What is CGI?

This page is designed to help teachers with articles, links, word problems, and resources for Cognitively Guided Instruction.  If you have found wonderful sites, articles, or word problems that you would like to share, please email me at: michelleflaming143@gmail.com.

Cognitively Guided Instruction (K-6)
Cognitively Guided Instruction (CGI) is a problem-solving mathematics program designed to improve number sense and computation for students in Kindergarten through third grades. It has been proven effective for boys and girls of diverse social class, racial and ethnic, and language proficiency backgrounds.

This K-6 instructional strategy focuses on student knowledge and encourages teachers to pose story problems that can be solved by any means chosen by the child. Problem-posing and problem-solving become the focus of the mathematics class, rather than the traditional emphasis on memorization of facts and algorithms. The research-based approach was developed by faculty at the Wisconsin Center for Education Research, University of Wisconsin- Madison.

Contact Michelle for more information on CGI professional learning.

Each participant will be required to purchase Children's Mathematics . This workshop consists of three professional days, followed by two advanced days later in the year.

 Top 8 Reasons How CGI Addresses the Common Core Standards in Math.

Second Grade Word Problems based on CGI schema

FREE CGI Questions to use with your students.

This is a GREAT site which links you to so many CGI resources 

CGI is named as a "Promising Practice" 

 National Council of Teachers of Mathematics share thoughts.

Problem types are an important component of CGI 

The beginning of a blog about CGI and the journey.

Research Report from ERIC

 What is CGI? Handout by a school using the program.

Using baseline data to determine the appropriate place to begin multiplication. 

A Case Study from a 1st Grade Bilingual Teacher.

"Children who come to expect help with every problem lose faith in their intuition and never develop the confidence needed to tackle problems alone".

Cognitively Guided Instruction = Engaging Students

As I was reading Steve Wyckoff's blog about creating students who are passionate, inspired, and remarkable, I thought, wow, Steve should have been tagging along with me the past couple of weeks.

I have been visiting kindergarten through third grade math classrooms.  Yes, I said math classrooms.  You may be wondering what planet I've been visiting.  These are classrooms where the primary focus is on problem solving using the Cognitively Guided Instruction approach.  CGI is a constructivist research-based strategy, which allows young children the opportunity to explore and discover how numbers work together to develop true number sense. 

Top 8 Ideas For Teaching One-to-One Correspondence

"Rote memorization of a set of numbers is meaningless" (Moore, 1973, p. 67) and counting is a skill, which should not be stressed until the child has shown understanding of the quantity level (general amounts in groups or sets).  Although one-to-one correspondence sounds like such a simple skill, may young children have problems with this developmental concept.  These eight ideas are designed to support young children in their efforts.

Schema Based Instruction

This is the understanding that story problems have different underlying mathematical structures.  This allows students to organize types of problems and therefore organize different strategies appropriate to the problem.  Thomas Carpenter, researcher of Cognitively Guided Instruction, organizes story problems into fourteen different categories.  For more information, check out Cognitively Guided Instruction.

What is Number Sense and How Do I Get It For My Students?

What is number sense?  I hear from school to school, teacher to teacher that kids don't have number sense or know their basic facts.  I've often wondered, not knowing the basic facts, is it the problem or the symptom of a greater problem.   I've come to the conclusion that not knowing the basic facts is a much deeper problem of not having strong number sense.  So what is number sense?

Dangers in Teaching Key Words

Defining Problem Solving

Educators say we need our students to be better problem solvers, so we need to determine what problem solving truly entails.   According to BusinessDictionary.com it is:

"The process of working through details of a problem to reach a solution. Problem solving may include mathematical or systematic operations and can be a gauge of an individual'scritical thinking skills."

Unitizing - The Foundation of Place Value

As I have worked with fourth and fifth grade students recently it has become extremely painful to me to realize how many of our students do not have place value and base ten understanding.  I see students who still solve problems by counting by one. 

Why a Variety of Student Strategies is Clarifying NOT Confusing

Why would we want to support and even encourage students to explore different strategies to solve problems?  Won't straying from the traditional algorithm be confusing for students?  I learned how to calculate problems this one-way and I'm doing fine, why shouldn't my students? 

Top 8 Reasons to Use CGI to address the New Generation Standards (CCSS)

I just came home from working with a district that has chosen to use Cognitively Guided Instruction (CGI) as their research-based strategy to improve math education.  The last day of our three-day training we took time to look specifically at the 8 mathematical practices from the common core and looked closely at several unpacking documents from Arizona, North Carolina, and Ohio.  During this time teachers began seeing many connections between the new Common Core Standards and Cognitively Guided Instruction.  When asked, why a district would choose to use CGI as a district strategy in relationship to the Common Core Standards the list below is what the group created.

Putting the Thinking Back Into Math

As a teacher I found myself often asking the question, "Are you even in the ballpark?"  meaning is your answer close. Many of my students didn't know if I mean Wrigley Field or Yankee Stadium.  If a student has no number sense and can not visually see what the answer should be about, there is no way they will be able to know if there answer is even close.  Students spend a large majority of their math classes memorizing vocabulary, rules, and procedures with little understanding.  When the brain is focusing on memorizing procedures it often doesn't take into account the size of the number or the common sense approach to solve the problem.  Let's look at an example:

Developing Number Sense Through CGI

As I work more and more with students I have come to the conclusion that the problem is NOT that they don't know their number facts, like we "teachers" often reply.  Not knowing their basic facts I believe is the symptom to a much larger problem.  Kids DON'T HAVE NUMBER SENSE. 

Cognitively Guided Instruction (CGI)

My journey with CGI began seven years ago when I was searching for a brain-based strategy in math.