Mathematics View Evolution And It's Pedagogical Implications

There is important realistic significance to better understand mathematics and its culture value that show mathematics panorama to students.We divide mathematical history to five eras that following mathematical development history and according to people's attitudes and faith in different times:1. The Ancient Babylon and Ancient Egypt Era (From 3000 BC to 600 BC):In this era, there was close relationship between mathematics and production practice. Necessary empirical basis was prepared for mathematics becoming an independent science finally.2. The Ancient Greece Era (From 600 BC to 600 AD):The key achievements were Euclid's Elements, Apollonius'Conic Sections and Archimedes'Mathematical-physics Methods in this era. The primary features were deductive and abstraction. Nature was designed by mathematics; this rationality view of nature had widely influence on philosophical thinking, artistic style and creative writing.3. The Middle Ages (From 6th century to 15th century):In this era, mathematics was at a standstill and became a servant-girl of the theology because of the Christian.4. The Early Modern Era (From 16th century to 18th century):In this era, early modern mathematics was established. Many subjects such as analytic geometry, probability theory, number theory, calculus were born. The primary features were the establishment of semiotic system, the generation of abstract conception and the transformation from constant to variable. Science mathematization was established because of the recovery of rationality view of nature. Mathematical rational spirit was injected into philosophy, art and literature. Axiomatic approach was applied in ethics, politics and economics successfully. Otherwise, quantitative analysis had a great achievement in physical science.5.The Modern Era(From 19th century on):The new subjects were non-Euclidean geometry, group theory, non-commutative algebra, abstract algebra, foundations of mathematics, real analysis, functional analysis, topology, cybernetics, mathematical economics and so on. The primary features were axiomatic movement, special trend, generalized prevalence, obviously boundary between pure mathematics and applied mathematics, uniform trend, and the application of computer. Mathematics view:the loss of mathematical truth and the stranding of logically compatible, but as the free creative production of the human mental, mathematics was the most effectively description of physical world as before, and the leading role in the entire field which could be introduced quantitative analysis.This text raises four aspects about ordinary high school program objective based on mathematical history and culture value:the basal knowledge and the basal technology, deductive thought and intuition thinking, culture value, and awareness of the mathematization. The selection point should change technology and calculation into denken and thought in the college entrance examination paper. Also, there are two supplementary suggestions on writing text books:first, writing elective text books to introduce deep-seated application of mathematics in other field for showing cultural value of mathematics. Second, text books should take reasonably pleading for every branch and every method to transform starting-point which is only teach-to-teach. In order to show mathematics panorama to students, teacher must have illuminating capacity:card the development of mathematical history, analysis the culture value of mathematics, elucidate the motive force of mathematical development.