Mind the Gap

All men - and women - were not created equal, and even more so - they didn't come to the world in the same circumstances. That's a rather general statement, so let's refocus on the issue of K12 education, and students achievements. No matter how we may measure these achievements, we are very likely to find out students are not equal. There are gaps between students in the same school, between schools in the same nation, between nations and between continents. With a little effort, we can find gaps in the investment in the education of these students, schools, nations and continents. We may even find some correlation between the investment and actual achievements.

So much for facts. When discussing these facts, soon enough people tend to talk about social justice. This ensures there will be very little done about the issue, because everyone has their own justice, and we start arguing about that instead of discussing the gap and what should or can be done about it. An alternative starting point is to agree that a large gap is bad for everyone - for the top percentiles as well as the bottom percentiles. One may think the reason it's bad is the issue of social justice for the bottom. Another may think the reason to avoid excessive gap is that it may create a revolution that's unpleasant for the top. Regardless of the motivation, we can agree in general that it would be good to limit the gap. We can then start working on how to minimize the gap, rather than argue about why to do it.

Another shortcut I am going to make for this post is that I will only discuss gaps within a nation. That's hard enough for now. Can't tackle the gap between nations and between continents at this point. Call me in a generation or two about that.

Managing the gap and the average level of achievement involves judicious allocation of resources. An illustration of resource management for a more simple example: Consider painting a fence. We have tow painters - Painter 1 does a length of 100-inch per minute, Painter 3 does a length of 300-inch per minute. We have two brushes - Brush 1 is 1-inch wide, Brush 3 is 3-inch wide. Who should get the 1-inch brush, and who should get the 3-inch brush? If we give Brush 1 to Painter 1 and Brush 3 to Painter 3, Painter 1 will do 100x1=100 square inch per minute, and Painter 3 will do 300x3=900 square inch per minute, and together they will do 1000 square inch per minute. If, however, we give Brush 3 to Painter 1 and Brush 1 to Painter 3, Painter 1 will do 100x3=300 square inch per minute, and Painter 3 will do 300x1=300 square inch per minute, and together they will do 600 square inch per minute. If we aim for overall achievement (the first case - 1000 square inch), we get more of a gap (100:900). If we go for equality (the second case - 300:300) we get lower overall achievement (600 square inch). Such is life.

When discussing education the relevant resources are mostly money, management attention and teachers. To reduce the gap in education, we need to allocate more resources to the weaker students and schools. To increase the average level of achievement, we need to allocate more resources to the stronger students and schools. You probably can't have it both ways... Or so it would seem, but it turns out that the successful overall countries, such as Finland, also seem to manage the gap between schools better than others - See Figure 5 on page 32 in this report. Just to make sure you don't think there is a magic formula, notice that even in Finland, the variance within schools is rather high.

Much research has been done with regards to the gaps, where they appear, and - tragically - how they are retained in certain groups. From what I have encountered, it seems that success stories are mostly anecdotal, and not clearly repeatable. More discussion is due as to what goals we need to set and how to balance overall achievement with minimal gap. More research is due how to realize these goals, though this research will suffer from being outside the consensus, as long as we have to choose between different types of justice. More research yet is due, to look into ways of doing both: Reduce gaps and improve overall/average achievement at the same time. I would normally think it is overly optimistic, but the Finland example above suggests it may be a good use for our time to look in that direction.