What Monkey's Teach Us About Problem Solving

Prior to the proliferation of the University system, the primary means of passing down knowledge was through apprenticeships. The mentor--usually someone currently practicing a craft or skill--would take someone on as an apprentice and through this relationship the mentor would receive help and labor and the apprentice would learn the craft. Many have argued that this was the most efficient and effective method for passing down information and teaching ever devised. Modern science has started to back that up.

In the 1980's and 90's, researches at the University of Parma, Italy were running tests on the macaque monkey and accidentally discovered what has come to be known as "mirror neurons". They noticed that the brain activity responsible for kinesthetic control not only showed up in the primates that were performing a particular function--say, grasping for some food--but also showed up in the primates watching the action being done. Essentially, the exact same neuron patterns fire when we watch someone else doing a task as the ones that fire when performing a task. Scientists have postulated that this neuron mirroring allows us to learn how to do something by observation. It is by careful observation of someone actually doing something and then doing it ourselves that we learn with the greatest comprehension and retention. So much for lecture. . .

The difficulty with teaching problem solving (mathematical, coding, or otherwise) is that the process is mental and therefore not overtly displayable. A keen mind may look at the work of another and discern his/her solution and even perhaps steps to solving the problem along the way, but this is through reasoning and deduction rather than mirroring actions in real time. The question becomes, is their a method whereby a mentor can teach the process of problem solving to a student?

How does one display the mental process of solving a problem? Clojure inventor Rich Rickey suggests that most problem solving happens at the unconscious level with the conscious mind playing skeptic to flush out its validity. Most of us have experienced unexplained bursts of insight when attempting to resolve something. But, can you teach people to be inspired?

Ultimately a problem is merely a question, and when broken down, a sum of many questions each with small answers discovered through previous knowledge and micro-inspirations. The core of solving new problems is solving old ones. Breaking problems into pieces and auxiliary problems by identifying the conditions, data, and unknowns circumscribes all problem solving. So on to teaching.

Consciously or subconsciously we are asking ourselves small questions throughout the process of solution finding. So to display this process to a student, the core tool is the socratic method. It is by asking successive questions to the student that we teach him/her how to ask themselves the key questions needed to solve all problems. By successively deconstructing a problem into simpler and simpler pieces and asking corollary questions we find a piece of the puzzle that they can solve. When you find that you've gotten down to the basest level and they can't answer the question you have ascertained a hole in the students knowledge that can then be filled through explanation and demonstration. The student now has an activity to mirror. If the process is continued often enough, the student will begin to ask themselves the questions without prompting.

There are many other parts and nuances to effectively teaching people how to solve problems. And like any complicated skill, it must be repeated by both student and teacher in order to gain proficiency. But at the core effectively teaching any skill requires the demonstration of both the seen and unseen parts. From this point we can proceed and add to our pedagogy.

The methodical application and practice of these basic principles will help a mentor teach his students problem solving skills rather than merely making them memorize steps to finish a puzzle. By teaching steps to a predetermined process we reduce the portability of the knowledge we are giving and ensure their long term dependents on our presence. By teaching the skills of solution finding we ensure that the student can then go about autonomously in a manner of self-teaching and solving.

Why You Hate Algebra

I recall being in a college algebra course several years ago while our instructor struggled to teach a complicated mathematical concept. Born of frustration, one of the students made the banal statement we've all heard and possibly said in some mathematics course; "When am I ever going to use this! I'm a (insert major here) major! And I'll NEVER use thaaaatt!!!"

Somewhere between learning long-division and intro calculus someone inserted a mental virus that replicated and persisted until you found yourself justifying your  D+ in math by mindlessly repeating the idea that math is not useful or needed in your career as a DJ/Event promoter. (In case you're wondering, I never got above a C+ in math from seventh grade until I learned that I loved it in a college.)

Wait! Don't stop reading! I know you think you know where this is going. I'm not going to list all the ways/professions in which math is used heavily with fantastic salaries. Nor am I going to give some contrived reason that learning to calculate P values will help you balance your checkbook. Rather, I'd like to articulate how math is a vehicle for a more important skill set: problem solving.

The process of solving a problem is one that can be taught and learned and it is the real skill to be learned through math. You see, somewhere in the process of attempting to fit a curriculum to fit all students, public education lost the teaching of math as a process of solving problems and developing critical thinking skills and reduced it to repeating steps given to us by an instructor.

By doing this, we have been robbed of the opportunity and pleasure of learning concepts, applying them to problems, and seeing results. We haven't learned to ask the crucial questions and methodically evaluate problems in order to solve them. Noted mathematician and professor George Polya wrote in his book "How to Solve It":

The worst may happen if the student embarks on computations or constructions without having understood the problem. It is generally useless to carry out the details without having seen the main connection or having made a sort of plan.

I can't think of a more perfect description of why math seemed tedious rather than interesting to me growing up. Rather than seeing the course of solving a problem to be exciting and stimulating (as I do now as a programmer) I felt as though I was learning a complex set of directions to a destination without description; a contest without context; a job with no satisfaction, like digging a hole only to fill it up again.

When it comes to professional and personal success, being capable of solving problems others can see will make you appreciated and valuable while solving problems that people don't even know exist will make you truly exceptional. Exceptional people have the exceptional ability to identify and clearly define problems that others don't see, and then work to solve them.

So how to develop this? Successful strategies may range from finding fun math word problems to solve, to picking up programming, to gamifying math through competitions. Once you begin to train you mind to see things as collections of knowns, unknowns and missing pieces, the process become transferable and replicable.

A note on the philosophical side:

The truth is, that regardless of whether you intend to be an entrepreneur, figure skater, programmer or stay at home parent, your day to day life will be filled with problems. Those who understand and undertake life's problems will feel empowered rather than victimized by life. They will find that their greatest accomplishments come from solving their biggest problems. It is our mandate as inheritors of this earth to overcome.

The payout of victimhood and being a product of our environments is meager, but the task is easy. True happiness and fulfillment comes at the high price of realizing our personal power through trial, tribulation, and triumph.