The Young Gifted-Plus

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The Young Gifted-Plus

• Who They Are and What They Need Mathematically
  Speaking
• Treat people as if they were what they ought to
  be and you help them to become what they are
  capable of being." Goethe

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Introduction

• JBL is an ex-physicist, immunologist, technology
  transferist and small business advisor
• Experience as independent consultant on remedial
  and gifted-to-exceptional young students
• Currently Math Teacher at Edmonton John Howard
  Society School for adults affected by crime,
  abuse, drugs or mental challenges, and continuing
  volunteer at Westbrook Elementary.

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OUTLINE

• John BL, PhD in physics. Retired from university
  10 years ago. Since then volunteer math/science
  tutor at JH/Elementary levels for remedials and
  gifted plus. Now, EJHS Math teacher for adults.
• INFORMAL AND INDEPENDENT NOTES ON
• THE ISSUE HOW SHOULD THE GIFTED PLUS BE LOOKED
  AFTER
• GIFTEDNESS SPECTRUM Intellectuality and
  Reward
• SOME VERY IMPORTANT ASPECTS OF LEARNING
  MATHEMATICS
• EXAMPLES AND ANALYSIS
• SYNTHESIS and SUGGESTIONS

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Topic List

• What is gifted?
• An unorthodox analysis of values- and
  character-building via mathematics
• Some of my experiences over the past 7 years
  guiding young G mathematicians
• Some resources for recognising (at home and
  school) G Elementary students
• Integration with and without an extra/volunteer
  mathematician in your school

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Giftedness Spectrum G-scale Please refer to the
relevant table

• G1 Fast arithmeticians (pride) AC- Extension -
  FastMaths
• G2 Well beyond grade (appetite) AC Adaptation,
  CC and Acceleration, Mclub ?
• G3 Really enjoy math theory (satisfaction/at
  home) Lets prove it! Math Club
• G4 In love with mathematics (fearless,original,ow
  n proofs etc.) Mentor, Math club

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Intellectuality and /-Reward

• In my experience, only G4 children dont need
  prizes or rewards, and compete with themselves.
• G1-3 compete and delight in recognition, as
  points and/or prizes, including sugar.
• All students make errors (me too) we learn to
  distinguish between plain rubbish and rewarding
  interesting rubbish in the answers.
• I teach students to teach, so they really
  understand. This rewards them.

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Blooms Revised Taxonomy

• Add Teaching status
• Real understanding is only reached when a concept
  or situation or process is so well and coherently
  formulated internally, that it can be
  transmitted, effectively, externally. This is the
  means by which Creativity is validated.

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Howard Gardners 9 Intelligences

• A definition of intelligence (See Notes)
• Flexibility (adaptability)
• Grasp (adaptation)
• Add Teaching an adaptation and adeptation to
  the challenge of transmitting wisdom to others in
  the interest of all, esp. those following on. We
  should all be good learners and teachers.

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V.I.P.s (Very Important Principles, built in to
the very structure of mathematics)

• Truth G Grade 1 Reg. 2
• Plausibility G Grade 1 Reg. 2
• Beauty G Grade 1 Reg. 1
• Humility G Grade 1 Reg. 3
• Revelation G Grade 1 Reg. 2
• Specialness G Grade 1 Reg. 1
• Fitness G Grade 1 Reg. 1
• A Big Q Where do fantasies etc. fit in?

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V.I.P.s (Continued)

• Math Creativity comes out of Revelation and
  Humility. Maths is an adventure written in a
  second language! We are all MSL students!
• The Big Answer Legends, fairy-tales, folk-lore,
  dreams, make-believe, fantasies, Art,
  imagination..., fit into maths- Everywhere!
• E.g. Negative numbers used to be evil, black.
• Complex numbers were crazy and deviant
• Dominant sevenths were disgraceful etc.

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Lunch Club Anecdotes G

• Grade 1
• Andrew Ecstatic. Backwards!Backwards! Gauss
  Series Summation
• Richard Fearless. Dont know what those signs
  mean, but..., then I can do it Binomial theorem
• Grade 3
• Mariya Fearless. Havent seen that before, but
  Im sure I can work it out. Logarithms

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Lunch Club Anecdotes G

• Grade 4
• Kristy Appetite. Wow! Ill have to find out
  why that happens. Primes falling on spiral
  diagonal.
• Kristy Eureka. Yes it does work above 1
  million, I did it! Extended parlour trick for
  instant cube-roots to above 993 .
• Grade 2
• Cute Where are the -3 cookies my hand? --gt

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Lunch Club Anecdotes G

• Grade 2
• After explaining why N0 1 Oh! Thats so
  obvious, why didnt I think of that! How do you
  learn to think like that?! Teach us! (Desire to
  learn to imagine and think strongly)
• Whats 19x19? Thats too easy.OK then, whats
  129x129? This time the speedster lost the race,
  because he had to think. Then he wanted to know
  how to do it, and caught up. Competitive became
  acquisitive.

