The Young Gifted-Plus :

1. 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

2. 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

3. Giftedness Spectrum: G-scalePlease 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”): Let’s prove it! Math Club G4 In love with mathematics (fearless,original,own proofs etc.): Mentor, Math club

4. Intellectuality and +/-Reward In my experience, only G4 children don’t 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.

5. 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.

6. 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.

7. 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?

8. 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.

9. 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

10. 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? -->

11. 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 acquisitive.

12. 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!

13. [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 Mathalso took the children into the hundreds(Reaction of the G+ set) in a few minutes

14. 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 limited

15. Modified A.C. 1 Pre-test/Re-test Student groups Challenges/Choices Models of Excellence A Generalisation: Bloom tie with Piagetian development and MRIs

16. 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?

17. 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

18. 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

19. 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!!

20. 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

21. 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@aol.com - ideas and staff development programs The NRICH Cambridge program 'Dr. Math' sites, etc.

22. 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 platform For G4s age 10+, we have Prof. Andy Liu!!

23. 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.

24. P.S. If you did want to email me, try: john.sage@mailnull.com and I’ll see if there’s something useful I can tell you.