表述杠桿的平衡條件要嚴(yán)謹(jǐn)

張平柯

科學(xué)教學(xué)要高度關(guān)注學(xué)生的前概念。如果學(xué)生的前概念和所要學(xué)習(xí)的科學(xué)概念比較接近，那么學(xué)生對(duì)該科學(xué)概念的理解一般比較容易，構(gòu)建的概念也比較牢固；相反，如果學(xué)生的前概念與要學(xué)習(xí)的科學(xué)觀念沖突明顯，要讓學(xué)生接受該科學(xué)概念就需要付出艱苦的努力，要讓所構(gòu)建的科學(xué)概念在學(xué)生頭腦中“固化”更不容易。同樣，如果學(xué)生在學(xué)習(xí)科學(xué)概念的過(guò)程中形成了錯(cuò)誤的概念，對(duì)他們后續(xù)的科學(xué)學(xué)習(xí)將造成很大的障礙。

在學(xué)習(xí)“杠桿的科學(xué)”內(nèi)容時(shí)，教師往往利用杠桿尺進(jìn)行研究，并要求學(xué)生實(shí)驗(yàn)后填寫表格（見(jiàn)下表）。

在這個(gè)表格中有2個(gè)關(guān)鍵數(shù)據(jù)，分別是“阻力點(diǎn)到支點(diǎn)的距離”和“用力點(diǎn)到支點(diǎn)的距離”。學(xué)生在完成實(shí)驗(yàn)后，通過(guò)分析記錄表中的數(shù)據(jù)，一般都能“正確地”回答教師提出的問(wèn)題：在阻力點(diǎn)到支點(diǎn)的距離小于用力點(diǎn)到支點(diǎn)的距離時(shí)杠桿省力，在阻力點(diǎn)到支點(diǎn)的距離大于用力點(diǎn)到支點(diǎn)的距離時(shí)杠桿費(fèi)力，在阻力點(diǎn)到支點(diǎn)的距離等于用力點(diǎn)到支點(diǎn)的距離時(shí)杠桿既不省力也不費(fèi)力。

學(xué)生通過(guò)實(shí)驗(yàn)所建構(gòu)的這一概念，很容易形成牢固的記憶，然而，這一概念的建立對(duì)中學(xué)學(xué)習(xí)杠桿的平衡條件卻會(huì)造成一定的負(fù)面影響。

我們知道，杠桿的平衡條件是“動(dòng)力乘動(dòng)力臂=阻力乘阻力臂”，而動(dòng)力臂是動(dòng)力作用線到支點(diǎn)的距離，阻力臂是阻力作用線到支點(diǎn)的距離。事實(shí)上，中學(xué)生在學(xué)習(xí)這部分知識(shí)時(shí)，很容易出現(xiàn)的錯(cuò)誤是把力的作用線到支點(diǎn)的距離弄成力的作用點(diǎn)到支點(diǎn)的距離。

很明顯，表格中恰恰就是用力的作用點(diǎn)到支點(diǎn)的距離取代了力的作用線到支點(diǎn)的距離。強(qiáng)調(diào)“用力點(diǎn)”和“阻力點(diǎn)”到支點(diǎn)的距離，并由此總結(jié)出在什么情況下杠桿省力、費(fèi)力的結(jié)論，一旦在學(xué)生的頭腦中形成牢固的概念，在中學(xué)階段要實(shí)現(xiàn)概念的轉(zhuǎn)化就很困難，從而影響中學(xué)的學(xué)習(xí)。

引入“力臂=力作用線到支點(diǎn)的距離”的概念對(duì)小學(xué)五六年級(jí)學(xué)生并不合適，但教師完全可以在學(xué)生總結(jié)實(shí)驗(yàn)結(jié)果并回答相關(guān)問(wèn)題后，提醒他們注意這些結(jié)論的成立是需要滿足一定條件的，并不是在任何情況下都成立。

為了強(qiáng)化這一認(rèn)識(shí)，可增加如下圖的演示實(shí)驗(yàn)。當(dāng)學(xué)生觀察到杠桿平衡時(shí)，左右兩個(gè)彈簧秤讀數(shù)的明顯差異，他們會(huì)深刻地認(rèn)識(shí)到，通過(guò)在杠桿尺兩端掛鉤碼得出的“在阻力點(diǎn)到支點(diǎn)的距離等于用力點(diǎn)到支點(diǎn)的距離時(shí)杠桿既不省力也不費(fèi)力”的結(jié)論是有條件限制的，他們自然還會(huì)想到“在阻力點(diǎn)到支點(diǎn)的距離小于用力點(diǎn)到支點(diǎn)的距離時(shí)杠桿省力，在阻力點(diǎn)到支點(diǎn)的距離大于用力點(diǎn)到支點(diǎn)的距離時(shí)杠桿費(fèi)力”的結(jié)論也是要滿足一定條件的。這樣不僅不會(huì)對(duì)中學(xué)的學(xué)習(xí)造成負(fù)面影響，還能為中學(xué)學(xué)習(xí)力臂的概念留下一個(gè)伏筆。

