The Perfect Pawn

Chess: a Case Study in Critical Thinking Skills

2010-03-02T22:55:00.001-06:00

Student expectations are as follows:

Deep, reflective thinking. Students will be expected to provide evidence of in-depth analysis. This doesn't mean that every problem must be solved perfectly or even to completion. It does mean that the student must show evidence of developmentally appropriate progress in gaining chess understanding, knowledge, and wisdom. Applying an understanding of learned chess facts in one's personal games provides evidence of increased knowledge. Using that knowledge to predict probable, opposing lines of play and to develop appropriate strategic and tactical plans shows evidence of increased wisdom in decision-making.
Functional behaviors. Students are expected to show up on time, complete assigned lessons, and adhere to reasonable expectations related to the teaching process. If a student can follow directions and make concessions (admit when they are wrong and display improved, adaptive behaviors), they will do well.
Character. In order to complete this course, students must develop self-discipline: self-control, humility (a willingness to examine personal weaknesses honestly), patience, attention and persistence to task, resilience during defeat, and dignity (relating to courtesy and sportsmanship).

Academic objectives include the following:

Learn specific problem-solving strategies and apply them in the appropriate context
Learn tactical motifs and develop precision in calculation
Develop an increasingly effectual, personalized praxis (critical thinking process) by consistently analyzing and refining formalized chess strategies.
Develop questioning skills, compare and contrast possible solutions, draw conclusions, and check for accuracy in searching for the best solution
Risk management: weighing potential risk vs. potential reward
Resource allocation: using limited resources wisely
Make decisions and accept responsibility for their consequences by responding maturely to adversity and success
Develop a rationale for how to prioritize (balance strategic and tactical concerns) based upon proven judgments established over time
Develop a playing style that complements individual strengths and weaknesses
Investigate the nature/value of creative brainstorming and reflection time

The Law of Calculation

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Chess is a closed logic system: it has finite rules and parameters. However, as a simple probability problem for the human mind, it's parameters might as well be infinite (or at least, undefined). It is impossible to master the game from a simple calculation standpoint.

The problem is two-fold: on one hand, the influence that any one move can have on the outcome of a game ranges from innocuous to enormous, depending on the situation; on the other hand, the probability of any player to predict the move of his opponent diminishes exponentially as he examines each ply of a possible line of play.

So why do players of the same skill level often see similar lines of play?

Great players don't calculate a far greater number of possible (candidate) moves than the average player; they simply perceive and investigate far better moves! As our tactical abilities are sharpened by practice, we are able to calculate far more quickly, eliminating poor moves (based upon prior experience) and intuitively selecting better candidate moves.

This is why training to recognize all the tactical motifs is essential to improved chess play.

In fact, strategic theories are really just reminders to investigate important tactical aspects of a position during analysis: for context is king. That is, the mathematical relationships that exist among the pieces is reality, and theory is just, well, theory.

The famous chess grandmaster Richard Reti makes this very point in his Modern Ideas in Chess (1922) when he writes of the method in which strategic theories are formulated:

What is really a rule in chess? Surely not a rule arrived at with mathematical precision, but rather an attempt to formulate a method of winning in a given position or of reaching an ultimate object, and to apply that method to similar positions.

If you can calculate a winning advantage, feel free to break any of the traditional rules associated with strategic theory: for perfect calculation forces predictable responses that lead to predictable outcomes.

The difference between strategic theory and the law of calculation is the difference between an opinion and a fact.

Personal initiative is an important character trait in life that promotes successful outcomes. On the chess board, the initiative that a player gains by playing one forcing move after another is also an enormous psychological advantage. (The player forced to respond feels controlled, uninspired, and typically dejected.)

While no one calculates perfectly at all times, perfect calculation (in part) is possible with practice.

The law of calculation is superior to strategic theory.

