Problem Solving III (10 Habits of Mind for Investors)

This material was originally posted by a mathematics teacher.
http://mathteacherorstudent.blogspot.com/2010/09/habits-of-mind.html

Barry Ritholtz author of the Big Picture was so impressed with its potential application for investors he posted it on his blog without any changes.

http://www.ritholtz.com/blog/2010/09/10-habits-of-mind-for-investors/

I think it is the best list of problem solving tips I have seen.

1. Pattern Sniff
. . .A. On the lookout for patterns
. . .B. On the lookout for shortcuts

2. Experiment, Guess and Conjecture
. . .A. Can begin to work on a problem independently
. . .B. Estimates
. . .C. Conjectures
. . .D. Healthy skepticism of experimental results
. . .E. Determines lower and upper bounds
. . .F. Looks at small or large cases to find and test conjectures
. . .G. Is thoughtful and purposeful about which case(s) to explore
. . .H. Keeps all but one variable fixed
. . .I. Varies parameters in regular and useful ways
. . .J. Works backwards (guesses at a solution and see if it makes sense)

3. Organize and Simplify
. . .A. Records results in a useful way
. . .B. Process, solutions and answers are detailed and easy to follow
. . .C. Looks at information about the problem or solution in different ways
. . .D. Determine whether the problem can be broken up into simpler pieces
. . .E. Considers the form of data (deciding when, e.g., 1+2 is more helpful than 3)
. . .F. Uses parity and other methods to simplify and classify cases

4. Describe
. . .A. Verbal/visual articulation of thoughts, results, conjectures, arguments, etc.
. . .B. Written articulation of arguments, process, proofs, questions, opinions, etc.
. . .C. Can explain both how and why
. . .D. Creates precise problems
. . .E. Invents notation and language when helpful
. . .F. Ensures that this invented notation and language is precise

5. Tinker and Invent
. . .A. Creates variations
. . .B. Looks at simpler examples when necessary (change variables to numbers, change values, reduce or increase the number of conditions, etc)
. . .C. Looks at more complicated examples when necessary
. . .D. Creates extensions and generalizations
. . .E. Creates algorithms for doing things
. . .F. Looks at statements that are generally false to see when they are true
. . .G. Creates and alters rules of a game
. . .H. Creates axioms for a mathematical structure
. . .I. Invents new mathematical systems that are innovative, but not arbitrary

6. Visualize
. . .A. Uses pictures to describe and solve problems
. . .B. Uses manipulatives to describe and solve problems
. . .C. Reasons about shapes
. . .D. Visualizes data
. . .E. Looks for symmetry
. . .F. Visualizes relationships (using tools such as Venn diagrams and graphs)
. . .G. Vizualizes processes (using tools such as graphic organizers)
. . .H. Visualizes changes
. . .I. Visualizes calculations (such as doing arithmetic mentally)

7. Strategize, Reason and Prove
. . .A. Moves from data driven conjectures to theory based conjectures
. . .B. Tests conjectures using thoughtful cases
. . .C. Proves conjectures using reasoning
. . .E. Looks for mistakes or holes in proofs
. . .F. Uses indirect reasoning or a counter-example (Park School)
. . .E. Uses inductive proof

8. Connect
. . .A. Articulates how different skills and concepts are related
. . .B. Applies old skills and concepts to new material
. . .C. Describes problems and solutions using multiple representations
. . .D. Finds and exploits similarities between problems (invariants, isomorphisms)

9. Listen and Collaborate
. . .A. Respectful to others when they are talking
. . .B. Asks for clarification when necessary
. . .C. Challenges others in a respectful way when there is disagreement
. . .D. Participates
. . .E. Ensures that everyone else has the chance to participate
. . .F. Willing to ask questions when needed
. . .G. Willing to help others when needed
. . .H. Shares work in an equitable way
. . .I. Gives others the opportunity to have “aha” moments

10. Contextualize, Reflect and Persevere
. . .A. Determines givens
. . .B. Eliminates unimportant information
. . .C. Makes and articulates reasonable assumptions
. . .D. Determines if answer is reasonable by looking at units, magnitudes, shape, limiting cases, etc.
. . .E. Determines if there are additional or easier explanations
. . .F. Continuously reflects on process
. . .G. Works on one problem for greater and greater lengths of time
. . .H. Spends more and more time stuck without giving up