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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."
                 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
    Giftedness Spectrum: G-scale
          Please refer to the relevant table
• G1 Fast arithmeticians (pride): AC- Extension -
• G2 Well beyond grade (appetite): AC
  Adaptation, CC and Acceleration, Mclub ?
• G3 Really enjoy math theory (satisfaction/“at
  home”): Let’s prove it! Math Club
• G4 In love with mathematics
  (fearless,original,own proofs etc.): Mentor,
  Math club
    Intellectuality and +/-Reward
• In my experience, only G4 children don’t need
  prizes or rewards, and compete with
• 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.
     Bloom’s 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.
 Howard Gardner’s 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.
    (Very Important Principles, built in to the very structure of
•   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?
            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.
     Lunch Club Anecdotes G+
• Grade 1:
  – Andrew: Ecstatic. “Backwards!Backwards!” Gauss
    Series Summation
  – Richard: Fearless. “Don’t know what those signs
    mean, but..., then I can do it” Binomial theorem
• Grade 3:
  – Mariya: Fearless. “ Haven’t seen that before, but
    I’m sure I can work it out.” Logarithms
      Lunch Club Anecdotes G+
• Grade 4:
  – Kristy: Appetite. “ Wow! I’ll 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? -->
      Lunch Club Anecdotes G+
• Grade 2:
  – After explaining why N0 =1: “Oh! That’s so
    obvious, why didn’t I think of that! How do you
    learn to think like that?! Teach us!” (Desire to
    learn to imagine and think strongly)
  – What’s 19x19? “That’s too easy”.OK then, what’s
    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
  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
  – Take-home: Same process for all levels!
     [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
       child’s got to 80.
     • Then we pretended there was another child and
       reached 100, the goal of that session. Smiles!
     • Take-home:Fun->Imagination->Discovery->Fun, the
       learning spiral
     • Magic Mountain Math also took the children into the
       hundreds(Reaction of the G+ set) in a few minutes
          A.C. Model (Maths)
• Pros for G+ students
  – probably essential for all G+s
  – can accomodate G1 and G2
• Cons for G+
  – Inadequate, and unsatisfying for G3 and G4
• Extendability of within-grade AC is
              Modified A.C. 1
•   Pre-test/Re-test
•   Student groups
•   Challenges/Choices
•   Models of Excellence
•   A Generalisation: Bloom tie with
    Piagetian development and MRIs
              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?
            In-class Activities 1
• Daily, weekly, monthly, annual
  – individual, pair, group
• Assistance in class
• Sharing knowledge and problems
  – within the G+ group
  – with the AC class
           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
     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!!
               Resources 1
• Maths for the Million: How to Master the
  Magic of Numbers by Lancelot Hogben (c)
• 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
                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
  – - ideas and staff development
  – The NRICH Cambridge program
  – 'Dr. Math' sites, etc.
              Personnel Resource
• Short of a staff person able to deal with G+s, find a
  volunteer –
   –   From parent community
   –   From retired JH or SH school –
   –   Or graduate student –
   –   Or retired professor – many of these haven’t even
       thought of this but would be willing.
• A staff person could use one of the above as a
• For G4s age 10+, we have Prof. Andy Liu!!
• 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.
• If you did want to email me, try:

• and I’ll see if there’s something useful I can
  tell you.