One of the concepts that has perhaps stuck with me most from high school is the differential between knowledge, understanding and complex reasoning. It is perhaps the piece that stood out for me from high school maths and it really was the composition of the exam. However I feel it’s a valuable distinction to make and helps guide that learning process. Essentially the three form a pyramid with knowledge on the bottom, understanding in the middle and complex reasoning forming the capstone. The exams were functionally composed of these three sections: knowledge, understanding and complex reasoning. Each tested different aspects of learning the topic and appeared proportionally to where they existed on the pyramid.

Knowledge is perhaps the most of obvious of the triad. Knowledge is your ability to recall straight facts and not a lot else. This could be remembering equations, formulas or basic principles regarding the topic. It would cover simple tasks that you should learn throughout and is generally knowledge you can pick up by reading Wikipedia. When people are talking about rote learning, typically what they’re talking about is the drilling of knowledge to acquire something. While knowledge is useful, it’s serving as the basis of the other two layers of the pyramid. Without knowledge you are limited to how you can progress towards understanding – you may know what the problem is and perhaps how to solve it but not necessarily why it occurred.

Understanding was the ability to take concepts you know and apply them outside of the framework that you normally saw the problem. Understanding highlighted the ability to identify that two problems were the same even if they didn’t look the same. Understanding implies a deeper comprehension than simple knowledge: it is the gap between being able to take what you know already and recognise the same problem stated differently. It is this level of recognition that understanding provides and is a deeper level of insight to knowledge. Understanding is built upon some level of knowledge and provides the ability to transfer learned concepts to an extent. Understanding can often provide you with the reason why something occurs and allows you to exclude solutions that don’t address the actual cause.

A simple example of distinguishing understanding from knowledge is perhaps best served in an office concept. The organisation I was working in at the time had amalgamated various other organisations and we were transitioning IT systems all over the place. In most cases we were the larger party and retained our systems and in other cases we conceded systems. Our records system was however one of the places where we were dominant. I recall one situation where a party was sent out to help re-train the staff at the remote office to scan into the new system. One of the observations was that the staff were only ever taught the steps (knowledge) to operate their scanning software, no time had been spent to help them understand what they were doing. This meant that as soon as the new system came they had no idea how to map the steps they were doing previously to the new software. In retraining them for the new system time was spent not to just provides the basic steps (which I’m sure were dutifully noted down with pen and paper) but also to try to provide a deeper understanding of what was happening and how it all tied together. This understanding provides the ability to help handle the situation where the underlying process changes however the net effect is the same. Understanding allows you to work out what has changed from your knowledge, ask questions and effectively move forwards.

The final aspect of learning that was tested was complex reasoning. There were only ever a few complex reasoning questions on the papers however they were the sort that combined together understanding of the topic from various subject areas to be able to solve a problem. Unlike knowledge or understanding where the steps to solve the problem were relatively simple (in the case of knowledge, usually one step and understanding a constrained set of steps), complex reasoning required absorbing multiple pieces of information and being able to realise that essentially it was composed of multiple understanding questions in one, working out what understanding was required and then applying that until the answer was found. Those capable of complex reasoning in a discipline can usually triage and resolve complex problems quicker than those who either only have knowledge or understanding of the potential solutions. And this provides an important distinction in terms of problem solving.

With knowledge you may be able to fix a problem but without understanding you may either only partially fix the problem or hide the problem while making it worse in the future. We’re all guilty of this where we complete something and state “It’s working, I don’t know why but it’s working.” These are some of the more worrying situations and I try to make a mental note to develop my understanding. The issue with pure knowledge here is that we may not be solving the problem and won’t actually know about it. At this point we run the risk of solving the symptom not the problem. I’ve seen extensive work done to resolve a symptom when the resolution for the problem was actually much simpler and more complete.

With understanding you gain the potential to identify if what you’re resolving is a symptom of the problem or the root cause of the problem. Understanding may lead you to realise that you have a design or architecture flaw that you need to resolve and at that point you gain insight into the trade off between resolving the symptom or building a workaround versus resolving the root cause of the problem. Understanding here is usually limited to a set of related steps to resolve a problem in a single domain, once multiple domains of knowledge are required then we delve into complex reasoning.

When dealing in enterprise systems integration sooner or later a problem will occur. As with any large system as the number of interactions increases the chance that some failure will occur. Complex reasoning covers the ability to quickly take the understanding from the different areas required (including an understanding of the pieces involved in the problem to begin with) and combine them to determine likely causes for problems and solutions. Not always will complex reasoning be available or readily apparent. Sometimes complex reasoning will come when trying to piece together the knowledge of unfamiliar system and building understanding of how that interacts inside itself and then how it interacts with the understanding of your own system.

It is important to realise and differentiate between knowing something, understanding something and being able to complete complex reasoning to complete a problem. A lot of focus is put on knowledge without the development of the next layers. However effective problem solving and complex problem solving requires development of all levels of the pyramid to be successful.