The Balance Conditions of Leverage should be Rigorous

ZHANG Pingke

中圖分類號(hào)：G424文獻(xiàn)標(biāo)識(shí)碼：ADOI：10.16400/j.cnki.kjdk.2021.24.002

ZHANG Pingke

Professor of Physics， Hunan First Normal University

Distinguished Professor of Changsha Normal University

Executive vice President of Hunan Youth Science and Technology Education Association

Science teaching should pay close attention to students’ pre concepts. If students’ pre concept is close to the scientific concept they want to learn， stu？ dents generally understand the scientific concept easi？ ly and build a solid concept； On the contrary， if the conflict between students’ pre concept and the scien？ tific concept to be studied is obvious， it needs to make arduous efforts to make students accept the sci？ entific concept， and it is not easy to "solidify" the constructed scientific concept in students’ minds. Sim？ ilarly， if students form wrong concepts in the process of learning scientific concepts， it will cause great ob？ stacles to their subsequent scientific learning.

Whenlearningthecontent of "lever science"， teachers often use lever ruler for research， and re？ quire students to fill in the form after the experiment（see the table below）.

There are two key data in this table， namely"distance from resistance point to fulcrum" and "dis？ tance from force point to fulcrum". After completing the experiment， students can generally "correctly" an？ swer the questions raised by teachers by analyzing the data in the record table： when the distance from the resistance point to the fulcrum is less than the distance from the force point to the fulcrum， the le？ ver is labor-saving， and when the distance from the resistance point to the fulcrum is greater than the distance from the force point to the fulcrum， the le？ ver is labor-saving， When the distance from the resis？ tance point to the fulcrum is equal to the distance from the force point to the fulcrum， the lever is nei？ ther labor-saving nor laborious.

The concept constructed by students through ex？ periments is easy to form a solid memory. However， the establishment of this concept will have a certain negative impact on the balance conditions of learning leverage in middle school.

We know that the balance condition of the lever is "power multiplied by boom = resistance multiplied by resistance arm"， and the power arm is the dis？ tance from the power action line to the fulcrum， and the resistance arm is the distance from the resistance actionlinetothefulcrum.Infact，whenmiddle school students learn this part of knowledge， it is easy to make the mistake of changing the distance from the action line of force to the fulcrum into the distance from the action point of force to the fulcrum.

Obviously， in the table， it is precisely the dis？ tance from the action point of force to the fulcrum that replaces the distance fromthe action line of force to the fulcrum. Emphasize the distance from the "force point" and "resistance point" to the ful？ crum， and summarize the conclusion that the lever is labor-saving and laborious under what circumstances. Onceasolidconceptisformedinthestudents’ mind， it is difficult to realize the transformation of the concept in the middle school stage， which affects the learning of the middle school.

The introduction of the concept of "force arm = distance from the force action line to the fulcrum" is not suitable for students in Grade 5 and 6 of prima？ ryschool，butteacherscanremindstudentsthat these conclusions need to meet certain conditions af？ ter students summarize the experimental results and answer relevant questions.

Inordertostrengthenthisunderstanding，the demonstration experiment shown in the figure below can be added. When students observe the obvious dif？ ference between the readings of the left and right spring scales when the lever is balanced， they will deeply realize that the conclusion that "when the dis？ tancefromtheresistancepointtothefulcrumis equal to the distance from the force point to the ful？ crum"， which is reached through the hook code at both ends of the lever ruler， the lever is neither la？ bor-saving nor labor-saving "， is conditionally limit？ ed， they will naturally think of the conclusion that"the lever is labor-saving whenthe distance from the resistance point to the fulcrum is less than the distance from the force point to the fulcrum， and the lever is labor-saving when the distance from the re？ sistance point to the fulcrum is greater than the dis？ tance from the force point to the fulcrum". This will not only have a negative impact on middle school learning， but also leave a foreshadowing for the con？ cept of learning arm in middle school.

When the distance from the action point of force to the fulcrum is equal， the reading of spring scale is signifi？ cantly different.