References

Reti, R. (1922). Modern Ideas in Chess

Why Strategic Theory Comes First

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It is necessary to teach the strategic principles that govern sound play before students fully understand why they are necessary and effective at an experiential level. Otherwise, students tend to develop bad habits and a haphazard style of play that has no foundation upon the strategic realities inherent to the game, even if they have developed a relative, tactical proficiency. For example, teaching students to recognize tactical patterns without also providing them with a sound framework for understanding how to utilize small advantages to create a long-term, strategic plan of attack leaves them ill-prepared to counter best play. It would be analogous to teaching someone how to operate a car without teaching them the rules of the road: they might be a technically proficient operator of the motor vehicle, but they wouldn’t possess the knowledge necessary to arrive safely at their intended destination.

Indisputably, there are strategic realities inherent to the game of chess that simply must be acknowledged, regardless of native, tactical ability: for tournament play is designed to pit players of equal ability against one another; and strategy remains an essential component of effectual play. All tactical opportunities stem from sound, positional play. Therefore, finding squares that magnify the influence and mobility of one’s pieces and better coordinate their ability to flexibly shift to defend and attack is a primary strategic goal and an important weapon in a player’s arsenal of skills. King security is vital. The value of space if premier. These are important facts to remember when determining how to resolve tactical concerns. An opinion (however imperfect) based upon some well-established, strategic facts is naturally superior to an opinion based upon false assumptions devoid of strategic understanding.

Here's an example: a player is certain to lose a minor piece (knight or bishop) and figures to at least capture a pawn in exchange. His logic is indisputable, tactically--for going down 2 points is infinitely preferable to going down 3 points! Unfortunately, he neglects to consider the strategic implications of his choice--for in so capturing the pawn, he opens a file (attacking alley) that his opponent gains control of--and eventually loses the game due to this loss of space. At the highest level of chess today, computers reign tactically, but the intuitive understanding of positional play remains the province of human beings.

Finally, the grand theme of strategic theory is that, for every situation we face, there is an appropriate and effectual strategy. This notion, once ingrained, provokes an intellectually conditioned (as opposed to emotional) response to life’s many adversities. Chess teaches us about life.

Why Play Chess?

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No other game mirrors life as perfectly as chess: for success is dependent upon a strong work ethic, a persevering and resilient mind set, and the ability to solve complex problems independently. Full of nuance and awash in deception, competitive play humbles the proud, teaches restraint to the impulsive, and provides ample evidence to every player that a studious, purposeful, and resilient disposition is necessary for much success. Its primary benefit as an educational tool is that it lends itself to self-mastery--for mature play is characterized by the ability to manage multiple processes at once--and to bring focus and unity to the intellectual, emotional, and psychological domains. Of course, young people develop higher order thinking skills by engaging mentors in personally meaningful conversations about concrete and abstract ideas; and this type of meta-cognition ('thinking about thinking') is necessary in order for them to learn how to correctly interpret and communicate complex ideas. Chess play inspires just such a discourse in an authentic, student-centered context: for those who love the game naturally desire to play well!

Perhaps, no better tool is available to educators to help students teach themselves about the importance of monitoring and accepting responsibility for their own choices: for in chess, the consequence of choice is immediate; and this fact alone requires students to develop emotional self-control and learn to adapt successfully to unexpected outcomes. Moreover, improved playing prowess is invariably accompanied by a growing self-confidence. In this sense, chess not only inspires critical inquiry, it teaches students to embrace adversity and view failure as a temporary but necessary stage of growth. The dedicated student quickly learns that sound play is a consequence of methodical, purposeful learning, just as sound teaching is a product of methodical, purposeful instruction.

Certainly the old adage, "Give a man a fish and you feed him for a day; teach a man to fish and you feed him forever," suggests that teaching students how to learn (manage their own learning processes) is equally important as teaching specific skills and imparting specific knowledge. Therefore, the principal task of the chess instructor is to introduce chess as a legitimate course of academic study--to convince students that a structured and studious approach to the game results in inspired play--and that effective preparation is as much a consequence of learning the right things in the right order as playing winning chess is about making the right moves in the right order. Mature play is a product of mature cognitive function: those fully self-aware, intellectual acts that are the product of a complex mental process involving the faculties of perception, imagination, logic, and judgment.

Simply put, chess study and play improves cognitive function.