Chess: a Case Study in Critical Thinking Skills

Student expectations are as follows:

1. 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.
2. 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.
3. 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:

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

The Law of Calculation

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