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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 ... Read More

Dr. Cotter on Problem Solving

A few years ago while on a shuttle to speak on math at a 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 ... Read More

Dr. Cotter on Manipulatives

Are manipulatives necessary for teaching math? What is their purpose? Are some manipulatives better than others? These are important questions to consider when teaching math to a child. A concrete manipulative is a physical object that a child ... Read More

Dr. Cotter on Teaching Math

I’d like to take some time to discuss the science and art of teaching math. I call it a science because much research has been done into how children learn in general and especially math. I call it an art because each child is different, requiring ... Read More

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 ... Read More

Dr. Cotter on Place Value

Place value seems to be a difficult concept for many children and even adults. Western children traditionally are taught to add by counting. Counting ignores place value. For children, thinking in terms of tens and ones becomes an unnecessary burden ... Read More