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How Children Learn Number Concepts: Counting

Written by Donna Boucher

Donna has been a teacher, math instructional coach, interventionist, and curriculum coordinator. A frequent speaker at state and national conferences, she shares her love for math with a worldwide audience through her website, Math Coach’s Corner. Donna is also the co-author of Guided Math Workshop.

Welcome to the first in a series of Book Study Mondays, a virtual book study of How Children Learn Number Concepts, by Kathy Richardson.  I hope you’ll join me each Monday to read my reflections and contribute your own.  The more the merrier!

Use these links to visit any of the chapters:

Chapter 1, Understanding Counting
Chapter 2, Understanding Number Relationships
Chapter 3, Understanding Addition and Subtraction: Parts of Numbers
Chapter 4, Understanding Place Value: Tens and Ones
Chapter 5, Understanding Place Value: Numbers as Hundreds, Tens, and Ones
Chapter 6, Understanding Multiplication and Division

I loved this book from the moment I took it out of the shipping box.  It just looks like a readable book.  Do you know what I mean?  It’s small, thin, and looks friendly.  What I have found is that in addition to be readable, it is usable.  This is one book that you will want to have within reach at all times.  After reading Chapter 1, I just wanted to go out, grab a Kindergarten child, and put what I read into action.

Kathy begins in the Forward by defining Critical Learning Phases as “understandings that must be in place if children are going to be successful in the study of mathematics.”  And while I mentioned Kindergarten in the last paragraph, the audience of this book is teachers in grades Pre-K through 4.  So where did the Critical Learning Phases come from?  Over forty years of Kathy’s classroom experience working with kiddos from pre-school through 6th grade.  This book reads like a wonderful road map!  So let’s delve in to Chapter 1.

Chapter 1, Understanding Counting

As adults, we take many of our abilities for granted.  It’s easy to forget that at one time we didn’t know how to organize objects to count them or count by twos instead of ones.  It is habit to us at this point.  The chapter starts out with an overview of the difference between truly counting and reciting numbers.  It distinguishes between how adults see numbers and how children see them.  As with each chapter (I peeked ahead…), Kathy lists the critical learning phases and then discusses each in just enough detail.  The counting critical phases include four broad groups: counting objects, knowing one more/one less, counting objects by groups, and using symbols.  Each broad category contains a number of phases.

A common thread through many of the counting critical phases is that children are beginning to make sense of numbers.  It helps to remember that the symbol 5 means nothing to a child unless they understand the quantity it represents.  Reciting numbers in sequence is just a memorization task.  The book points out that when children begin to adjust estimates or catch the fact that a mistake in their counting doesn’t make sense, they are beginning to make sense of numbers.

Another point that I found interesting is that the critical phases are not all or nothing.  A child might be able to keep track of an unorganized pile up to a certain number, but then struggle as the numbers get larger.

I found the section on counting objects by groups particularly fascinating.  She first points out that when kids count by groups without actually counting objects, it can lead to misconceptions (back to that CRA idea).  What can result is students pointing to single objects and counting by, say, 2s, because they don’t completely understand the idea behind counting by groups.  We actually reinforce that misconception when we ask kids to count by nickels or dimes, because they point to one object but count by 5s or 10s.  So what does that mean in the classroom?  To me it means children need lots of concrete practice counting objects in groups prior to recitation.

Maybe it’s just me, but I automatically thought of having a checklist to keep track of students’ progress along these phases.  Use the links below to grab yours!

Checklist, Word document (editable)
Checklist, PDF (better formatting)

I hope you enjoyed this chapter as much as I did!  See you next Monday night for Chapter 2.

 

22 Comments

  1. Amy B

    I really was amazed after reading chapter 1. I never realized the stages of counting that our children move through. My aha moment was when she talked about counting money and just how confusing that can be for a child. We always have our kids count to 100 or now 120, but don’t always take that skill through the different stages explained in this book.
    I really enjoyed this chapter and it was an easy read. It left me wanting to read chapter 2, which I haven’t had a chance to do yet.
    Amy Burton

    Reply
    • Donna Boucher

      Awesome book, right? I can just see it being a go-to book for teachers when they want to know “why did they do that?”

