2.1.1 數學的本質和數學教育的趨勢
(一) 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。
(二) 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
(三) 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
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