- Understanding of established concepts
– Thorough study of literature
– Do or re-do similar or related problems
– Massive amount of calculation tasks
- Takes long time to build up basics
– High school curriculum (ancient to 17th century)
– Undergraduate (18th to 19th century)
– Post-graduate (20th century and recent)
- Requires two extremes of abilities
– Calculations: routine but easily rewarding
– Imagination: attractive but abstract
- Attitude
– Logical and rigorous
- Presentation of known materials
– Demonstrate of exercise solution
– Seminar presentation
– Survey or expository writing
- Mostly work on given texts or articles
- Achievement
– A tricky problem is conquered
– A clever method is found
– A hard text is understood
– Peer admiration
- Knowledge
– Building a jigsaw puzzle
– Seeing the elegance and coherence
- Only a little from joy of creation
- Understanding of established concepts
– Recognition of key concepts
– Pinpointing major arguments
– Handling complex patterns and procedures
- Presentation of known materials
– Logically written calculations
– Deductive analysis
– Minor presentation skills
- Exactitude: contrary to personalize
- Long duration of assimilation
– Usually up to finishing an MPhil
- Difficult to raise questions
– A culture of taste: simple and important
– Aim of questions is usually misdirected
- Narrow margin for solutions
– Strict format
- Consequence: research only at PhD level
- Keep the existing characteristics
– Learning methods
– Rewards
– Assessments
- Encourage research oriented skills
– Raising questions
– Atypical methods or strategy
– Guess, imagine, and just do something
– Communication
- A collection of problems
– Of 1st year undergraduate level
– With solution
- 3 to 4 groups of 3 students
– Formed with teacher coordination
- Framework
– From given problem to their own problems
– Enjoy the fail attempts to solve them
– Communicate with and assess each other
- Each group select a problem (1 week)
- Give a brief introduction (1 week)
- Explain the given solution (2 weeks)
- Formulate their own problems (3 weeks)
– Outline their problems to others - Observations and predictions (2 weeks)
– May reformulate the problems - Present all their works and results (3 weeks)
-- Teacher Roles
- Problems compilation
- Encourage
– From very beginning - Guidance
- Encourage
– Especially when students are stuck - Refrain from teaching
– “I don’t know” is a good answer
--Peer Roles
- Talk to the audience
- Listen to unfamiliar familiarity
- Discuss and work with group-mates
- Assess own group
– Assess group-mates with a taste of self-assess - Assess other groups
– On a few domains including presentation
– Free comments
- Understanding of established concepts
– Study the selected problem and solution
– Added: acquired through discovery
- Presentation of known materials
– Several levels of exposition and report
– Not necessarily deductive
- Exactitude
– The ultimate attitude is still there
- Detailed + Skeletal Understanding
– Own study + others’ work
- Accept ill-stated problems
– Clarify through reformulation
- Rough ideas, wild guess, and reasoning
– To give reasons for unfounded ideas is helpful
– Enhance imagination and creativity
- Partial result and unfinished work
- Tend to be lenient
– Exception: self-reflection
- Consistent
– Among students
– With teacher’s assessment
– Slight deviation on knowledge domain
- Appreciative
– Most valuable
- Still far from research
– Problems are too elementary
– Involved too less background search
– Narrow scope, restricted ideas
- Deconstruct and construct
– More accepting attitude favors exploration
- Peer Assessment
– Establish values more than a grading tool
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