新泽西STEM创新奖学金

The 2024 NJ STEM Innovation Fellowship program will form a Professional Learning Community (PLC) that includes elementary and middle school teachers as well as university faculty members. The PLC will learn to implement a design innovation that develops foundational through advanced understanding of the mathematical concepts of equality and equivalence. The innovation uses a familiar and ancient technology – the balance scale – as a powerful learning tool that students can think with as they explore and come to understand increasingly complex ideas. 因为PLC包括各级数学和科学教育工作者, this innovation will support learning from a child’s earliest mathematical explo比ns through college graduation and into the workforce.

什么是相等和等价? 在初级阶段, children are introduced to these concepts through the basic arithmetic ope比ns of addition, 减法, 乘法, 和分裂. Understanding the concept of equality – as in 5 = 3 + 2 – prepares children for more complex mathematical concepts such as equations and equivalent fractions. These concepts are essential for building a solid mathematical foundation and preparing students for middle and high school mathematics.

在中学, students encounter a broader range of mathematical concepts built upon equality and equivalence, 从比率和百分比到线性方程和函数. 理解等效——如2/3 = 6/9, 10 – 7 = 6 ÷ 2, 而4x + 12 = 4(x + 3) -则需要用于解决涉及速率的问题, 比, 坡, 和相似性. 没有这些概念, students cannot make connections across the mathematical topics that would enable them to solve real-world problems.

在高中时, students explore more advanced topics such as polynomial and exponential functions, 有理表达式和方程, 相似的数据, 以及涉及面积和体积的定理和建模. Mastery of equality and equivalence remains important for understanding these subjects, 作为学生，必须能够处理方程, 解决复杂问题, 并根据数学原理进行逻辑推理.

没有坚实的基础概念, students may find themselves unready for college-level coursework in mathematics and natural science. Students who struggle with first-year math/science courses are less likely to persist in STEM majors or enter the STEM workforce (Chen, 2013; Cohen & Kelly, 2020; PCAST, 2012). The innovative use of a balance scale as a mathematical model for teaching the concepts of equality and equivalence provides students with an engaging, 有意义的, hands-on approach to thinking and reasoning about abstract concepts and deepening their understandings.

参考文献

• 陈,X. (2013). STEM人员流失:大学生进入和退出STEM领域的路径. 统计分析报告. 生均2014 - 001. 国家教育统计中心.
• 科恩,R., & 凯利,. M. (2020). Mathematics as a factor in community college STEM performance, persistence, and degree attainment. 科学教学研究，57(2)，279-307.
• 坏了的,我. J., & Roschelle J. (2002). The mathematics of change and variation from a millennial perspective: New content, new context. 《十大博彩推荐排名》(页). 155-170). 劳特利奇.
• 总统科技顾问委员会(2012年). Engage to Excel: Producing One Million Additional College Graduates with Degrees in Science, 技术, 工程, 和数学. 从检索 http://obamawhitehouse.archives.gov/sites/default/files/microsites/ostp/pcast-engage-to-excel-final_2-25-12.pdf
• Roschelle J.卡普特，J. J., & Stroup W. (2012). SimCalc:加速学生对变化数学的参与. 在科学和数学教育的创新(页). 60-88). 劳特利奇.

创新在自然科学中的应用

The concepts of equality and equivalence are used by students to understand and succeed in natural science courses at the secondary and college levels. In many cases, students use an actual balance scale as part of the science learning activity. Some examples of equality and equivalence in biological and physical sciences include:

物理

力学

Students encounter the concept of equilibrium in the context of equality in forces. 例如, 当研究处于静力平衡状态的物体或计算系统中的力时, 学生必须用平等的思想来解决问题.

电与磁

在电磁, Ohm’s Law (V = IR) and Kirchhoff’s Laws (for conservation of charge and energy) students must use equivalence and equality to understand and analyze electrical circuits and phenomena.

热力学

The concept of energy balance is necessary for understanding the equality between energy input and output in various processes. Equivalence is used to understand the relationship between different forms of energy (e.g. 动能和势能)和它们的转换.

量子力学

在更高级的物理课程中, 等效是用来理解粒子波二象性和量子叠加的. The concept of equality is applied in equations for the conservation of energy and momentum in quantum interactions.

化学

化学反应

化学计量学是以相等原理为基础的, where chemical equations must be balanced by students to ensure that the number of atoms of each element remains the same before and after a reaction. 这是用来确定反应产率和了解反应机理.

平衡

在化学平衡中, the equilibrium constant expression involves the equality of forward and reverse reaction rates. Students use this concept to predict the direction of a reaction under different conditions and calculate equilibrium concent比ns.

定量分析

Students use equality and equivalence in quantitative analysis techniques such as tit比ns, where the equivalence point signifies the equality between the moles of reactants and products. 这是测定未知物质浓度所必需的.

生物学

种群动态

Mathematical models for population growth and dynamics use the concept of equality to study the way birth rates are expected to equal death rates under certain conditions. Students also apply equivalence in models for carrying capacity and limiting factors.

生化途径

在研究生化途径和代谢过程时, 学生用等效来理解质量和能量守恒. Students use the concept of mathematical equality to study stoichiometry of chemical reactions within cells and the balance between substrate and product concent比ns.

地球科学

地质过程

侵蚀的数学模型, 沉积, 构造运动被用来预测地球随时间的变化. These require students to understand equations in which quantities before and after an event are equal.

气候模型

Students use equivalence for climate modeling in equations for the balance between incoming and outgoing radiation to determine the planetary energy budget. 这有助于学生了解气候变化的预测和影响.

资助者

我们要感谢我们的奖学金资助者. 他们的慷慨 & 支持对这个项目的发展和可持续发展是无价的.