In our last post, we discussed an enlightening sentence from Daniel Kahneman: “Intelligence is not only the ability to reason; it is also the ability to find relevant material in memory and to deploy attention when needed.” It’s one of those “yeah, duh” sorts-of-statements, but in deciphering some of the nuances of what each of those components of intelligence refer to, we recognized some cultural perceptions that can get in the way of teachers or parents setting a clear goal for the purpose of education. This week, we’ll dive into the easiest of the three components to decipher – reasoning – in service of developing a better educational heuristic (or mental model that is easy to deploy) for teachers and parents.
In some senses, the idea of ‘ability to reason,’ has undergone the opposite cultural pressures from memory – recent pedagogies and school practices have begun to shift further in the direction of developing student abilities to reason as a replacement for memorization-style tasks. Now, that’s not to say that this is the case everywhere, as we see differential rates of shifting educational trends across the States. Yet, the evidence that the shift is and has occurred is plentiful, from the development of different styles of charter schools (Waldorf, Expeditionary Learning, Montessori Secondary, etc) to the promotion of curriculums like Jo Boaler’s YouCubed that support ‘low-floor, high-ceiling,’ project-based learning.
The key characteristic of these pedagogies is that students are given one massive task or project that they must not only use many skills they have learned to propose a solution for, but also decide which skills are actually useful and potentially throw out ones that are not useful. This model is in contrast to the “complete these thirty Quadratic Formula problems that are all the same but for the numbers,” way of doing things that was formerly predominant. Obviously even in classrooms supporting these sorts of methods, my own included, there is still a semblance of the skill work I just described. The idea is that once students have learned how to complete-the-square on a quadratic, they can then reason through the derivation of the Quadratic Formula itself. The skill of getting so good at completing-the-square that they can do it with constants instead of discrete numbers helps them to reason through that derivation. The hope is that by deriving that formula rather than being told to memorize it will allow them to do two things very well: first is to place the use of this particular formula into a broader context; if we think of the Quadratic Formula as a tool, then we should hope that these budding mathematicians become competent enough that they don’t (metaphorically) try to hammer a nail using a tape measure. The second thing we hope for is that when these students encounter problems that have not previously been solved, the idea of deriving is natural to them and they will go forth continuing that reasoning process, rather than being stuck at ‘the point where there were no more formulas left to plug-and-chug.’ I have written about this process somewhat extensively in The Degeneration Effect – it’s worth an exploration.
Of course, the mention of the Degeneration Effect brings up the fact that both reason and memory, two components of intelligence that Kahneman lists which I think would come to most people’s minds most readily as being the only factors of intelligence, have an incredibly powerful tool at their disposal in the modern world – endless data. The internet has completely and irreversibly changed the way we memorize and reason, making our lines of thought faster and potentially more all-encompassing than ever before. At the same time, however, the internet has also profoundly changed the third and least obvious component of intelligence: the ability to deploy attentional resources when needed.
Thank your lucky stars, you got a short post this week! See you next for a real doozie on the last component of intelligence.
-mmm
Vena Cava 