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  • 當前位置:首頁 > 活動方案 > 教學設計 > 《一次函數》復習課教學設計與反思

    《一次函數》復習課教學設計與反思

    時間:2019-06-19 11:07來源:http://www.16mnyg.com點擊:

    《一次函數》復習課教學設計與反思

    一、復習目標

    1.知識目標:掌握一次函數的概念、圖象和性質;能正確畫出一次函數的圖象,并能根據圖象探索函數的性質;能根據具體條件列出一次函數的關系式。

    2.能力目標:理解數形結合的數學思想,強化數學的建模意識,提高利用演繹和歸納進行復習的能力。

    3.情感目標:通過對一次函數知識點的系統整理,讓學生認識到事物是有規律可循的,幫助他們提高復習的效果,增進數學學習的興趣。

    二、教學重點與難點

    重點:根據不同條件求一次函數的解析式。

    難點:根據函數圖象探索其性質。

    三、教法與學法

    教法分析: 經過精心整理,把本單元知識歸納成“三求”,采用“演繹法”向學生傳授。由于是復習課,采用邊講邊練和問題教學的方式。

    學法指導: 在這節課之前,讓全班同學擬定復習計劃書,很多同學在計劃書中都提出函數是難點,希望能多復習一點,把這一信息反饋給班級,使全班同學都有一種意見得到尊重的滿足感,并產生了強烈的主動求知欲望。另外,通過學生向學生展示本單元的歸納,培養學生自己動腦,自己歸納總結的能力,從而掌握一種良好的復習方法。

    四、教學過程

    (一)、知識回顧: 學生代表帶領大家復習本章內容。

    (二)、提出“三求”:本單元的知識點比較繁多,而且在初中數學中所占的地位也比較重要。因此,我用“三個求”來對于本單元進行復習:

    1、求范圍:

    ⑴、求自變量的取值范圍:初中階段不外乎三種情況:一是當自變量在分母上時,分母的式子不等于零;二是當自變量在根號內時,根號內的式子大于等于零;三是當自變量既不在分母上,也不在根號內時,自變量的取值為任意實數。

    ⑵、根據函數的圖象或函數的解析式,給出x的取值范圍能判定y的相應的取值范圍,或給出y的取值范圍判定x的相應的取值范圍,這是一類較難的問題,講解時,要特別注意數形結合。

    2、求系數(指數):

    例1、已知函數y=(k-1)x + m-2

    ①若它是一個正比例函數,求k , m的值。

    ②若它是一個一次函數,求 k , m的值。

    分析:這類題目是考察同學們對函數解析式的特征的理解,在講解時要突出兩個疑難:一是一次函數中自變量的指數等于1,而不是0;二是一次函數解析式中自變量的系數不為零。

    3、求解析式:一般用特定系數法求函數的解析式,特定系數法的一般步驟是“設→代→解→答”。當然,在一些日常生活實際問題中,則可以根據題意直接列出解析式,這里應該說明:自變量的取值范圍是函數解析式的一部分,但具體求法不作要求。

    (三)、課堂練習:

    1、在函數2x+1=5 ,y=3x-5x中,一次函數有_個.

    2、已經y與x+1成正比例,當x=5時,y=12,求y與x的函數關系式。

    (四)、小結:本節課歸納的“三個求”不是互相孤立,而是互相依托,互相滲透的,只有將知識融會貫通,舉一反三,才能學有所樂,學有所成。

    (五)、布置作業:作業的布置應精心設計,體現分層教學和因材施教的原則。



    三、教學反思

    這節課,我對教材進行了探究性重組,同時放手讓學生在探究活動中去經歷、體驗、內化知識的做法是成功的。通過充分的過程探究,學生得出了圖象的性質,借助直觀圖象的性質而得到一次函數的性質。真正的形成往往來源于真實的自主探究。只有放手探究,學生的潛力與智慧才會充分表現,學生也才會表現真實的思維和真實的自我。在新課程理念的指導下,我們的一切教學都要圍繞學生的成長與發展做文章,真正讓學生理解、掌握真實的知識和真正的知識。

    首先,要設計適合學生探究的素材。教材對一次函數的性質是從增減來描述的,我們認為這種對性質的表述是教條化的,對這種學術、文本狀態的知識,學生不容易接受。當然教材強調所呈現內容的邏輯性、嚴密性與科學性是合理的。但是能讓學生理解和接受的知識才是最好的。

    其次,探究教學的過程就是實現學術形態的知識轉化為教育形態知識的過程。探究教學是追求教學過程的探究和探究過程的自然和本真。只有這樣探究才是有價值的,真知才會有生長性。要表現過程的真實與自然,從建構主義的觀點出發,就是要尊重學生各自的經驗與思維方式、習慣。結論是一致的,但過程可以是多元的,教師要善于恰倒好處地優化提煉學生的結論。

    最后,教師在學生探究真知之旅上應是一個促進者、協作者、組織者。要做善于點燃學生探究欲望和智慧火把的人,要善于讓學生說教師要說的話,做教師想做的事,這就是一個成功的促進者。數學教學的過程是師生共同活動、共同成長與發展的過程。真正的知識不全是由教材和教師講授的途徑獲取的,其實學生也是課程資源的開發者,要徹底拋棄“唯書論”“唯師論”,與學生一起去探究協作,尋覓適合學生自己的真知才是最有效的教學。要開展成功的探究,教師要科學設置問題情景或問題素材,使探究的問題具有層次性和探究性,適時、適勢、適度地用教學機智調控課堂。在教學設計中,要預設多種意外和可能,這樣探究真知的過程就會艱辛并順利展開。這才是一個成功的組織者。

    但是,本節課也反映了不少問題,比如說學生與老師配合度不高,導致知識總結時間過多,在第三個環節求解析式時時間緊,任務重,雖說完成了教學任務,但是結尾有些倉促了。另外,單純的讓學生帶領學生復習,不直觀,導致部分學生跟不上。所以,本節課的設置還需要逐步改善。
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