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 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 - 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 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. 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. 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? 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 acquisitive. 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! [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 limited 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 challenges/projects – 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) 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 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 – email@example.com - ideas and staff development programs – 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 platform • For G4s age 10+, we have Prof. Andy Liu!! 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. P.S. • If you did want to email me, try: • firstname.lastname@example.org • and I’ll see if there’s something useful I can tell you.