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自然界與現(xiàn)實(shí)社會(huì)，在諸多方面展現(xiàn)著數(shù)學(xué)思維的運(yùn)用。但是在教學(xué)中，怎樣將現(xiàn)實(shí)問(wèn)題轉(zhuǎn)化到數(shù)學(xué)課堂？以何種視角建構(gòu)起現(xiàn)實(shí)問(wèn)題與數(shù)學(xué)問(wèn)題之間的聯(lián)系？

蘇城外國(guó)語(yǔ)學(xué)校高中部的數(shù)學(xué)課堂有著屬于自己的闡釋與演繹。

The application of Mathematics can been seen everywhere in the real world. The Mathematics class in the SCFLS senior high school has its own interpretation for turning real-life questions into Maths problems, and the connection between these two.

教師簡(jiǎn)介 Teacher Profile

在這節(jié)課之前，學(xué)生已經(jīng)學(xué)習(xí)了一些關(guān)于直線(xiàn)的基本知識(shí)，比如如何求直線(xiàn)的表達(dá)式，斜率的意義，如何通過(guò)表達(dá)式畫(huà)出對(duì)應(yīng)直線(xiàn)等。

教學(xué)目標(biāo)：

讀懂散點(diǎn)圖，通過(guò)數(shù)據(jù)畫(huà)出散點(diǎn)圖。

在散點(diǎn)圖中找出最佳擬合直線(xiàn)，并求出表達(dá)式。

Before this class, students have had some prior knowledge, for example: how to find the linear function, the meaning of slope and how to draw the corresponding line of a given function. Based on these, the teaching objectives are:

To understand and draw the scatter plot of given data.To find the line of best fit for the scatter plot and find the equation

教師呈現(xiàn)出一組關(guān)于學(xué)生每周學(xué)習(xí)數(shù)學(xué)的時(shí)間和學(xué)生期中考試成績(jī)的數(shù)據(jù)，引導(dǎo)學(xué)生根據(jù)這一組數(shù)據(jù)畫(huà)出散點(diǎn)圖。然后讓每一組學(xué)生思考這一組數(shù)據(jù)兩個(gè)量之間的關(guān)系和如何能夠添加輔助線(xiàn)來(lái)描述這兩個(gè)量之間的趨勢(shì)，并同時(shí)在紙上畫(huà)出，以此來(lái)鍛煉他們作為Inquirers，Thinkers的能力。

Teacher presented a set of data about students’ weekly study time in math and the mid-term math score of each student, guiding students to draw the scatter plot based on the given data. After that, students were encouraged to think what could be added to describe the trend between these two variables and show it on paper. Through this activity, they were trained to be inquirers and thinkers. 

同學(xué)們經(jīng)過(guò)思考得出不一樣的結(jié)論，老師在黑板上展示了幾張不同的答案，同學(xué)們也相互討論，投票選出他們認(rèn)為最能描述兩個(gè)量之間趨勢(shì)的圖，在這一過(guò)程中，充分展現(xiàn)了學(xué)生們communicators與open-minded的特質(zhì)。

After discussion, different answers were presented by teacher on the blackboard. Students had to justify their answers and voted for the best graph, demonstrating their abilities as communicators and open-minded.

老師提取同學(xué)們討論中的關(guān)鍵信息，正是這一節(jié)課的教學(xué)重點(diǎn)，并延伸開(kāi)去講解如何挑選最佳擬合直線(xiàn)，什么是預(yù)測(cè)函數(shù)，如何求解預(yù)測(cè)函數(shù)，如何利用預(yù)測(cè)函數(shù)來(lái)解決實(shí)際問(wèn)題。老師精當(dāng)?shù)闹v解可以讓學(xué)生更加knowledgeable。

Teacher extracted the key point of student’s discussion and extended to the topic: how to choose the line of best fit and prediction function and applications in real life. Students will be more knowledgeable with teacher’s explanation.

教師在課堂中對(duì)學(xué)生進(jìn)行再次分組，從原來(lái)有利于促進(jìn)討論的異質(zhì)分組換為同質(zhì)分組，根據(jù)每組學(xué)生不同的學(xué)習(xí)能力分配難度不同的習(xí)題，能力最強(qiáng)的一組除了基礎(chǔ)的練習(xí)，會(huì)補(bǔ)充更開(kāi)放的思考題。

Students were regrouped according to homogeneous intelligences, and assigned with tasks of different levels. The higher-level group had more open-ended questions apart from some basic problems.

任何的數(shù)學(xué)模型都有它的局限性，這節(jié)課學(xué)習(xí)的直線(xiàn)預(yù)測(cè)模型也不例外。學(xué)生要結(jié)合他們這堂課的學(xué)習(xí)知識(shí)和現(xiàn)實(shí)生活經(jīng)驗(yàn)來(lái)思考直線(xiàn)模型的局限性。直線(xiàn)模型只能用來(lái)預(yù)測(cè)一定范圍內(nèi)的數(shù)據(jù)，當(dāng)自變量很大時(shí)就會(huì)變得不準(zhǔn)確。比如學(xué)習(xí)的時(shí)間變長(zhǎng)，成績(jī)也不會(huì)超過(guò)試卷的滿(mǎn)分；也可能直線(xiàn)模型并不是描述關(guān)系的最佳選擇。

Restrictions exist in any mathematical model, so does the model in this class. Students discussed the restriction based on the real-life experience and knowledge in this class. Here are some possible answers: the linear prediction function only works in a suitable range; the linear model is not the best choice.

中文撰稿：顧佳玲  

 英文翻譯：沈紫煙   

攝影：宋柏霖 

英文審核：語(yǔ)言中心

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