When we think of integration we can think of a folding together of ideas to gain a fuller understanding of something. If we are teaching a mathematics concept such as multiplication with two digits we may bring into the learning experience some manipulatives such as concrete arrays, or a multiplication rectangle, or base ten blocks. These concrete manipulatives help children to access the concept. They are resources or tools used in the learning experience. We are not focused on students having a deep understanding of base 10 blocks--they are tools in the process of learning, the focus being on base 10, and specifically on multiplication. These tools are thus considered to be integrated into the learning experience to enable students to have a better understanding of the concept.
Almost all of our work in integration has started with curriculum concepts. We always ask the question "what is it that we should teach, for example, Grade 3 children (specific Grade 3 children in a specific school)." Almost as soon as we ask the curriculum question we are adapting the curriculum for a specific group of children. All of the different types of integration are really different types of curriculum integration, from a simple one-subject form of integration (as in the above example) to a variety of subjects organized around a common concept.
Some people might consider integration to occur when two subject areas are taught together, focused on the same topic. For example, we might combine science and mathematics in a dinosaur study, where the science component could explore dinosaur habitats, and the mathematics component could explore the lengths and heights of dinosaur bodies. Together, these two subject areas contribute unique and specific understandings to an overall understanding of dinosaurs. If we take this two-subject area idea a bit further we can combine a variety of subject areas--even within the dinosaur unit. We can study science,