There is a lot of interest in metalearning and metacognition. Metalearning deals with deconstructing the way we learn. Metacognition deals with deconstructing the way we solve problems. Today I prepared an especially good selection of reading material. Please do spend your time to read here, here, here, here, and here.
Four stages of problem solving
Arguably the best currently available scientific way of analyzing cognition is fMRI imaging of people performing various tasks. It is hard to generate experiments that show meaningful fMRI results, but once we see this results we can learn from them quite a lot.
The new brain imaging study from CMU identifies four distinct stages that someone’s mind goes through when he or she is problem solving. The July 2016 study, “Hidden Stages of Cognition Revealed in Patterns of Brain Activation,” appears in the journal Psychological Science. For this study, John Anderson and colleagues at CMU combined two analytic strategies along with fMRI brain imaging data to pinpoint the specific mental stages that people go through in real-time as they were struggling to solve a difficult math problem. More specifically, the method combines multi-voxel pattern analysis (MVPA) to identify cognitive stages and hidden semi-Markov models to identify their durations.
Four Stages of Problem Solving by Anderson et al.: Encoding, Planning, Solving, Responding. The research dealt with mathematical problems. I will try to reinterpret it in a wider context.
Encoding: understand the question
When we are asked to solve a problem, the problem is stated in terms that are different from the terms we use in our own vocabulary. Quite often we have an inner toolbox of problem and solutions, occasionally we visualize them using their mechanics or the problems they solved in the past. When we get a new problem to solve, we need to redefine it in terms of the templated we know.
My kids are still in elementary school and their biggest problem in math is understanding what they are asked to do. The learn the basic mathematical operations very early. Then they get a story, and from the story they need to deduct which mathematical operation they should use. In the second class of the elementary school, the encoding was the biggest problem I could see. They were literally struggling to map the story into their math toolbox. The questions do repeat, so with time they learned encoding templates and strategies.
Planning: define process, activities and milestones
Once we understand the question and can associate it with our “toolbox” we can start planning. Occasionally we will need to develop a new tool: this is the hardest type of assignements and most of us fail it. Assume we have all the tools we need. Then we need to define a process which will lead to solution. Often there are several available processes: from examples to general case, from simple case to exceptions, from contradictions to the only solution left, by trial and error, combining another examples we already solved.
Once we defined the process we define the specific activities. Typically we think which tool to execute and what the expected result will be. We try to connect various activities in a converging way. Quite often we already solved similar tasks so we try to copy and adapt some known plan.
Solving: activate the heavy machinery
Now that we know all the tools we need to use and in which order we need to use them we do the heavy lifting. Basically, we use our brain as a computer, to perform the known tasks in the given order. In the future, this stage will probably be fully computerized. Numerical problems are already computerized. Computers already solve some symbolic problems better than humans…
Responding: analyzing the final result
Once we executed our plan and got the results we need to reassess situation. Sometimes we solve the problem as we expect. Quite often we solve only a part of the problem, and need to devise a new plan to solve another parts of the problem. If our plan fails, we get enough new clues to develop a better solution. And if our project expires we need to describe the results we got and the methods we used to the other parties. Explanation and visualization of the result may involve more effort than solving the problem.
Perculating creative solutions
Quite often we simply cannot solve a problem via systematic analysis. Then we need to think “out of the box” and come up with creative solutions.
Participants in this study who gave their ideas time to incubate, and waited until they had an intuitive flash of insight scored better on a wide range of tests. In fact, rushing to find the correct answer by overthinking the problem often backfired. This research unearths some valuable new clues that help to deconstruct the brain mechanics of the “Eureka! I’ve found it” phenomenon. The March 2016 study, “Insightful Solutions Are Correct More Often Than Analytic Solutions,” was published in the journal Thinking & Reasoning. The research team involved in this study included: Carola Salvi and Mark Beeman of Northwestern University; Edward Bowden of the University of Wisconsin-Parkside; Emanuela Bricolo of Milano-Bicocca University in Italy; and John Kounios of Drexel University. For this study, the researchers conducted four experiments in order to identify how participants’ problem-solving strategies influenced their solution accuracies across different types of problems. One problem dealt with linguistics, one was visual, and two were a mixture of visual-linguistic.
