Teachers’ understanding of the concepts they teach affects the quality of instruction and students’ learning. This study used a sample of 303 teachers from across the USA to examine elementary school mathematics teachers’ knowledge of key concepts underlying fraction arithmetic. Teachers’ explanations were coded based on the accuracy of their explanations and the kinds of concepts and representations they used in their responses. The results showed that teachers’ understanding of fraction arithmetic was limited, especially for fraction division, yet a moderate relationship was found between teachers’ understanding of fraction addition and division. Furthermore, more experienced teachers seemed to have a deeper understanding of fraction arithmetic, whereas special education teachers had a substantially limited understanding.

老师对所教概念的理解会影响教学质量和学生的学习。这项研究使用了来自美国各地的303名教师的样本，研究了小学数学教师对分数算术基础知识的了解。教师的解释是根据他们的解释的准确性以及他们在回答中使用的概念和表示形式进行编码的。结果表明，教师对分数算术的理解是有限的，尤其是对于分数除法，但教师对分数加法和除法的理解之间存在中等关系。此外，经验丰富的老师似乎对分数算术有更深的了解，而特殊教育老师的理解却很有限。