Research has identified several students’ misinterpretations of the principles of the photoelectric effect (PE). Students cannot interpret the formula using the graph’s context despite the linear dependence inherited in it. Many studies pointed out that the graphical representation of kinetic energy of the ejected electrons versus frequency of incident photons is unclear when a blend of mathematical and scientific reasoning is applied. While research suggests various ways to help improve the understanding, little attention is given to the algebraic structure of the equation and its corresponding graphical representation. Detailed scrutiny revealed that some phases of the PE’s algebraic expression do not support its visual representation. This paper suggests a more consistent alignment of the rules of mathematics with the PE process. This suggestion emerged as an alternative algebraic representation of the law of conservation of energy in the form of a piecewise linear function. It is hypothesized that such covariational relation between photons’ frequency and the ejected electrons’ kinetic energy is more consistent with observable phenomena behaviour and students’ mathematics knowledge. While formulating the law of conservation of energy, a physics simulation, The Photoelectric Effect (http://phet.colorado.edu), was used. The process of mathematical modelling of the PE that concluded with a covariational relation of the kinetic energy of ejected electrons was delivered to a group of 20 (N = 20) high school physics students. A didactical outline of the instructional unit is included.

研究已经确定了几个学生对光电效应 (PE) 原理的误解。尽管继承了线性相关性，但学生无法使用图形的上下文来解释公式。许多研究指出，当应用数学和科学推理的混合时，喷射电子的动能与入射光子频率的图形表示不清楚。虽然研究提出了各种方法来帮助提高理解，但很少关注方程的代数结构及其相应的图形表示。详细审查显示，PE 代数表达式的某些阶段不支持其视觉表示。本文建议数学规则与 PE 过程更加一致。该建议以分段线性函数的形式作为能量守恒定律的替代代数表示出现。假设光子频率与射出电子动能之间的这种协变关系更符合可观察到的现象行为和学生的数学知识。在制定能量守恒定律的同时，进行物理模拟，光电效应(http://phet.colorado.edu)，被使用。以喷射电子动能的协变关系结束的 PE 数学建模过程被交付给一组 20 ( N = 20) 名高中物理学生。包括教学单元的教学大纲。