The word understand is not always used very precisely. It is often seen in the phrase "knowledge and understanding". But how is knowledge the same or different to understanding? Here's how we can understand that particular problem.
If I give you a list of people on a basketball team, it would not make sense to ask if you understood the list. You might realise that it's a list of basketball players, but that's about it. We don't use the word understand for such straightforward kinds of applications. If, however, we were to watch a basketball game, it would make sense for me to ask "do you understand what you're seeing?"
The reason this works is that understanding applies to relational knowledge - when elements of the thing were talking about are connected or related in certain ways. The names on the list are not very closely related to each other. The elements of a basketball game, however, such as the court markings, the ball, the hoop, the referee, the player and the crowd, are all interrelated. It is for elements with what we call a "high degree of interactivity" that the word understanding is usually reserved.
I might add that an implication of this is that the word understand does not represent a cognitive verb. Understanding is a state to be attained it is not an instruction that you can give to students in the same way that, for example, we might instruct students to justify or evaluate or identify or undertake any other cognitive task that we represent by a verb.
This definition of understand is important when we consider expertise. Experts have an understanding of their domain. They understand how all the elements of their area of speciality ''click''or "'hang'' together. How they relate to each other and the dynamics of how the whole system works. We call such knowledge ''schematic'' knowledge, it is knowledge organised into a ''schema''. Importantly, a knowledge schema for expertise also contains information about the kinds of problem that an expert finds in their domain, including knowledge about how these problems are solved. Expert knowledge then is not just about knowing lots of stuff, it's also about knowing how that all hangs together including knowledge about problem-solving.
The significance of this for teaching for thinking is that pedagogical experts require a knowledge schema that represents their understanding of the kinds of challenges and problems faced in the domain of teaching for thinking and how these challenges are met and these problems are solved. Knowledge, whether for understanding or for the development of expertise, is core business in education.
One of the advantages of working with schematic knowledge is that using schematic knowledge requires very little working memory. Working memory is a very limited cognitive resource. We can only hold and manipulate a very small number of items of knowledge in our working memory. For example, if I ask you to remember the words scissor, fruit, book, dog, glass, light, and tape, and to recite them after 60 seconds, the success rate for most people would not be high. The words fade from our attention and memory and we lose both the content and their order quite quickly.
If students have to recall individual bits of information that, like the list of words above, seem unconnected, but are required to solve a problem, most of their cognitive effort goes to remembering that information rather than solving the problem. But knowledge that is laid down within a schema can be recalled with little or no use of working memory. It’s a kind of magic. Thinking with schematic knowledge is therefore far more effective than thinking with individual pieces of knowledge. Focusing, therefore, on student thinking, recognising the need to build effective schematic knowledge, means we will produce more effective learners.
Implications for learning
We want students to develop an accurate understanding of concepts. We also want students to build this understanding schematically. In other words, we are laying the foundation for the future development of expert knowledge for our students. But the knowledge of how to do this requires expert understanding, which means pedagogical experts need to develop their own schematic understanding about teaching for thinking. Whichever way we look at it, building schematic knowledge is an essential part of the project of Teaching for Thinking.