Teaching Critical Thinking.page

How do we learn best?  That is the question my roommate and I have set out to answer as we build up a set of tools to complement and aid the natural learning process.  Our ideas have come from multiple sources, but I recently came across an article published in College Teaching (2005) which succinctly tied together many of those ideas and put them in the context of grounded cognitive science research.  (Full text may be available here, although there’s no way to know if it’s available outside my school’s ip range.)  Because the article so nicely tied together many of the theoretical aspects of our project, I thought I would take the time to summarize them here in order to make the project’s foundation more clear.

The article primarily dealt with critical thinking (and specifically how you teach critical thinking in a classroom), but its suggestions and conclusions can apply to any educational goal in general.  Below is a list of the key points and how they relate to the theory behind our project.


“Learning Is Hard”

The author discussed how few people in society are able to exhibit critical thinking skills.  It is not that we are unable to think critically, but we are not naturally inclined to do so.  Critical thinking, along with almost any other skill that (should) be taught in school, is what cognitive scientists call a “higher-order skill.”  In other words, it is built on a foundation of simpler skills which we must first acquire.  How does this relate to our project?  It all comes down to fluency.  In order to perform well at any higher-order skill, one must be fluent in the foundational skills.  If you want to do a calculus problem, you must know the language of arithmetic (a lower-order skill) and the language of algebra, to name two.  An inability to work well in these “languages” will severely hamper your ability to do calculus.  Imagine if you needed to look up how to compute 2+3 every time you took an integral!  The above case is an extreme, but I’ve encountered many situations in my math and science classes where I have to hunt around for some elusive theorem every time I start a homework problem.  This is a strong indication that I am not fluent in the foundational aspects of a certain problem; if I were able to recall and use theorems quickly and efficiently, I would become much better at the given subject and it would allow myself more time to think about higher-order concepts.

At the end of the day, a good handle on the tools available to solve a problem will allow you to divert more intellectual energy to understanding what is going on.  But what is the best way to build fluency in the foundational concepts?  We believe that Spaced Repetition is the most promising lead.  Technology can help us keep track of the concepts we have difficulty with and force us to review those more often.  If SRS works well for fluency in a foreign language, it should work equally well for fluency in, say, mathematics.  Using SRS to commit definitions and key theorems to memory will allow you to perform better at the higher-level tasks which require a knowledge of those theorems and definitions.  If you are concerned about rote memorization, SRS could even be used to help remember how particular theorems are derived.  The only limit is your own dedication to the subject.

“Practice Makes Perfect”

A study done in 1994 by Ericsson and Charness suggested that to become an expert in any given field would require 10 years of practicing four hours a day.  So most people will never become experts, but the lesson is still sound: to become good at anything, you need to practice, practice, practice.  The study describes what is called “deliberate practice,” or practice which,

Is done with full concentration and is aimed at generating improvement
Is not only engaging the skill itself but also doing the special exercises designed to improve performance in the skill
Is graduated, in the sense that practiced activities gradually become harder, and easier activities are mastered through repetition before harder ones are practiced
Has close guidance and timely, accurate feedback on performance
The key point here, which we hope to incorporate, is the idea that specific sub-skills must be practiced until they are mastered, and then built upon to develop higher-order skills.  This is the same question of fluency, and can again be answered by Spaced Repetition.  Not only does SRS offer the repetition until mastery, it can be employed with intelligent semantic links between ideas to provide the “graduated” structure of deliberate practice.  It also offers timely feedback in that you can immediately assess whether you understood the concept.  Hopefully, as our project matures, we will also be able to offer more personal feedback from professors.

“Practice for Transfer”

Many people experience the problem of learning something in one context but then being unable to apply it in other contexts.  Referred to as the “problem of transfer,” this is likely one of the biggest hurdles anyone could face in a generalized education.  We hope, however, that our project will help people see the connections between different aspects of a subject by visualizing semantic links between “chunks” of knowledge.  Computers can help quickly visualize the connections between a particular fact or skill and a multitude of other problems or skills.  Harnessing this power will hopefully help form connections in the student’s mind; the old adage that neurons which fire together will grow together applies here.  If a concept or skill is continuously contextualized with other concepts or skills, the student will form connections which may not have been obvious from the linear nature of, say, a textbook.  Our project will incorporate tools which allow these sorts of connections to form quicker and more easily.

“Map it Out”

Studies have found that in undergraduate level classes on critical thinking, students who map out arguments on paper demonstrate gains in reasoning skills during a single semester equivalent to gains obtained by other students during their entire four years of college. (Twardy; van Gelder, Bissett, and Cumming, 2004)  The idea is that students who map out their arguments can more easily see areas where there is too little supporting evidence or where objections have been dropped, and it allows them to decompose a complex strain of reasoning into manageable chunks.  Our project will hopefully harness some of these advantages, allowing students to not only see how different ideas are linked together (described above) but also how well they understand different parts of a lesson based on data from the SRS algorithms.  Hence, they can easily assess their understanding and put in more work to make up for areas where they are having difficulty.

Overall, there are many ideas which can be incorporated into the “ideal” learning system.  Hopefully we have hit on some good ones, and after reading this article it seems that there is a body of cognitive science research to back some of them up.  It’s a promising indication, if nothing else!  But only time and experience will differentiate between the successful techniques and the duds.