PROVIDING FOR MATHEMATICALLY GIFTED STUDENTS

based on a workshop by:

Dr Kate Neiderer

kniederer@Cognitioneducation.com

Helen Withy

November, 2015

FIVE KEY COMPONENTS ... The Concept

Characteristics

Identification

Programmes

Ongoing self-review

1. THE CONCEPT OF GIFTEDNESS AND TALENT

The concept of giftedness and talent varies from culture to culture and is shaped by each group’s beliefs, values, attitudes, and customs. It also varies over time and in response to different experiences.

Ministry of Education (2012)

VISION OF THE MINISTRY OF EDUCATION ...

Gifted and talented learners are recognised, valued, and empowered to develop their exceptional abilities and qualities through equitable access to differentiated and culturally responsive provisions.

Ministry of Education (2012)

ROPS DEFINITION ... (ONEDRIVE) Gifted and Talented Students at Royal Oak

Primary School demonstrate higher levels of ability in one or more of the following areas when compared with others of similar age, culture, experience and background:

Visual and /or performing arts Academic and intellectual aptitude Technological aptitude Emotional intelligence: - intrapersonal (e.g.

self-critique, self-reflect, self-regulate) - interpersonal skills (e.g. leadership, organisational skills)

Physical and sporting Cultural traditions, values and ethics Our school recognises that within its group of

gifted and talented students there is a wide range of ability. All of these students will be catered for through differentiated learning programmes within the classroom. They may also take part in additional individually tailored programmes.

1. GIFTED & TALENTED – THE DIFFERENCE ...

Giftedness – the ability

Developmental process

Talent – the performance

2. CHARACTERISTICS OF GIFTED AND TALENTED LEARNERS ... Energy and persistence Make connections readily (“oh, yesterday, we ...)

Grasp structure of a problem easily Quick to see patterns and relationships Strive for accurate and valid solutions to problems Expert problem-solvers Good recall on a range of knowledge Logical thinkers Mathematical perception of the world Reason things out for self Like intellectual challenge Finds, as well as solves, problems Supports ideas with evidence Likes working independently Easily bored with routine tasks

3. IDENTIFICATION ... More easily detectible in the early years. See them making connections. Have not had time yet to plateau due to

lack of intervention/boredom etc.

HOW DO I IDENTIFY A GIFTED CHILD? Standardised test Teacher assessment Problem-solving test – teacher

nomination

Parent nomination – less helpful Peer nomination – less helpful Self-assessment – less helpful

If mathematically gifted, the child is generally academically gifted.

CHICKEN BEFORE THE EGG?

Provide the high level of challenge, then identify – the child could be

further on than what you realize! (Should be at 70th percentile)

Don’t identify, then provide the high level of challenge.

MATHEMATICAL KNOWLEDGE AND SKILLS ... Mathematical terms Mathematical notation Estimation Checking / proving Diagrams Flow charts Graphs Problem solving Specific areas e.g statistics, geometry

SUGGESTIONS ... What do they know already?

What will they need to know as they progress?

Use teachable moments

Learn from each other

Focus on HOW a problem was solved and the thinking involved, rather than the answer

HINTS ... Keep instruction to a minimum

Don’t tell them the type of problem they are being given to solve

Provide choice wherever possible

Encourage sharing of solutions

Be open to different approaches

Working with mathematically gifted others provides opportunities for ...

Collaboration

Confrontation

Affirmation

Socialisation

IN THE PIT ...BUILD RESILIENCE

4. PROGRAMMES ... Put at its simplest, the purpose

of gifted education is to enable gifted and talented students to discover and follow their passions – to open doors for them, remove ceilings, and raise expectations by providing an educational experience that strives towards excellence.

Ministry of Education (2012)

PITCH IT RIGHT! DIFFERENTIATION IS ...

DIFFERENT STARTING POINTS

Get the curriculum out and pitch the learning at the correct level ...

DIFFERENTIATE BY ... Being responsive to students’ individual

strengths an needs Ongoing assessment Recognising uniqueness of each student (interests, expectations, motivations, abilities,

resources, skills, culture, home and family, way and rate of learning etc)

Inviting guest speakers Taking students on field trips Working with specialist teachers Making modifications for language skills Providing different activities, not simply more of

the same things

MY CLASSROOM ROLE ... Establish a starting point

Above-level testing until appropriately challenging level is discovered

Track progress Does the child plateau? Why?

Review at end of each term / year

Discuss child with G&T team – what else could be done?

OTHER PROVISIONS ...

5. SELF-REVIEW ...

WWW.NZMATHS.CO.NZ

PROBLEM ... Sarah went to the shops and bought 4

magazines; Metro, the Listener, More and the New Zealand Woman’s Weekly.

In how many different orders can she read her magazines?

Answer:

ANSWER: 6 combinations per book x 4 books

M WW Me L M WW L Me M Me WW L M Me L WW M L Me WW M L WW Me = 6 So 6 x 4 = 24 ways

PROBLEM ...Tim’s neighbours have just moved to another

town. The new neighbours will arrive next week. Tim has discovered that two of the new neighbours are children. He wonders what the chances are that at least one of the children will be a boy.

What do you think?

Answer:

ANSWER: BB BG GB GG So ¾ or 75% chance

PROBLEM ... If I add a father’s age to that of his

son’s, the total is 50 years. The father is 28 years older than the son.

How old is the father and how old is the son?

Answer:

ANSWER:

Son 11 Father 39 Total 50

Check this solution out: 25 + 14 = 39 25 – 14 = 11

PROBLEM ... The answer is 20 – what is the question?

You are looking for sophisticated answers, e.g 5% of 400

40 – 20 x 2 half of 40

PROBLEM ... The aim is to shift the tower of disks from

one platform to another. You are only permitted to shift one disk at a time from the top of one pile to the top of another pile. You are never allowed to put a larger disk on top of a smaller disk.

ANSWER: https://www.youtube.com/watch?v=z6lB

OAzjvhQ

PROBLEM Take any 2-digit number. Reverse the

digits to make another 2 digit number. Add the two numbers together.

How many answers do you get which are still 2-digit numbers?

What do the answers have in common?

E.g 34 + 43 = 24 + 42 =

PROBLEM ... Brian, Margaret, Kim and Jo were all

looking at the shapes above. Brian says, “Hey, the first one is the odd

thing out.”. Margaret says, “No, Brian, the second

one’s the odd thing out.” Kim says, “No, it’s the third one.” Jo says, “Well you are all wrong. The last

one is clearly the odd thing out.” Who is right and why?

REFERENCES:Gifted and Talented StudentsMeeting Their Needs in New Zealand

SchoolsMinistry of Education (2012) Wellington

file:///C:/Users/Mark/Downloads/Gifted%20and%20talented%20students%20-%20meeting%20their%20needs%20in%20New%20Zealand%20Schools.pdf