In complex problems, insight solutions are correct more often than analytic solutions. The “out of the box” methodology tends to be less predictable since less planning is involved.
In each of the four experiments, participants self-judged if a solution was more of an intuitive “insight” or strictly analytical. On average, the insightful solutions were more accurate than analytic solutions. Interestingly, people who tended to have more insights didn’t rush to find immediate solutions and were more likely to miss a deadline.
Our brain does not need to follow a linear path to the solution. It’s unconscious visual areas are capable of solving several problems in parallel. The solved parts of the problem “surface” to the consciousness. We can consciously reinterpret the problem for further analysis. Ultimately either we have no solution, or all the “dots connect”. We are less likely to get half-baked solutions, simply because such solutions will not surface to our consciousness. So either we get a full solution, or we get parts that do not connect, e.g. no solution at all.
The intuitive solution is based on many try-and-error stages. The trial and error mechanism activates orbitofrontal cortex (OFC) region of the frontal lobes.
The other processes come from a stage very similar to daydreaming, characterized by “unclamping” prefrontal cortex, unleashing the power of creative visualization to run free using its own mechanism. We are not always aware of such visualizations. Sometimes the visual solution passes to us when we sleep or meditate. As you can see, the mechanisms involved in “aha!” moments are very different from the systematic thinking.
Mindfully enhance creativity
To increase the effectiveness of the insightful solutions, we can mindfully enhance our creativity and create our own luck. The mindful methods are quite strange, so let us examine some of them together.
- Working with dreams. During dreams or daydreams our consciousness can connect with our unconscious visual processes. The connection is biderectional: we can see imagery showing the preliminary results of our process and we can consciously generate symbols and visualizations to be incorporated in our dream. It does not really matter which form of visualization, meditation, hypnosis, art or lucid dreaming you use. If you are an analytical person and do not really trust the spiritual talks, try surrealistic art: draw or doodle whatever comes to your mind on a paper. This will improve your creativity and motor skills, and with some luck you will have enough materials for an exhibition.
- Mood management. Reduce stress and negativity, which can trap our visualization in vicious circles. There are many ways to do this. Meditation, sports, casual gaming, socialization, zen-like repetitiveness of home chores. You do not need to get too excited or passionate, better do not overload your brain emotionally. It is not recommended to use chemical substances, since the unconscious mind may get preoccupied with getting toxins out of the system.
- Sensory deprivation. We are often most creative when bored. Reducing the sensory input we allow the brain to analyze its own inputs. Swimming and sunbathing, walking in nature, driving the car often do the trick. Personally I love working far from home, since then I get several hours of driving. I also love to have a great view from office window (not necessarily mine) and staring outside the window helps me be creative.
- Confidence. When we are confident we are more open, and hence more open to things that surface from unconsciosness. When we feel threatened, we focus on the task at hand and do not listen to our unconsciousness.
- Try new things. Visual parts of our brain deal with images and symbols. We may need new symbols and images to activate the right associations. Personally, I love reviewing art, jokes and fun facts. You do not really need to get out of comfort zone…
- Take action! Whenever there are some clues surfacing from our subconsciousness, it is best to take action. Write or doodle the clues, make some research. The things we do not act upon go into oblivion. We can procrastinate while we listen, when we heard something useful procrastination is unacceptable.
Connecting with other methodologies
What I wrote here is just some reference to “in the box” and “out of the box” methods based on some of the articles I recently read. There are much more structured methods to do creativity. Some of these methods are mentioned in other posts available in this blog. Do search for “creativity” and “convergent and divergent thinking” to find out more.