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      淺談數學教學中“讀書”的思考
      【字體:
      淺談數學教學中“讀書”的思考
      作者:邵曉玲    文章來源:本站原創    點擊數:    更新時間:2008-1-14

       

          數學教學過程是一個不斷變化發展的過程,其中人的因素起決定性作用 ,它不是一種機械運動,不可能有一種統一的操作方法,因此教學方法、教學環節可以有各種派系、各種模式,勢必知無不言 ,言無不盡 ,共同探索。同時在不斷的教學實踐當中, 立足于培養和發展學生的各方面能力,在教學過程中總結出讀書、聯想的做法。

      其一,讀書。

      讀書有三道:眼到,口到,心到。

      教科書是教師傳授知識的依據,是學生獲得知識培養能力的主要源泉。現在中學生畢業以后,如若考不上的,也有大部分靠自學成材,即使升學,也要具備相當的自學能力,才能很好完成學業。同時在中學階段要發展知識培養學生能力也必須從培養學生閱讀能力入手,養成獨立思考自學探究的習慣。這樣既可以為教師講解打下基礎,又可以彌補教師講課不足。教師在教授知識時,不僅要把知識的精髓教給學生,而且還要教會學生看書,指導學生閱讀方法,養成學生良好的讀書習慣。只有學生看通弄懂了教材,熟悉有關數學語言,懂得了定義、定理、性質、法則、公式的真實意義,才能掌握知識,運用知識。

      培養學生的閱讀能力應該從低年級就開始。目前中學生讀數學書存在著以下幾個問題:

      1)不看書,教學課本僅作為抄習題、練習之用。

      2)看書,一晃而過,像看小說、連環畫,不思考,不探求。

      3)語文水平低,語法結構不清,讀不通。

      4)數學語言、數學詞匯難懂,障礙多,讀不懂。

      5)興趣容易轉移,易受外界干擾,持久性差。

      針對以上情況可以采取以下方法:

      1)初中一年級學生重點應放在培養讀書習慣。可以在課堂上由教師帶領閱讀,分析章節內容,掃清文字障礙,難以理解的數學名詞或句子,可先作一些解釋。

      2)學生初步養成閱讀習慣后,可以把讀書分成兩個階段:講前預習,講后閱讀。講前預習可以不用要求太高,也可指定范圍,要求學生通過閱讀對教師所要講的內容大體了解,將難懂的地方用鉛筆做上記號,以便教師講授時,集中精力聽講。講后閱讀重點放在獨立思考上,根據課堂講授與書本內容兩相對照,弄通、弄懂各種數學概念,該識記的定義、定理、公式、性質,就要下功夫記,既要動腦子又要動手,重要的難懂的定理和例子,要親自動筆推證和演算。通過講后閱讀還搞不懂的問題再用鉛筆做記號,也可請同學或老師幫助解答。當然對于初中學生,每次閱讀時間不宜過長。

      3)根據教材的不同內容和各年級的特點,教師要幫助學生辨析數學用語、數學名詞和數學符號,提高了提高到都不不都”,“”,“僅當當且僅當”,“僅有有且僅有至少至多不超過不低于等。對難懂的長句子要幫助學生找出句子的主要成份和附加成份。還可引導學生把數學語言翻譯成數學式子,或把數學式子用數學語言敘述。

      4)指導學生通過閱讀寫提要,在教材上劃著重點(找重點),寫批注,添補內容(如補圖形、補步驟、擴張概念等)。

      5)引導學生閱讀時注意數學結構,分清定義、公理、性質、法則、定理,推論的內涵和外延,弄清邏輯關系。

      6)強調學生閱讀時注意教材中數學語言的嚴謹、簡練,注意例題的格式,要求學生以課本上的規范糾正自己作業中的錯誤。

      7)考試時適當考一些課本中的數學概念或常識,以提高學生看書的興趣,達到督促的目的。

      二、聯想

      培養能力,必須基于培養學生的思維能力,如邏輯思維能力、空間想象力、抽象思維能力等等。簡單地說,就是要培養學生的想象力。愛因斯坦說過:想象力比知識更重要,因為知識是有限的,而想象力概括著世界一切,推動著進步,而且是知識進化源泉。要培養學生豐富的想象力,首先從培養學生聯想能力入手,因為它比較具體、直接。培養學生聯想能力,大致可分以下幾種類型:

      1)類比聯想。所謂類比是指同類的比較和類似的比較。要比較,就要聯想。

      通過類比提高想象力,加以分析歸納,再進行抽象思維,尋求規律性的東西。數學中類比是比較豐富的,如代數中的二次三項式、一元二次方程、一元二次不等式和二次函數,以二次函數為最基本,二次函數的零點(y=0)、正數值(y>0)、負數值(y<0)與一元二次方程的根、一元二次不等式的解集緊密聯系,可以通過二次函數的深入研究,綜合其它相應的主要內容,讓學生聯想比較,既便于記憶,又便于了解它們的相互聯系。再如平面幾何中全等三角形的判定,與相似三角形的判定,也可以進行類似比較。

      2)形數聯想。數學中形數之間關系是彼此相依的,要啟發學生用來鞏固與研究,利用鞏固研究。講函數時,一定要強調學生記性質、想圖形,畫圖形、想性質;對于不等式、方程一類的問題也要強調學生形數聯想,利用圖解。

      3)結構聯想。數學結構是數學知識中心和靈魂,如果搞不清數學結構,學生知識是支離破碎,以單元進行教學,每個單元的數學概念、定義、法則、性質、定理、推論等等可以自成體系,學生可以融會貫通;啟發學生,對概念問題想定義,計算問題想法則,推證問題想定理。引導學生結構聯想也要注意年級特征,如初一年級有理數概念,只作描述來下定義,重點放在法則上,可啟發學生看例題想法則,對照法則看例題,作習題想法則,對照法則想習題。又如平面幾何中要強調學生根據每一單元的公理、定義、定理的邏輯關系,綜合分析以結構為中心把知識系統化。

      4)新舊聯想。數學教學中必須注意新舊知識之間聯系,只有溫故才能知新。如講解用求根公式對二次三項式的因式分解時,就應引導學生回憶聯想用乘法公式和十字相乘法等對二次三項式的因式分解,這種平行的新舊知識對比,加深了對新知識的認識。

          總之,在教學中,要教會學生怎樣讀書,引導學生進行聯想,善于發現各個問題之間的聯系,揭示問題之間聯系的規律,有利于開拓學生的智力,培養學生的邏輯思維能力,從而提高教學效果。

       

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