2010/6/28
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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;
“
Flexibility and reversibility of mental processes in mathematical activity;
“Ability to transfer learning to novel situations
(Mark McGee,1979)
Ability to handle spatial relationships
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(Ellerton, 1986)
Ability to pose problems with more complicated mathematical structure
(Miller, 1990)
Flexible and creative in problem-solving
(Renzulli, 1998)
Intense interest and passion (in math)
.
. etc.
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http://www.edb.gov.hk/index.aspx?langno=2&nodeID=3614
Selection Tools
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Prof Debaroh Eyre:-
Giftedness
Support
Opportunity
Expertise
School-based
Gifted Education
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How to cater for the learning needs of mathematically gifted students？
*More chances for them to develop their strengths, such as:
• Logical thinking
• Handling spatial relationships
• Transfer of learning/ Application
• Creative Problem solving
• Problem posing
• Reasoning analytically, deductively, and inductively
• Generalizing patterns & relations
• etc.
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Useful learning activities or topics for gifted S
1. Maths Inquiry
2.
Cross-curricular activities
3. Problem solving
4. Maths application
5. Independent study
6. Estimation
7. Geometry
8. Probability & Statistics
9. Higher Maths etc.
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School-based Maths Gifted Education Programme
Including:
•pull-out(抽離模式) ：e.g. Group the more able students and provide them with further training in maths。
•regular classroom(常規課堂)
： e.g.
Differentiation in the regular classroom
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Differentiation in the regular classroom
(
)
A useful strategy to cater for learner diversity:
Tomlinson’s Equalizer
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Tomlinson’s Equalizer
Carol Ann Tomlinson (2005)
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1. Clearly
Defined
Problems
清晰定義的問題
Fuzzy Problems
模糊不清的問題 (學生
需自行定義問題或自
行搜集資料界定問題)
Investment
An 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)
Investment
Choose 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
具體的 (淺白的)
Abstract
抽象化 (尋找深層的數學
規律、關係、公式..)
Solve: a) 2x+3y=8 x+4y=9 b) 4x-3y=20
6x+y=8 c) 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
簡單的
Complex
複雜化 (賦予多些細節
或層面)
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 details 。 b) 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
高度組織 (多限制
的、高度指引的)
Observe the given histogram, then answer the following questions :
1 . How many students score 4 marks in the test?
Topic:
Statistics (KS 3)
More Open
開放的 (少限制的 、 容
許學生自行決定及自由
回答的)
Observe the given histogram. Write down as many as possible what you can discover from it.
2. How many students are there totally in the class?
3.
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6. Fewer
Facets
少層面的
Multi- Facets
多層面的 (多些層面 、 多
些變量 、 跨科的...)
Read simple graphs:
Distance (m)
Topic: Linear
Graphs (KS 3)
Distance from starting point (m)
John made a graph to represent a 4 x 100m relay of his team in the sports day:
Time (s) a) What is the speed of the first runner？ b) Anything wrong in the graph if we consider the real situation?
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Time after starting the relay (s)

7. Dependence
依賴
Math project
1.Topic:
Geometry in daily life
2.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)
Independence
獨立 (提供較少指引和
協助)
Math project
How 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*
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8. Foundational
( 基礎的 )
Calculate the following areas: a)
Topic:
Areas of simple polygons (KS 3)
Transformational
可轉化的 (有啟發性的
/可產生新意念的 )
In the 4x4 dotted board below, use a rubber band to encompass a triangle of a) maximum area, b) minimum area b)
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9. Slower
較慢
Give more help or more time to those in need when doing their classwork.
Topic:
Any topics
(classwork)
Quicker
較快 (學習速度較快)
Award some interesting
& challenging problems to those more able students who can finish their classwork very quickly.
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*Points to consider when designing a learning activity for Math gifted students
Q1. What major mathematical idea(s) can link up the learning activity?
e.g. Teaching similar figures
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e.g. Teaching reflection
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Q2. Can the activity provide more able students with an opportunity to develop their mathematical abilities , such as:
 Logical thinking

Handling spatial relationships

Creative Problem solving

Transfer of learning/ Application

Generalizing patterns & relations

Problem posing/Asking Question

Reasoning analytically, deductively, and inductively

Finding interconnections between concepts

Progress to a higher level of the Van Hiele Model
 Others. Please state:
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Of
Geometrical Understanding
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How students differ in their geometrical understanding?
• Van Hiele Model
– Level 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
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How students differ in their geometrical understanding?
• Van Hiele Model
– Level 0 ( visualization ) geometric shapes are recognized on the basis of their physical appearance as a whole
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How students differ in their geometrical understanding?
• Van Hiele Model
– Level 1 ( Analysis ) form recedes and the properties of figures emerge
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How students differ in their geometrical understanding?
• Van Hiele Model
– Level 2 ( informal deduction )
A network of relations begins to form
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How students differ in their geometrical understanding?
• Van Hiele Model
– Level 3( formal deduction ) the nature of deduction is understood …
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D
A
B
C
In US, Children who are in Level 0 think all except D are triangles
E F
Children in Level 1 know that only D and E are triangles
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Concept (Big Idea) link up the whole topic
Concept
Building
Concept
Consolidation
Concept
Application
Jigsaw
+
Tiered Tasks
Tied Tasks
+
Anchor Activities
Real World
Applications
(Connected to other disciplines)
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Resources
1. << 數學遊戲 ( 中學適用 )>> http://resources.edb.gov.hk/gifted/tr/200707-03026-S2S4C/
2. << 抽離式校本數學資優培訓課程系列 中學篇 >>
--系列① 空間與圖像 http://resources.edb.gov.hk/gifted/Learning_&_Teaching_Res ourcesII/math_pullout_booklet_sec_final.pdf
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3. 「第五屆香港小學及第一屆香港中學數學創意解難
比賽」資料匯編 http://resources.edb.gov.hk/gifted/ge_resource_bank/files/Aw ards/CPS_booklet_0809CKf.pdf
4. 甄選工具 http://www.edb.gov.hk/index.aspx?langno=2&nodeID=3614
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