Engaging the reflective mind

The image of a good problem solver is one of an intelligent person. But years of teaching Physics to intelligent young people has convinced me that intelligence isn’t the only criterion for a successful problem solver. Common sense is perhaps more critical than many have recognized. Without it, an intelligent individual may have a lot of knowledge  and the capacity to make complex connections, but may simply lack the practical wisdom to apply it appropriately. Unfortunately, recognition of the fact that common sense is critical to effective problem solving is where most people stop. Possibly this resistance to dig deeper is due to an underlying belief that if you don’t have a whole lot of common sense to begin with, you are never going to get more.

Daniel Willingham, in a recent article, raises the question of whether common sense can indeed be taught. Willingham debates this question from a psychological perspective and eloquently references psychologist Keith Stanovich who, in his new book What Intelligence Tests Miss, offers a way to understand the difference between intelligence and common sense.   Stanovich sticks to a more traditional definition of intelligence that focuses on the ability to solve problems and make effective decisions. Stanovich suggests that there are three components to the cognitive system that handles these functions: the autonomous mind (which engages in quick thinking based on simple associations and past experiences), the algorithmic mind (which processes information by making comparisons and combining concepts), and the reflective mind (which interprets goals and beliefs and determines appropriate actions to achieve those goals). What most people don’t realize is that typical intelligence tests measure the efficiency of the algorithmic mind, but fail to consider the moderating effect of the reflective mind.

To problem solve effectively, you don’t only need to decide which facts should be combined to generate a solution. You have to test and adapt that selection (made by the algorithmic mind) to the situation at hand. In other words, the solution needs to fit into the environment of the problem, or the solution will never be practical. And this is the job of the reflective mind. According to Willingham, “You need to see your environment for what it is, you need to set realistic goals, and you need to select actions that move you towards those goals.” Intelligent people (categorized this way by typical intelligence tests) don’t always successful engage their reflective minds (the source of common sense) to determine the appropriateness of their solution. The result? Intelligent people are not always naturally good problem solvers. But could they become good problem solvers? To the critical question, “can common sense be taught?” Willingham’s response is “To some extent, yes. With sufficient practice, people can come to recognize the types of errors the reflective mind makes, and learn to avoid them.”


Common sense – the stepping stone to successful problem solving

“My kids seem to have no common sense.  What do I do?”

 Before we consider whether common sense is something that can be acquired through exercise or practice, a curious reader may well ask, “But how do we know if we (or our children or students) have enough common sense?”  How much is enough?  Was I born to struggle with issues that require common sense?  Is my lack of common sense just the result of my genetic coding?  And why is problem solving hampered by the absence of common sense?  Can’t I find a way to become good at problem solving without growing my common sense?

These questions introduce complex topics that promise to weigh down the most athletic mind.  It’s easy (and extremely informative) to get caught up in the theories and debates that psychologists and educators invest themselves in.  My experience, however, is that most parents and teachers need practical solutions that will make learning easier for the children, and not a bunch of theoretical textbook quotations.  So here, we will rather focus on the practical issues, and how to overcome real-life hurdles that keep students from succeeding.  Parents and teachers may find they identify a little better with their children and students if they first challenge themselves to a fun, common sense test (an example is found at http://www.kathimitchell.com/commons.htm).  The score doesn’t matter nearly as much as the insight this test will offer us into recognizing why common sense is so very important in the problem solving process.


How do we challenge and motivate students?

Every teacher knows that getting our students excited about learning is not always easy.  There are, however, some successful ways to engage learners and raise their excitement levels.  Elena Aguilar describes one such approach in the article, Do Your Final Projects Challenge and Motivate Students? | Edutopia.  Give students a clear goal, a practical way to express what they have learned, and you will encourage learning.  Aguilar describes how “dangling” the final project in front of the students actually lures them into the learning process.  For the students, “the purpose of learning discrete skills” becomes apparent.  “They see how the learning will be applied, they know that there’ll be an audience at the end, and they anticipate the fun.”


Taking arithmetic exercises out of the classroom

Most kids dread mathematics homework, but won’t mind playing a game.  The LPN Game is a very simple, fun, number-based activity suitable for the whole family.  The game, which is customizable in difficulty, can be played by all the members of the family, play group, or students in the classroom, and is a great way to introduce very young family members  or students to the process of combining numbers in a fun, non-threatening environment.  Without realizing it, your children or students will soon be “doing arithmetic” exercises outside of the classroom without the need for books or pencils.

The LPN Game (available in print format) will soon be available as an affordable download from www.drpearllewis.com.  The low-cost download version is ideal for teachers and parents on a tight budget.


Mathematics as a Family Activity

Mathematics doesn’t belong exclusively in the maths classroom. Parents can, and should, integrate it in a number of enjoyable family activities. In most cases, when they are enjoying themselves, children will not even be aware that they are developing their mathematical skills as they play. Do parents require special skills or need to take some course to encourage their children to develop basic mathematical skills early? Fortunately not. In fact, you don’t even need to be “good at Mathematics” to have fun with your kids. And that is the key: fun. Children need to learn that addition, subtraction, multiplication, and division (and later calculus and trigonometry) are not just useless, intimidating procedures weighing down their homework. The best way for children to learn this, is to learn it without directly associating the learning with formal Mathematics.

As part of this blog, I will share some of the mathematics-oriented family activities that I enjoy, and which don’t require special training. Some of these ideas will be so obvious and “everyday” that you will wonder why you haven’t been “playing” all along. Join me as we explore these ideas and develop them into games for the whole family.