Tag Archives: Young Children’s Mathematics

What is Cognitively Guided Instruction?

 ChildrenCounting

What is Cognitively Guided Instruction? Why do we do it?

Early on a Saturday morning a few weeks ago, I had a conversation with more than 200 teachers and administrators (and a few school board members) about Cognitively Guided Instruction (CGI). The conversation started when I posed the questions, “What is CGI and why do we do it?”

The response was inspiring, thought-provoking, and humbling.

  • Inspiring because the ideas shared highlighted the wisdom and commitment to young people.

  • Thought-provoking because the response pushed me to reconsider my own ideas of CGI.

  • Humbling because it reminded me about the power of collective work and how even in the most challenging times for education, together we can push back and work to change the status quo.

Before sharing what the group came up with, I want to explain why I began this conversation. Over the last year I have found myself needing to define or position CGI in particular ways. As I considered how I might do this, I recognized that CGI is not mine to define. CGI is not mine. It’s not even Tom Carpenter and Eliz Fennema’s. And it never has been.

Continue reading

Supporting Development of the Cardinal Principle

young-childrens-mathematics_mg5d5729

Adapted from Young Children's Mathematics: Cognitively Guided Instruction in Early Childhood Education

By: Thomas P. Carpenter, Megan L. Franke, Nicholas C. Johnson, Angela Chan Turrou, and Anita A. Wager


Capturing a child’s understanding of the cardinal principle while they are counting can be challenging, as children don't necessarily end the process of counting by explicitly stating the total amount that they have in their collection. A child may know that counting objects involves reciting a sequence of numbers, but not that the outcome of this process is a number that represents the total quantity. A child may say “1,2,3,4” as they count a collection of four, but this does not necessarily mean that the child understands that there is a quantity of four objects. Applying the cardinal principle requires that children name the set according to the last number used in their count. In this case, that last number used was four, so there are four objects in the collection. Because the process of counting and what the count tells you are not necessarily the same thing, figuring out what a child knows about the cardinal principle often requires waiting for a child to complete their count and then asking a question like, “So, how many do you have in your collection?” Other ways to get at the cardinal principle could include saying to the child: “Here are some blocks. How many are there?” Or “Do you have enough to give me 4?” Asking children to make a group of counters of a given size rather than counting a given collection also can focus them on the cardinal principle. 

Continue reading

Supporting the Development of One-to-one Correspondence

young-childrens-mathematics_mg5d5729

Adapted from Young Children's Mathematics: Cognitively Guided Instruction in Early Childhood Education 

by Thomas P. Carpenter, Megan L. Franke, Nicholas C. Johnson, Angela Chan Turrou, and Anita A. Wager


Supporting the Development of One-to-One Correspondence

Developing one-to-one correspondence occurs as children work to coordinate the counting of each object with one and only one number word. You can support the development of one-to-one correspondence by counting together with children, emphasizing matching the action of pointing, touching, or moving each object with the saying of a single number word. Or you might pose a question to the student such as, “How will you keep track of which ones you’ve counted and which ones you haven’t counted yet?” Some children benefit from putting the objects into a container as they count (such as during clean up), as it slows down their count and focuses them on one object at a time. Other children find that spreading out their collection or working with a partner is helpful. However, supporting children to use strategies to keep track of the objects counted will not immediately move children to use the one-to-one principle. Developing understanding of and the ability to use the one-to-one principle takes time and a range of experiences.

Continue reading

Supporting the Development of Counting

carpenter_ycm_quotegraphic_9

The following post is adapted from the newest book in the Cognitively Guided Instruction family: Young Children's Mathematics: Cognitively Guided Instruction in Early Childhood Education.


Supporting the Development of Counting

By Thomas Carpenter, Megan Franke, Nicholas Johnson, Angela Chan Turrou, and Anita Wager

When thinking about how children’s counting develops, there are four big ideas to keep in mind:

  • Details matter when we look for what students know about counting.
  • Students can have more counting understanding than we see in a given moment.
  • Counting principles do not emerge in a set sequence.
  • Counting principles emerge concurrently

Continue reading