BLOG

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

Dr. Cotter on Counting

Most people think of counting as the foundation of math. So we teach kids to memorize the long string of 100 counting words. Next, to count objects, we teach them to touch each block in turn while saying the next word in the string. After completing ... Read More