*Designing and Implementing School-based Mathematics Gifted Education Programme for Sec. School 2010/6/28

*Characteristics of math gifted students(House, 1987)Ability to think logically and symbolically about quantitative and spatial relationships;Ability to perceive and generalize about mathematical patterns, structures, relations, and operations;Ability to reason analytically, deductively, and inductively;Ability to transfer learning to novel situationsFlexibility and reversibility of mental processes in mathematical activity;(Mark McGee,1979)Ability to handle spatial relationships

*(Miller, 1990) Flexible and creative in problem-solving

(Renzulli, 1998)Intense interest and passion (in math)(Ellerton, 1986)Ability to pose problems with more complicated mathematical structure. .etc.

*http://www.edb.gov.hk/index.aspx?langno=2&nodeID=3614

*GiftednessExpertiseProf Debaroh Eyre:-School-based Gifted Education

*How to cater for the learning needs of mathematically gifted students*More chances for them to develop their strengths, such as: Logical thinkingHandling spatial relationshipsTransfer of learning/ ApplicationCreative Problem solving Problem posingReasoning analytically, deductively, and inductivelyGeneralizing patterns & relationsetc.

* Maths Inquiry Cross-curricular activities3. Problem solving4. Maths application5. Independent study6. Estimation7. Geometry8. Probability & Statistics9. Higher Mathsetc.Useful learning activities or topics for gifted S

*Including:pull-out() e.g. Group the more able students and provide them with further training in mathsregular classroom() e.g. Differentiation in the regular classroom

School-based Maths Gifted Education Programme

*Differentiation in the regular classroomA useful strategy to cater for learner diversity: Tomlinsons Equalizer()

*Carol Ann Tomlinson (2005)9 dimensionsTomlinsons Equalizer

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1. Clearly Defined Problems Fuzzy Problems ()InvestmentAn investment of $10000 was increased by 10% in the first year and decreased by 20% in the second year. Find the total amount after the second year.Topic:Percentages (KS 3)InvestmentChoose some shares from different categories (e.g. banking, manufacturing, etc.) and find their percentage changes in share prices over the previous 2 weeks. Hence recommend which share to buy in the short run.

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3. Concrete ()Abstract (..)Solve:a) 2x+3y=8 x+4y=9b) 4x-3y=20 6x+y=8c)d)Topic:Linear equations in 2 unknowns (KS 3)Find a general solution (or formula) for solving equations of the type: ax+by=c dx+ey=f where a,b,c,d,e and f can be any integers.

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4. Simple Complex ()Try to estimate the number of grains of rice in a bowl.

Topic:Estimation in Measurement(KS 3)a) Design three mathematical ways of estimating the number of grains of rice in a bowl.Describe your estimation processes in detailsb) Point out the source of errors in each of your methods.c) How to reduce errors in each case?

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5. Structured() More Open()Observe the given histogram, then answer the following questions: 1. How many students score 4 marks in the test?

2. How many students are there totally in the class?

3.Topic:Statistics (KS 3)Observe the given histogram. Write down as many as possible what you can discover from it.

*Time (s)

6. Fewer Facets Multi- Facets(...)Read simple graphs:Topic: LinearGraphs (KS 3)John made a graph to represent a 4 x 100m relay of his team in the sports day:

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7. DependenceIndependence ()Math project1.Topic: Geometry in daily life2.Steps:A) Read the article from the web http://www.?????????B) Then answer the following questions:a.What are geometric shapes?b.Where can we find geometric shapes in our daily life?c...Topic:Geometry(KS 3)Math projectHow to use geometry in daily life? (e.g. in architecture, art, astronomy, or any other areas of interest)

*Students can choose their own ways of data collection and research methods. They will only consult the teacher when necessary*

*In the 4x4 dotted board below, use a rubber band to encompass a triangle of a) maximum area, b) minimum areaTopic:Areas of simple polygons (KS 3)Calculate the following areas:a)

b)Transformational (/)8. Foundational()

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9. SlowerQuicker ()Give more help or more time to those in need when doing their classwork.Topic:Any topics (classwork)Award some interesting & challenging problems to those more able students who can finish their classwork very quickly.

**Points to consider when designing a learning activity for Math gifted studentsQ1. What major mathematical idea(s) can link up the learning activity?e.g. Teaching similar figuresMajor math idea: Proportional enlargement/reduction !

*e.g. Teaching reflectionMajor math idea: Object & Image are Equidistant from the line of reflection (like a mirror) !

*Q2. Can the activity provide more able students with an opportunity to develop their mathematical abilities, such as:

Logical thinkingHandling spatial relationshipsCreative Problem solving Transfer of learning/ ApplicationGeneralizing patterns & relationsProblem posing/Asking QuestionReasoning analytically, deductively, and inductivelyFinding interconnections between conceptsProgress to a higher level of the Van Hiele ModelOthers. Please state:

*Van Hiele ModelOfGeometrical Understanding

*How students differ in their geometrical understanding?Van Hiele ModelLevel 0 (Visualization)Level 1 (Analysis)Level 2 (Informal Deduction)Level 3 (Formal Deduction)Level 4 (Rigor)Learning and Teaching Geometry, K-12- 1987 Yearbook of NCTM

*How students differ in their geometrical understanding?Van Hiele ModelLevel 0 (visualization) geometric shapes are recognized on the basis of their physical appearance as a whole

*How students differ in their geometrical understanding?Van Hiele ModelLevel 1 (Analysis) form recedes and the properties of figures emerge

*How students differ in their geometrical understanding?Van Hiele ModelLevel 2 (informal deduction) A network of relations begins to form

*How students differ in their geometrical understanding?Van Hiele ModelLevel 3(formal deduction) the nature of deduction is understood

*How children think what triangles are?In US, Children who are in Level 0 think all except D are trianglesChildren in Level 1 know that only D and E are triangles

*DifferentiationConcept (Big Idea) link up the whole topicConcept BuildingConcept ConsolidationConcept ApplicationJigsaw +Tiered Tasks

Tied Tasks+Anchor ActivitiesReal World Applications (Connected to other disciplines)

*Resources1.

http://resources.edb.gov.hk/gifted/tr/200707-03026-S2S4C/2. --- http://resources.edb.gov.hk/gifted/Learning_&_Teaching_ResourcesII/math_pullout_booklet_sec_final.pdf

*3. http://resources.edb.gov.hk/gifted/ge_resource_bank/files/Awards/CPS_booklet_0809CKf.pdf 4. http://www.edb.gov.hk/index.aspx?langno=2&nodeID=3614