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 – ssulgit2@aol.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:• john.sage@mailnull.com

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