      Reply
  2. WendyMK

    I was also impressed and facinated by this book. I trained to perform the assessments several years ago but we just began using them for kindergarten last fall. I wish I had read this book then. After just the first chapter I have a better sense, and better way of explaining, what the Counting Objects assessment is about.
    I had an “aha” moment about counting by groups, too. It makes sense but sometimes it takes seeing it in print to make me aware of the implications.

    Reply
    • Donna Boucher

      I love how this book is so direct and to the point. I can see how it would be a great companion to the assessments.

      Reply
    • Donna Boucher

      Thanks, Sara! I added your blog post to the linky.

      Donna

      Reply
  3. Donna Boucher

    What do you guys think about the checklist? Is this something you think teachers would find useful?

    Donna

    Reply
    • Sara Kovach

      Yes. I was working on one too.

      Reply
    • Sara Kovach

      Yes. I was working on one too.

      Reply
  4. Colleen

    Donna,

    Thanks for recommending this book. I will be working with a focus on math next year and this will help tremendously. I have the book in hand, just haven’t had a chance to get going yet. I’ll try to join in the conversation next week!

    Colleen

    Reply
    • Donna Boucher

      Looking forward to hearing your thoughts!

      Donna

      Reply
  5. teachersrock1971

    Just ordered it! Looking forward to sharing ideas and learning from others!

    Reply
    • Donna Boucher

      Ooh, you’ll LOVE it!

      Donna

      Reply
  6. Cristina Favreau

    I’m reading this as a future home schooling Mom. My son is presently in 1st grade, but will be doing 2nd grade with him. He EXCELS in math EXCEPT when it comes to word problems. I’m going to re-read the 1st chapter to see if I can spot where he needs more help.

    Some concepts are a little foreign to me–I don’t remember learning some of this stuff in elementary school and I’m not “in” it every day like teachers are. I’m also hoping the author will give more concrete examples of what a deficiency looks like or exercises to see if a child understands a certain concept. Again, it’s probably because I’m not a teacher by profession…

    I look forward to reading on and gaining more insight into my childrens’ mathematical development.

    Reply
    • Donna Boucher

      I could see how the book might seem to lack detail. The author, Kathy Richardson, has a lot of other books that include very detailed assessment tasks and instructional tasks. They would probably be helpful for background and a good compliment to this book. Another book that might be more helpful with word problems is Building Mathematical Comprehension, by Laney Sammons.

      Reply
  7. ThinkWonder Teach

    I can’t wait to order this book and join in. Every since you announced it I have been drooling over this book and have anxiously awaited your study to begin so I can at least catch a glimpse of what is going on. Unfortunately, I just spent $200 on textbooks so it is not in the budget. I usually have a little left over to buy books I want but not this round. Soon hopefully! Thanks for sharing.

    Misty
    Think, Wonder, & Teach

    Reply
    • Donna Boucher

      It is a great little resource. I’m sure you’ll get a lot from the book study without even having the book. But definitely put it on your wish list!

      Donna

      Reply
  8. Kathy Evans

    Excellent teaching resource, I can see how we jump to quick to abstract and need to use more concrete resources even with kids in second grade & older.

    Reply
  9. Sam

    I would love to buy a copy of this book, but Amazon don’t ship (new) copies to Australia. Any ideas?

    Reply
  10. Cindy

    Love this book! It confirms what I have been telling Kinder teachers for years. So many try to skip these important steps. They have the misconceptions mentioned in this chapter. Can’t wait for the next chapter.

    Reply
  11. Terry

    I have read this book a few years ago. I see students struggling in my second grade class with number sense especially when counting groups. Thanks for this book study!

    Reply

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