Department of Biology, Brigham Young University, Provo, UT 84602.
Department of Mathematics Education, Brigham Young University, Provo, UT 84602.
CBE Life Sci Educ. 2021 Jun;20(2):ar22. doi: 10.1187/cbe.20-09-0219.
Hardy-Weinberg (HW) equilibrium and its accompanying equations are widely taught in introductory biology courses, but high math anxiety and low math proficiency have been suggested as two barriers to student success. Population-level Punnett squares have been presented as a potential tool for HW equilibrium, but actual data from classrooms have not yet validated their use. We used a quasi-experimental design to test the effectiveness of Punnett squares over 2 days of instruction in an introductory biology course. After 1 day of instruction, students who used Punnett squares outperformed those who learned the equations. After learning both methods, high math anxiety was predictive of Punnett square use, but only for students who learned equations first. Using Punnett squares also predicted increased calculation proficiency for high-anxiety students. Thus, teaching population Punnett squares as a calculation aid is likely to trigger less math anxiety and help level the playing field for students with high math anxiety. Learning Punnett squares before the equations was predictive of correct derivation of equations for a three-allele system. Thus, regardless of math anxiety, using Punnett squares before learning the equations seems to increase student understanding of equation derivation, enabling them to derive more complex equations on their own.
哈迪-温伯格（HW）平衡及其伴随的方程在基础生物学课程中被广泛教授，但高数学焦虑和低数学能力被认为是学生成功的两个障碍。群体水平的概率方格已被提出作为 HW 平衡的潜在工具，但课堂上的实际数据尚未验证其使用。我们使用准实验设计在一门基础生物学课程中用两天的教学时间来测试概率方格的有效性。经过一天的教学，使用概率方格的学生比学习方程的学生表现更好。在学习了两种方法之后，高数学焦虑预测了概率方格的使用，但仅适用于先学习方程的学生。使用概率方格也预测了高焦虑学生的计算能力提高。因此，教授群体概率方格作为一种计算辅助工具可能会减少学生的数学焦虑，并为高数学焦虑的学生创造更公平的竞争环境。在学习方程之前学习概率方格可以预测对三等位基因系统的方程的正确推导。因此，无论数学焦虑程度如何，在学习方程之前使用概率方格似乎都会增加学生对方程推导的理解，使他们能够自行推导更复杂的方程。
