چگونه مسئله حل کنیم

how to solve it

Contents

part1 . in the classroom

• Helping the sttudent
• Questons, recommendations, mental opertations
• Generality
• Common sense
• Teacher and student. Imitation and practice
• Four phases
• Understanding the problem
• Example
• Carrying out the plan
• Example
• Looking back
• Example
• Various approaches
• The teacher's method of questioning
• Good questons and bad questions
• A problem of construction
• A problem to prove
• A rate problem

part2. how to solve it

• A dialog

Part3. short dictionary of heurustic

• Analogy
• Auxiliary elements 
• Auxiliary problem 
• Bolzano
• Bright idea
• Can you check the result?
• Can you derive the result differently?
• Can you use the result?
• Carrying out
• Condition
• Contradictory
• Corrolary
• Could you derive something useful from the data?
• Could you restate the problem?
• Decomposing and recombining
• Definition
• Descartes
• Determination, hope, success
• Diagnosis
• Did you use all the data?
• Do you know a related problem?
• Draw a figure
• Examine your guess
• Figures
• Generalization
• Have you seen it before?
• Here is a problem relater to yours and solved before
• Heuristic
• Heuristic reasoning
• If you cannot solve the proposed problem
• Induction and mathematical induction
• Inventor's paradox
• is it possible to satisty the condition?
• Leibnitz
• Lemma
• Look at the unknown
• Modern heuristic
• Notation
• Pappus
• Pedantry and mastery
• Practical problems
• Problems to find, problems to prove
• Progress and achievement
• Puzzles
• Reductio ad absurdum and inditect proof
• Redundant
• Rules of descovery
• Rules of style
• Rules of teaching
• Separate the various parts of the condition
• Setting up equations
• Signs of progress
• Specialization
• Subconscious work
• Symmetry
• Tems, old and new
• Test by dimension
• The future mathematician
• The intelligent reader
• The traditional mathematics professor
• Variation of the problem
• What is the unknown?
• Why proofs?
• Wisdom of proverbs
• Working backwards

part4. 

• Problems
• Hints
• Solutions

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