Topic Based Learning

Until someone else shows up here, I'm just going to blab away about my pet theory of education.

The topic of today's post is topics. The way that education is structured today in most (all?) schools in the US is by grade level and by course (in middle school and high school). This is too coarse-grained to give an accurate picture of what a child has learned. There are two different unfortunate outcomes that can result from the course-based system. First, a child may pass the course even though there are essential skills and knowledge that he missed. This makes the followup courses that much more difficult, because he must not only learn the new material, but also catch up on the material that he should have learned, but didn't. The second unfortunate outcome is that the child may fail the course and must repeat the whole thing, even if he was successful in learning some of the material.

The more precise approach to assessing a child's achievements is to break material down into much smaller topics, where a topic covers a small enough range of subject matter that it is feasible to completely master it. (There also can be synthesis topics that involve several smaller topics. More about this later.) For example, in mathematics, topics might include: addition of 1-digit numbers, addition of multi-digit numbers, multiplication of 1-digit numbers, multiplication of multi-digit numbers, etc. The goal should always be mastery of topics.

To take the example of multiplication of multi-digit numbers, if a child can only correctly do 80% (say) of such problems, then that means that there is some aspect of multiplication that he does not understand. It is a mistake, in my opinion, for teachers to say: well 80% is not too bad, so let's move onto more advanced topics (division, or fractions, or whatever). It's a mistake because the more advanced topics depend on thoroughly understanding the more basic topics. It is so important to catch and correct gaps in understanding as soon as possible, because otherwise the flaws in understanding can go on to "infect" many followup topics.

In addition to base topics that are about a single thing such as multiplication, there will be synthesis topics that require applying several base topics. In mathematics, being able to solve "word problems" is an example of such a synthesis topic. The base and synthesis topics naturally form a hierarchy in which the mastery of one topic requires the mastery of lower-level topics. It is very important to have an accurate map of such a topic hierarchy, because that allows an effective approach to dealing with a child's lack of success in a topic: Find out what dependent topics the child has failed to master, and work on mastering those, first.

The advantage of such a topic based approach, with a hierarchy that is understood by all, is that both teachers and students know precisely what it is that they need to work on. This is much more effective than the information kids currently have about their skills, which is along the lines of "I'm bad at math".

In science and math, the topics and their dependencies are pretty straightforward. I believe, though, the topic-based approach is potentially useful in
"softer" subjects such as language, art, music. There is a difference between the hard and soft subjects, in that it might possible to become perfect at, say, adding multi-digit numbers, but there is no clear notion of being perfect at writing sentences or paragraphs or essays. So there will be a certain element of subjectivity to the assessment of such subjects. However, I think that the notion of mastery is still useful there, by interpreting topics as projects. Writing a story, writing an essay, learning to play a piece of music---each such activity can be considered a project in which the goal is excellence. The child should work on a project to the point that both the child and teacher agree that he has done an excellent job. A child learns most from doing things well, and learns very little from doing things in a mediocre way.