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
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.
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