Cognitively guided instruction, which is abbreviated as CGI, is a set of research results about how children learn about addition, subtraction, multiplication and division. It isn't primarily research that tells you how to teach, but it does tell you how children learn. It tells you: if you provide appropriate problems, what problems will they be able to figure out earliest? What methods will the develop to figure them out? As an early childhood teacher, it's really important to know this. This information lets you give problems that will be accessible for young children, and it tells you how to appropriately raise the difficulty level when children are ready.
This research was conducted at UW-Madison, and the children are all in the K-grade 2 age range, so this is research and information that is directly applicable to you and the children you will be teaching. As you watch the videos included with the book, you'll notice some children who you'll think are more advanced than you expect. This is largely an effect of the math program they've been in. A general trend in children's learning and understanding is that they progress from understanding things in a concrete way to understanding things in an abstract way. Their ability to move to new and more abstract thinking depends primarily on their experiences. While certain abilities improve with chronological age, the effect of what they have experiences, been taught, and practiced generally has a larger effect on their ability to learn new and more abstract ideas. So, what you see in the videos is typical of what one can achieve with children at this age, if you provide appropriate experiences for the children. In order to provide appropriate learning experiences for children, it helps to understand what the accessible starting points are; what the difficulties that may require addition care and instruction are, and what prior learning and understanding are needed in order to succeed for each task. The cognitively guided instruction research gives you, as the teacher, a lot of those tools you need to plan instruction.
One primary structure that is used to explain the CGI results is "problem types"--these are ways of classifying word problems into groups depending on how children process them. Word problems are a key feature because they provide the concrete contexts in which to think about mathematical operations: 3 apples + 5 apples is more concrete than 3+5, and "I give you 3 apples, and then I give you 5 more apples" is more concrete still: the context (apples and getting more) illuminates the way we think about what it means to add or subtract (or multiply or divide). One of your tasks in this unit will be to understand what makes a problem typical of one problem type rather than another. Once you have learned that basic vocabulary distinction, you'll learn which types of problems are easier, and how to word a problem to make it more accessible to a younger/less advanced learner. You'll also learn what some of the things are that make a harder problem harder, and what concepts you might need to help children understand in order for them to learn how to transfer their knowledge to more difficult or more abstract types of problems. As you learn about the different types of problems, you'll also see some of the strategies children figure out to solve those problems. You'll learn some of the skills children need to solve problems of different types, and some ways you can illustrate different solution strategies.
As you move through this learning unit, there will be short sets of questions and answers, and also longer assignments where you'll be showing your progress in putting together this information into a mental toolkit that will help you as you help children learn the basic math concepts that will help them throughout their life and their schooling.