After you have addressed a child’s belief in his own ability and desire to do math, where is the most important place to start instruction? Let’s start with three questions:
What are the most important things a child needs to learn in math by the time they finish elementary school?
What are the biggest stumbling blocks to math success?
What makes a child “good at” math?
IT ALL COMES DOWN TO PLACE VALUE. We can’t overstate the importance of place value instruction.
According to Sherman, Richardson, and Yard, “Place value is perhaps the most fundamental concept embedded in the elementary and middle school mathematics curriculum.” Place value provides the foundation for regrouping, multiple-digit multiplication, and more in the base-ten (decimal) system, as well as a starting point for the understanding of other base systems. (Demme Learning, Place Value Is Important.)
Math is all about patterns, and our number system is based on patterns of ten. Once a child truly understands this, they can work with any number, including negative numbers and including decimals. Big numbers work the same way smaller numbers do.
Kindergarteners and first graders absolutely must develop their understanding of the permutations of ten. Then they must understand how those addition patterns can be applied to multiples of ten. Older students must understand how and why the digits in large numbers and after decimal points are based on multiples of ten. However, they can’t do this if they didn’t master the primary grade concepts.
Indeed, when I meet an older child struggling in math, the very first thing I assess is their understanding of place value. I would say 90 percent of the time that is the foundational problem.
For further reading:
The Yale National Initiative has a great article on Cracking the Place Value Code
The Concept and Teaching of Place Value in Math
Effectively Teaching Place Value
See my follow up articles for my favorite games, projects, and hands on activities for teaching this concept which is the foundation of all math.
Beginning Place Value: Tens and Ones
I love this. I’ll be teaching 5th Grade Math for the first time after teaching 8th grade and up for about 20 yrs.
I am so sorry I somehow missed your comment, Delores! I am really glad it’s helpful to you. I have learned so much about how kids learn math in the last few years and am excited to have a place to share it. Please let me know if there is anything specific you’d like to see on the site.