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2.1.1   數學的本質和數學教育的趨勢

 

() 數學的本質

Ÿ           為什麼要了解數學的本質?

Ÿ           對教授的科目有比較深入的認識。

Ÿ           這些認識包括科目內容、結構和聯繫、它的歷史發展、研究對象和方法及與其他科目的關係。

Ÿ           數學老師對數學的觀感,往往影響他的教學方法。

 

() 數學教學趨勢

a.   美國數學教育發展的趨勢

Ÿ     學校數學的課程與評鑑標準

Ÿ     數學教學的專業準則

b.   英國數學教育發展的趨勢

Ÿ     數學教學的調查報告書

Ÿ     中小學數學教學

 

() 香港數學教育發展的趨勢

a.   六零年代至七零年代

Ÿ     老師對課程不滿

Ÿ     老師在教學上感困難

Ÿ     升中試對教學產生很大影響

b.   八零年代

Ÿ     開始重視一些教育家的理論

Ÿ     老師仍然面對學能測驗的困擾

Ÿ     學習差異的問題頗為嚴重

c.   九零年代

 

The aims of mathematics teaching

l           Math as an essential element of communication

l           Math as a powerful tool

l           Appreciation of relationships within math

l           Awareness of the fascination of math

l           Imagination, initiative and flexibility of mind in math

l           Working in a systematic way

l           Working independently

l           Working cooperatively

l           In-depth study in math

l           Pupils confidence in their mathematical abilities

 

Objectives

a.       Facts

b.       Skills

c.        Conceptual Structures

d.       General Strategies

e.       Personal Qualities

 

a.                  Facts

l           Remembering terms

l           Remembering notation

l           Remembering conventions

l           Remembering results

 

b.                  Skills

l           Performing basic operations

l           Sensible use of a calculator

l           Simple practical skills in math

l           Ability to communication math

l           The use of computer in math activity

 

c.                   Conceptual Structures

l           Understanding basic concepts

l           The relationships between concepts

l           Selecting appropriate data

l           Using math in context

l           Interpreting results

 

d.                  General Strategies

l           Ability to estimate

l           Ability to approximate

l           Trial and error methods

l           Simplifying difficult task

l           Looking for pattern

l           Reasoning

l           Making and testing hypotheses

l           Proving and disproving

 

e.                  Personal Qualities

l           Good work habits

l           A positive attitude to math

 

Why Teach Mathematics?

 

Ÿ         Perhaps impossible - to live a normal life without making use of mathematics of some kind.

Ÿ         There is greater pressure for children to succeed at mathematics.

Ÿ         Usefulness - e.g. arithmetic skills for home or office, basis of scientific development or a management tool

Ÿ         Mathematics provides a means of communication which is powerful, concise and unambiguous - e.g. tables, charts and diagrams

Ÿ         Ability to predict

Ÿ         Importance and usefulness in many other fields.

Ÿ         Develop powers of logical thinking, accuracy and spatial awareness might not be the major reason for studying mathematics.

Ÿ         Inherent interest of mathematics - enjoyment, increased mathematical understanding

 

Implication for teachers

 

Ÿ         Enabling pupils to develop mathematical skills for adult life

Ÿ         Providing pupils with mathematics for their study in other subjects

Ÿ         Helping pupils to develop their appreciation and enjoyment of mathematics

Ÿ         Providing pupils with a powerful means of communication