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 … [Read more...] about Dr. Cotter on Division
Dr. Joan A. Cotter
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...] about Dr. Cotter on Addition and Subtraction Facts
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...] about Dr. Cotter on Measurements
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 … [Read more...] about Dr. Cotter on Manipulatives
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 … [Read more...] about Dr. Cotter on Place Value
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 … [Read more...] about Dr. Cotter on Multiplication
