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6. Montessori

Dr. Cotter on Problem Solving

A few years ago while on a shuttle to speak at a math convention, I started talking to a young man next to me. When he found out I was involved in math, he said he could solve story problems as long as someone told him what operation to use. The young man didn’t realize

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6. Montessori

Dr. Cotter on Division

Long division used to be considered the ultimate goal of arithmetic. An earlier division algorithm was so complicated it wasn’t taught until college. Today some students learn a mnemonic in order to remember what to do when in the long division process. One example is DMSB (Divide, Multiply, Subtract, Bring down). To make it memorable,

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6. Montessori

Dr. Cotter on Addition and Subtraction Facts

Addition  Addition can be thought of as finding the whole when the parts are known. Place value greatly simplifies finding the sum of two numbers. To be efficient in adding, we start with the sums of numbers 1 + 1 through 9 + 9. These are best learned through strategies, especially visualizable strategies, and through frequent usage. 

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6. Montessori

Dr. Cotter on Measurements

Measurement is an application of math that is an important part of everyday life. We measure length, area, volume, mass (weight), temperature, time, angles, and many other attributes. For more than simple comparisons, we need numbers and a basic unit. Sometimes, two or more units are combined. For example, we speak about speed as miles

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6. Montessori

Dr. Cotter on Manipulatives

When teaching math to a child, there are three important questions to consider: Are manipulatives necessary for teaching math? What is the purpose of manipulatives? Are some manipulatives better than others? First of all, let’s define manipulatives. A concrete manipulative is a physical object that a child handles in order to learn mathematics. Some math

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6. Montessori

Dr. Cotter on Place Value

Place value is the very foundation of arithmetic. Place value packages numbers into groups of tens and tens of tens. This makes calculating large numbers similar to adding single-digit numbers: 3 + 4 is similar to 30 + 40, 300 + 400, 3000 + 4000, and so on. We need to regard place value as

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General Info

Dr. Cotter on Multiplication

Multiplication has been the mathematical downfall of many children (and adults!). It’s not so much the problem of the algorithms, but rather it’s the problem of the memorization of the 100 facts. Before expecting the child to learn the facts, we need to teach the meaning of multiplication. So often, we say it is the same as

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6. Montessori

Dr. Cotter on Counting

Most people think of counting as the foundation of math; therefore, they teach kids to memorize the long string of 100 counting words. Next, to count objects, they teach them to touch each block in turn while saying the next word in the string. After completing this counting ritual, the child must be ready to

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Card Games

2023 Summer Game #11: Fraction of Twelve

My two youngest children were six and eight when I started schooling them together in RightStart™ Math Level B. About half way through Level D it became apparent that my older son was ready to “fly” while my younger son was ready to “camp.” When the older of the two was in Level G and the younger one was in Level

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Card Games

2022 Summer Game #12: Difference of Two Squares

As the summer temperature rises, you may be looking for a non-competitive game. The Difference of Two Squares, game P35 in the Math Card Games book, hits the spot. It’s like a puzzle that two people work on together. You will need 20 basic number cards. Just a nice selection, no specific numbers are needed. Paper and pencil too. My

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RightStart Math: Free Support, Resources, and Training

September 2025 Newsletter We want to remind you of the many free resources available to you as a school that uses RightStart Math. 1. Year-Round Continue Reading

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Start Math Right Dr. Cotter’s Greatly Anticipated Book is Here!

We are excited to announce the release of Dr. Joan Cotter’s new book, Start Math Right—a valuable resource designed to empower educators and parentsContinue Reading

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Thank you teacher!

We want to take a moment to say a special thank you for the incredible work you do. We see the dedication, the late nights, the creativity, and theContinue Reading

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RightStart Math and Classical Education

Classical education is built on the foundation of strong reasoning, deep understanding, and mastery of fundamental skills. When it comes toContinue Reading

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Happy New Year! Welcome to 2025!

January 2025 Newsletter Welcome to the New Year 2025!  We hope everyone had a fabulous winter break! As you start the new year, here are someContinue Reading

Quilting and the Cotter Abacus

I am a quilt designer. I’ve made over 250 quilts in my lifetime, 98% of my own design. I’m currently working on my sixth quilt from someone else’s pattern.I have the directions in front of me as I’m approaching on the final steps of Bonnie Hunter’s Allietare quilt design. I find myself struggling to understand how

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Dr. Cotter’s Abacuses

How many different abacuses do you think Dr. Cotter has? Here’s a clue…. Dr. Cotter is holding one of her first abacuses: a Japanese abacus, purchased by a friend who had visited Japan. She became so efficient using this abacus that she was faster and more accurate than she was with a calculator!While you try

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Start Math Right – Fractions Chapter

Kathleen is here to walk you through the Fractions chapter of the new Start Math Right: The Journey to Mathematics Excellence book. She begins with a story of fractions and confusion from 1972, then goes on to discuss what a fraction is and how to teach fractions. Kathleen also discusses how not to teach fractions!

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Start Math Right – Division Chapter

Listen to how division is addressed in the new Start Math Right: The Journey to Mathematics Excellence book. Teresa Foltin talks about how division is the most challenging of the arithmetic operations, and shares that there are two distinct ways to think about division. One way is to find the size of a group; another

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Start Math Right – Multiplication Chapter

Are you curious how the new Start Math Right: The Journey to Mathematics Excellence book addresses multiplication? Listen to Allison Fitzgibbon share her discoveries from the new book. Allison admits that the multiplication chapter was packed with more information than she had time to cover! She chose to focus on patterns found in math. Multiplication

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Start Math Right – Addition & Subtraction Chapters

Rachel is here to give you a summary of the Addition and Subtraction chapters from the new Start Math Right: The Journey to Mathematics Excellence book! Rachel Anderson was one of the proofreaders for Dr. Cotter’s book and shares her insights during the January 2025 Online Conference. She begins with a quote from the book.

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