从“配平”回归“建模”——基于比拟的量纲分析教学重构RETURNING FROM BALANCING TO MODELING: INSTRUCTIONAL RECONSTRUCTION OF DIMENSIONAL ANALYSIS ON ANALOGY
王啸,郭子怡,陈宗佑,周天弈
摘要(Abstract):
针对量纲分析教学中存在的重代数运算、轻物理机制以及由果溯因式的公式验证等现状,本文提出了物理机制主导、问题导向的教学重构方案。引入与量纲分析数学原理相同的化学方程式配平作为认知脚手架,借鉴其原理主导配平的思维范式,重构了涉及量选取与单位制确定的物理逻辑。在涉及量选取环节,界定了普适常量的机制转换作用,构建了基于物理规律的选取流程;在单位制确定环节,类比化学原子团与离子反应概念,挖掘量纲的物理独立性内涵,提出了量纲独立化与冗余删除操作。通过4个典型案例的对比分析,表明了物理机制主导方案在还原物理图景、提升分析效力及简化数学运算方面的优势。该教学重构旨在引导学生从机械地配平回归对物理本质的探究,有助于提升科学思维与模型建构素养。
关键词(KeyWords): 量纲分析;单位制;跨学科比拟
基金项目(Foundation):
作者(Author): 王啸,郭子怡,陈宗佑,周天弈
DOI: 10.27024/j.wlygc.2026.03.02.03
参考文献(References):
- [1] 梁灿彬,曹周键.量纲理论与应用[M].北京:科学出版社,2020.LIANG C B,CAO Z J.Dimensional theory and applications[M].Beijing:China Science Publishing & Media Ltd,2020.(in Chinese) [2] 谈庆明.相似分析[M].北京:北京大学出版社,2019.TAN Q M.Similarity analysis[M].Beijing:Peking University Press,2019.(in Chinese) [3] 付茂林,邹喜洋,刘世清.量纲分析的线性代数方法[J].大学物理,2001,20(11):25-27.FU M L,ZOU X Y,LIU S Q.A linear algebraic method for dimensional analysis[J].College Physics,2001,20(11):25-27.(in Chinese) [4] 沈国光.量纲分析的几何联想[J].力学与实践,1997(3):55-56.SHEN G G.Geometric association of dimensional analysis[J].Mechanics in Engineering,1997,19(3):55-56.(in Chinese) [5] 孙博华.量纲分析以及应用[J].物理与工程,2016,26(6):11-20.SUN B H.Dimensional analysis and applications[J].Physics and Engineering,2016,26(6):11-20.(in Chinese) [6] 陈博闻.基于量纲分析的爆破振动频率公式[J].水利水电技术,2012,43(2):54-57.CHEN B W.Blasting vibration frequency formula based on dimensional analysis[J].Water Resources and Hydropower Engineering,2012,43(2):54-57.(in Chinese) [7] VASWANI A,SHAZEER N,PARMAR N,et al.Attention is all you need[J].arXiv preprint arXiv:1706.03762,2017. [8] IOFFE S,SZEGEDY C.Batch normalization:accelerating deep network training by reducing internal covariate shift[J].arXiv preprint arXiv:1502.03167,2015. [9] 魏环,许贺菊.量纲理论与量纲分析法的教学方案的探讨[J].物理与工程,2019,29(3):19-25,28.WEI H,XU H J.Discussion on the teaching scheme of dimensional theory and dimensional analysis method[J].Physics and Engineering,2019,29(3):19-25,28.(in Chinese) [10] 严导淦.量纲分析及其应用[J].物理与工程,2012,22(6):22-26,21.YAN D G.Dimensional analysis and application[J].Physics and Engineering,2012,22(6):22-26,21.(in Chinese) [11] 王宏.量纲分析法及其在原子物理学中的应用[J].西南师范大学学报(自然科学版),2009,34(2):189-192.WANG H.Analyzed method of dimension and its application in atomic physics[J].Journal of Southwest China Normal University (Natural Science Edition),2009,34(2):189-192.(in Chinese) [12] 潘鹤林,宗原,黄婕.《化工原理》课程中的量纲分析法[J].教育教学论坛,2019(2):165-167.PAN H L,ZONG Y,HUANG J.Dimensional analysis means in the principles of “Chemical Engineering”[J].Education Teaching Forum,2019(2):165-167.(in Chinese) [13] 白光富,胡林,刘盛华.大学物理教学中量纲分析与应用[J].物理与工程,2012,22(2):14-16,28.BAI G F,HU L,LIU S H.Dimensional analysis and application in university physics teaching[J].Physics and Engineering,2012,22(2):14-16,28.