and down until it became his permanent Number Sense. We played with ten’s and stacks of one hundreds. We played games with a 120 chart as well. It wasn’t until Anden started preschool that he learned the words eleven and twelve. But because he had a strong sense of number and counting with language that gave him an innate understanding of number connection to operation and place value, he started school way ahead of the game.

When Anden was in first grade, I asked him how many numbers there were in multiple hundred charts.He answered, 500, 600, 700, 800, 900 because since he understood the language, he could replace it with the correct word. When he got to the word 1,000, he said, 10 hundred, 11 hundred, 12 hundred, 13 hundred, then continued with, 20 hundred, 30 hundred, and so forth. Imagine your first graders understanding the same structure. This wasn’t done by memorization, but by practicing counting during many small interactions over time wherein the pattern and place value already built in was repeated over and over. Language is key to understanding mathematics!

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The Quadrant

As many of you know, the coordinate