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Lunch Club Anecdotes Remedial

• Grade 2 performing at a C
• A 15 3x3 Magic Square. Discovered every line sums
  to 15. Amazed. Can I show my teacher how to make
  those. She did. And was converted to liking
  math gets good grades now.
• Discovery gave loss of fear then same spiral of
  interest, appetite, satisfaction and more
  discovery.
• Take-home Same process for all levels!

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Other Anecdotes Remedial

• Grade 2 (first term), 3 kids learning to escalate
  numbers to 100 and over
• shoes off, fingers and toes ready,learned
  5,10,15,20 by wiggling.
• I know how to count more by using her fingers
  and toes. Got to 40, added mine, gave 60, added
  the third childs got to 80.
• Then we pretended there was another child and
  reached 100, the goal of that session. Smiles!
• Take-homeFun-gtImagination-gtDiscovery-gtFun, the
  learning spiral
• Magic Mountain Math also took the children into
  the hundreds(Reaction of the G set) in a few
  minutes

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A.C. Model (Maths)

• Pros for G students
• probably essential for all Gs
• can accomodate G1 and G2
• Cons for G
• Inadequate, and unsatisfying for G3 and G4
• Extendability of within-grade AC is limited

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Modified A.C. 1

• Pre-test/Re-test
• Student groups
• Challenges/Choices
• Models of Excellence
• A Generalisation Bloom tie with Piagetian
  development and MRIs

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Modified A.C. 2

• Virtual Acceleration
• Researching a higher-grade topic
• Quasi-Acceleration
• Attend higher-grade Math classes. Does it matter
  if the timetables don't fit?

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In-class Activities 1

• Daily, weekly, monthly, annual challenges/projects
  
• individual, pair, group
• Assistance in class
• Sharing knowledge and problems
• within the G group
• with the AC class

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In-Class Activities 2

• Creative problem solving
• Transport/Energy/learning or teaching
  math/design/'an invention'
• Brainstorming
• A new language (Not a code)
• A code
• A game
• Publish Magazines or online

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Out-of-class Math Activities

• Self-study mentoring books, web
• Math clubs
• in school
• joint/exchange between schools
• Math competitions
• in school, bewteen schools, province, national
• Math Fairs just starting in Edmonton
• Mentors junior, senior
• For G4s age 10, we have Prof. Andy Liu!!

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Resources 1

• Maths for the Million How to Master the Magic of
  Numbers by Lancelot Hogben (c) 1937
• Math Education for Gifted Students by S. Johnsen
  and J. Kendrick
• Teaching the Gifted in an Inclusion Classroom by
  Rosemary Callard-Szulgit
• Math Charmers by Alfred Posamentier

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Resources 2

• The Magic of Mathematics by Theoni Pappas and her
  book The Joy of Mathematics
• The Mathematics Calenders by Theoni P.
• Crux Mathematicorum
• Appendix A from S. Callard-Szulgit's book
• Online
• ssulgit2_at_aol.com - ideas and staff development
  programs
• The NRICH Cambridge program
• 'Dr. Math' sites, etc.

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Personnel Resource

• Short of a staff person able to deal with Gs,
  find a volunteer
• From parent community
• From retired JH or SH school
• Or graduate student
• Or retired professor many of these havent even
  thought of this but would be willing.
• A staff person could use one of the above as a
  platform
• For G4s age 10, we have Prof. Andy Liu!!

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Conclusion

• Know where your children are on the Piaget scale,
  and keep them on the leading edge, as he advised.
• Know where your children are on the Bloom scale,
  nurture accordingly.
• Find where your children are on the G-scale and
  stimulate appropriately.
• Keep your G-children always math-fit and
  math-fed, and math-happy, in class and out.

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P.S.

• If you did want to email me, try
• john.sage_at_mailnull.com
• and Ill see if theres something useful I can
  tell you.