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    如何做好小學數學和初中數學的銜接?

    如何做好小學數學和初中數學的銜接?

    初一數學教材,涉及數、式、方程和不等式,這些內容與小學數學中的算術數、簡易方程、算術應用題等知識有關,但初一數學內容比小學內容更為豐富,抽象,復雜,在教學方法上也不盡相同。這里我們先看看小學數學和初中數學的內容方面有哪些銜接?
           1.算術數與有理數
      小學數學是在算術數中研究問題的,而中學數學一開始就有有理數,因此,從算術數過渡到有理數是一大轉折,為此,須抓住以下幾點:
      (1)清楚具有相反意義的量,是引入負數的關鍵.
      了解引入負數的必要性及負數的意義.例如,如何區別零上溫度和零下溫度這兩個具有相反意義的量呢?
      又如,珠穆朗瑪峰的海拔高度和吐魯番盆地的海拔高度是具有相反意義的量等等,多舉一些例子,了解為了區別具有相反意義的量必須引入一種新的數——負數.
      (2)逐步加深對有理數的認識
      首先,清楚地認識到有理數與算術數的根本區別,有理數是由兩部分組成:符號部分和數字部分(即算術數).這樣,對有理數的概念的理解,運算的掌握就簡便多了.
      其次,清楚有理數的分類與小學的算術數相比只是多了負整數和負分數.
      (3)有理數的運算,其實是由兩部分組成:
      小學學習過的運算加上中學學習過的“符號”確定,只要特別注意符號的確定,那么有理數的運算就不成為難點了.如:(-2)+(-4)先確定符號為“-”再把數字部分相加即可,
      即(-2)+(-4)=-(2+4)=-6
      2.數與代數式
      從小學數學的特殊的、具體的數到中學的一般的、抽象的代數式,這是數學思維上的一次飛躍.
      (1)用字母表示數的必要性
      在小學學過的用字母表示數的例子,如:加法交換律a+b=b+a;乘法交換律ab=ba及一些公式如速度公式v=s/t.正方形周長、面積公式L=4a,S=a2等,說明由字母表示數能簡明、扼要地表達數量之間的關系.可以更方便地研究和解決問題.
      (2)加深對字母a的認識
      許多同學由于對字母a表示數的意義理解不透,經常錯誤地認為-a一定是負數,因此,要正確理解a的含義,知道a可能是負數,而-a不一定是負數等問題.
      首先讓學生弄清楚符號“-”的三種作用.①運算符號,如5-3表示5減3,2-4表示2減4;②性質符號,如-1表示負1,5+(-3)表示5加上負3;③在某個數前面加上“-”號,表示該數的相反數,如-3表示3的相反數,-(-3)表示-3的相反數,-a表示a的相反數.
      然后再說明a表示有理數,可以是正數,可以是負數,亦可以是零.即包括符號和數字,這樣,學生才能真正理解a,-a所包含的意義.
      (3)加強數學語言的訓練及列代數式的訓練
      如:a是正數表示為a>0,a是負數表示為a< 0,某數a的2倍表示為2a等。
      3.算術解法與代數解法
      在小學,解應用題采用算術解法,而中學需用代數解法(列方程).算術解法是把未知量放在特殊地位,設法通過已知量求出未知量;而代數解法是把所求的量與已知量放在平等的地位,找出各量之間的等量關系,建立方程而求出未知量.另外,算術解法較強調套類型,而代數解法則重視靈活運用知識,培養分析問題和解決問題的能力,這是思維方法上的一大轉折.但學生開始往往習慣于用算術解法,而對用代數解法不適應,不知道如何找相等關系.要明白有些問題用算術解法是不方使的,最好用代數解法,只要找出相等關系,用等式表示出來就列出了方程,再利用解方程的方法,就可以求出未知數的值.
      初一《代數》第一章“代數初步知識”是以小學數學中的代數知識為基礎的.從用字母表示數一直到簡易方程,在小學高年級數學課中占有相當大的比重,是對小學數學中的代數知識的比較系統的歸納與復習,但本章內容又是從初中代數學習的客觀需要出發的,不是小學知識的簡單重復.
      進入中學后,需逐步發展抽象思維能力.但初一新生在小學聽慣了詳盡、細致、形象的講解,如果剛一進入中學就遇到“急轉彎”往往很不適應.
      初一學生往往考慮問題較單純,不善于進行全面深入的思考,對一個問題的認識,往往注意了這一面,忽視了另一面,只看到現象,看不到本質. 例如:往往誤認為2a>a,理由很簡單:2個a顯然大于1個a,忽視了a包含的意義,a表示有理數,可以是正數,負數或零,從而造成了錯誤.
    我的終極目標:考啥啥會,蒙啥啥對!

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