Thanks for joining me for Book Study Mondays! We are doing a virtual book study of Kathy Richardson’s book, How Children Learn Number Concepts.
Use the links to step through the entire series of posts:
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
Wow, what a powerful chapter! I continue to be amazed at how much is packed into each chapter of this book and how easy it is to read and follow.
She really sets the tone of this chapter by adding Parts of Numbers to the title. You just can’t know addition and subtraction without understanding parts of numbers. Take a look at this statement on the very first page of the chapter:
“When children know the parts of numbers through 10, they automatically know the basic facts.”
What could be more important in Kindergarten and 1st Grade than to help children understand numbers and their relationships? If they slip through without that understanding, they will likely struggle throughout their mathematical career. Again, that’s why this book is so perfect–it’s a roadmap of the critical phases.
The first critical learning phase related to addition and subtraction involves…drum roll…subitizing! Children need to recognize quantities in a variety of different configurations so they are not just memorizing a picture and associating it with a number. For example, the dot patterns on dice. I made a set of cards showing the numbers 2-5 in various patterns. Of course you would start with the smaller numbers first and gradually work your way up to the 5s. Click on the picture to grab your copy.
Once students recognize small groups, they’ll begin to see those smaller numbers in larger numbers. Look at the pictures above. Think about the smaller numbers you see in each configuration. Do you see 4 and 1 in the first picture?
In the next phase, children learn to combine parts. This is not just one step, but a series of stages. A key milestone is understanding that amounts are not changed when the parts are moved around. For example, if a student is working with 5 counters, they recognize that it will still be 5 counters whether they group the counters as 4 and 1 or as 2 and 3. As they continue to work with numbers, children start to use combinations they know to help with those they don’t. They might realize that knowing 3 + 3 can help them solve 3 + 4. She makes the point, and I think it’s an important one, that it is better for children to make that discovery on their own, rather than trying to teach them. The teacher’s job is to carefully craft experiences to lead children to make the discoveries on their own.
After combining comes decomposing. This involves finding missing parts. We’ve all seen versions of missing part games. You show a child 5 counters and then hide some. The child has to tell you how many are hidden.
Three ranges of numbers are identified for combining and decomposing: numbers to 6, numbers to 10, and numbers to 20. I found it kind of interesting that the first range was numbers to 6. I think we routinely think of the first range as numbers to 5. She included a cautionary note about combinations for 5, and explained why the first range is to 6. She said that teachers are often fooled into thinking that students know the parts of 5, when in fact they have only memorized the pairs. If students truly know the combinations for 5, they should be able to use that knowledge to determine combinations for 6. If they can’t, it’s a signal that they don’t really understand the parts of 5.
Finally, it takes time!! And, not surprisingly, children learn about number parts more quickly when they have lots of concrete experiences.
Great chapter with lots of powerful information! As with the other chapters, I’ve created a checklist you can use with your kiddos. I find it’s helpful for me to make the checklists–it helps me organize my thoughts from the chapter.
Next week, Chapter 4, Understanding Place Value: Tens and Ones.