How Children Learn Number Concepts: A Guide to the Critical Learning Phases by Kathy Richardson
Publisher: Math Perspectives Teacher Development Center
Publication Date: 2012
Book Summary: A "must-have" book for every educator wanting to know how young children develop an understanding of number concepts. Through her years of research and extensive work with young children, Richardson has identified the stages, or Critical Learning Phases, children go through as they develop mathematical understanding.I am so excited about this book!! This is a very user-friendly, easy to read book that I am sure that I will keep as a handy reference when teaching and assessing math. I work with students with mild learning disabilities in grades 5 - 8, most of which are fully included in the general education classroom. And, although this book is geared to grades K-5, I think it is important to know where my students are coming from - and many times still are.
This important resource will help all math educators understand how children make sense of numbers and what mathematics they are ready to learn at each phase of development.
I love how the author identifies phases for the number concepts. I often wonder why many of the students I work with have a lack of number concepts. Since beginning this book, I am starting to see what is going on. As with stages to human growth and development, there are also stages - or in this case, phases - to learning number concepts. It only goes to reason, doesn't it? I think it actually helps me to better understand where my students are coming from. After all, we should be teaching them from where they are, and if we do not know the phase in which they are, how do we adequately teach them?
Chapter 1 - Understanding Counting
While reading through these phases, I started thinking about how my youngest daughter struggled through math. I have always been strong in math, and to see her struggle really threw me for a loop. Try as I would, I struggled to get it across to her. Everything was such a habit for me that I did not have to think about it - but it was automatic. I really had to break everything down for her. Now seeing it explained this way, it makes so much sense.
There are 4 categories to the critical learning phases to counting: 1) counting objects, 2) knowing one more / one less, 3) counting objects by groups, and 4) using symbols. Each category has different phases, with counting objects being the largest category. Having the author describe each phase really made sense to me - everything sounds so obvious, but I had never really thought them through before. Very informative, and helpful to me.
Counting is where number sense really begins. Although students can identify a number does not mean that they understand the quantity - or know "how many". When students begin to count, they know that they should point to an object, not necessarily touch or "identify" an object for each number they recite. Beginning counting is "labeling", or what the author refers to as "count and land".
There is just so much in this chapter!! One important aspect that the author points out is that although a student may be able to perform some of the tasks described in the phases, they may only be able to do it up to a certain number. A student may be able to count out something up to 10, but not able to count out up to 15. Or they might be able to identify a number that is one more than a number up to 20, but not be able to identify a number one less than 20. These really are phases, and each student falls along a continuum - each one at a different location within the phases. The depth and the breadth varies so much per student.
I found the misconception identified in the counting objects by groups quite interesting. We ask students to count a group of objects by 2s or 5s - often the beginner will move one object per word - of course this does not match the one-to-one correspondence - causing confusion. When we have students count coins - and only moving one object - this reinforces that misconception. Those that do fully understand phase will form groups as they go, counting each group by the correct sequence - thus matching in a one-to-one correspondence.
One thing that this chapter really reinforced for me was the need for repeated and consistent practice in a concrete format. Moving from that concrete practice, to a visual representation, and then finally to a symbolic format.
I'm in the process of creating a working checklist for this chapter. I will add it later.
Wow! That is such a rough summary of the contents of chapter one. You'll have to pick up the book yourself to get the real break-down. Click on the cover image above to be taken to the page to purchase your copy.
Make sure you visit the Math Coach's Corner to see her post on chapter 1 & join in on the discussion.