(in Chinese) [14] 张瑜瑜,胡自翔,董建军,等.量子力学狄拉克符号量纲问题[J].物理与工程,2024,34(4):110-113.ZHANG Y Y,HU Z X,DONG J J,et al.The dimension of the Dirac notation in quantum mechanics[J].Physics and En gineering,2024,34(4):110-113.(in Chinese) [15] 熊兆华,杨琳朔,梁淇玮,等.热力学·统计物理教学中的量纲问题[J].物理与工程,2024,34(2):54-65.XIONG Z H,YANG L S,LIANG Q W,et al.The dimension pedagogy in thermodynamics and statistical physics[J].Physics and Engineering,2024,34(2):54-65.(in Chinese) [16] 王明美.黑体辐射公式的量纲分析[J].大学物理,2009,28(2):21-23,27.WANG M M.Dimensional analysis of formula of blackbody radiation[J].College Physics,2009,28(2):21-23,27.(in Chinese) [17] 王建国,黄海燕,许利军.关于雨滴降落终极速度的量纲分析[J].河北北方学院学报(自然科学版),2008,24(6):18-20.WANG J G,HUANG H Y,XU L J.Dimensional analysis of terminal velocity on raindrops landing[J].Journal of Hebei North University (Natural Science Edition),2008,24(6):18-20.(in Chinese) [18] HUNTLEY H.Dimensional analysis[M].London:Macdonald & Co,1952. [19] 李生荣.解方程法配平化学方程式[J].青海师专学报,2008(5):251-253.LI S R.To bring the chemical equations into balance by equation technique[J].Journal of Qinghai Junior Teachers' College,2008(5):251-253.(in Chinese) [20] 赵怀豫.配平化学方程式的数学方法[J].教学与管理,1988(1):66-69.ZHAO H Y.Mathematical methods for balancing chemical equations[J].Teaching and Administration,1988(1):66-69.(in Chinese) [21] 孙会霞,职桂珍.线性方程组的基本理论在配平化学方程式中的应用——改进的线性代数法[J].郑州轻工业学院学报,2001(4):68-71.SUN H X,ZHI G J.Application of the basic theorem of a system of linear equations to balancing chemical reaction equations:the improvement on linear algebra method[J].Journal of Zhengzhou Institute of Light Industry,2001,16(4):68-71.(in Chinese) [22] GENTNER D.Structure-mapping:a theoretical framework for analogy[J].Cognitive Science,1983,7(2):155-170. [23] VYGOTSKY L,COLE M.Mind in society:The development of higher psychological processes[M].Cambridge:Harvard University Press,1981. [24] WOOD D,BRUNER J,ROSS G.The role of tutoring in problem solving[J].Journal of Child Psychology and Psychiatry,1976,17(2):89-100. [25] PIAGET J.The Psychology of Intelligence[M].London:Routledge,2001. [26] FOURIER J,FREEMAN A.The Analytical Theory of Heat[M].Cambridge:Cambridge University Press,2009. [27] MACAGNO E.Historico-critical review of dimensional analysis[J].Journal of the Franklin Institute,1971,292(6):391-402. [28] CAVENDISH H.Experiments to determine the density of the earth[J].Philosophical Transactions of the Royal Society of London,1798,88:469-526. [29] GILLIES G.The Newtonian gravitational constant:recent measurements and related studies[J].Reports on Progress in Physics,1997,60(2):151-225. [30] BRIDGMAN P.Dimensional Analysis[M].New Haven:Yale University Press,1922. [31] BIPM.The International System of Units (SI)[S].9th ed.Paris:BIPM,2019.
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