表述杠桿的平衡條件要嚴謹

張平柯

科學教學要高度關注學生的前概念。如果學生的前概念和所要學習的科學概念比較接近，那么學生對該科學概念的理解一般比較容易，構建的概念也比較牢固；相反，如果學生的前概念與要學習的科學觀念沖突明顯，要讓學生接受該科學概念就需要付出艱苦的努力，要讓所構建的科學概念在學生頭腦中“固化”更不容易。同樣，如果學生在學習科學概念的過程中形成了錯誤的概念，對他們后續的科學學習將造成很大的障礙。

在學習“杠桿的科學”內容時，教師往往利用杠桿尺進行研究，并要求學生實驗后填寫表格（見下表）。

在這個表格中有2個關鍵數據，分別是“阻力點到支點的距離”和“用力點到支點的距離”。學生在完成實驗后，通過分析記錄表中的數據，一般都能“正確地”回答教師提出的問題：在阻力點到支點的距離小于用力點到支點的距離時杠桿省力，在阻力點到支點的距離大于用力點到支點的距離時杠桿費力，在阻力點到支點的距離等于用力點到支點的距離時杠桿既不省力也不費力。

學生通過實驗所建構的這一概念，很容易形成牢固的記憶，然而，這一概念的建立對中學學習杠桿的平衡條件卻會造成一定的負面影響。

我們知道，杠桿的平衡條件是“動力乘動力臂=阻力乘阻力臂”，而動力臂是動力作用線到支點的距離，阻力臂是阻力作用線到支點的距離。事實上，中學生在學習這部分知識時，很容易出現的錯誤是把力的作用線到支點的距離弄成力的作用點到支點的距離。

很明顯，表格中恰恰就是用力的作用點到支點的距離取代了力的作用線到支點的距離。強調“用力點”和“阻力點”到支點的距離，并由此總結出在什么情況下杠桿省力、費力的結論，一旦在學生的頭腦中形成牢固的概念，在中學階段要實現概念的轉化就很困難，從而影響中學的學習。

引入“力臂=力作用線到支點的距離”的概念對小學五六年級學生并不合適，但教師完全可以在學生總結實驗結果并回答相關問題后，提醒他們注意這些結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。

為了強化這一認識，可增加如下圖的演示實驗。當學生觀察到杠桿平衡時，左右兩個彈簧秤讀數的明顯差異，他們會深刻地認識到，通過在杠桿尺兩端掛鉤碼得出的“在阻力點到支點的距離等于用力點到支點的距離時杠桿既不省力也不費力”的結論是有條件限制的，他們自然還會想到“在阻力點到支點的距離小于用力點到支點的距離時杠桿省力，在阻力點到支點的距離大于用力點到支點的距離時杠桿費力”的結論也是要滿足一定條件的。這樣不僅不會對中學的學習造成負面影響，還能為中學學習力臂的概念留下一個伏筆。

The Balance Conditions of Leverage should be Rigorous

ZHANG Pingke

中圖分類號：G424文獻標識碼：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.