When we look at the theoretical relationships between the three types of geometry, we find that the most primitive type is topology and that both Euclidean and projective geometry are derived from this earlier type. Therefore, Piaget described the first stage or level of understanding geometry as topological understanding. In this study, the geometric thinking conditions of mathematics teacher candidates were examined and what they think about the topology course was determined by surveying their opinions about the undergraduate courses. The participants of the study consisted of 36 teacher candidates studying in the Mathematics Department of the Faculty of Science attached to a university in Turkey. The findings of the study revealed that none of the teacher candidates used topological thinking to solve the questions in the data collection instrument. Those candidates who considered topology as an abstract course did not associate topology with geometry. A thorough understanding of the meaning of topology and topological thought is an advantage to young children as well as college‐age students; improving mathematics curricula on this topic, particularly at the graduate level, will ensure that all future teachers are appropriately trained for their future responsibility of educating others. We believe that it is necessary to give Topology and topological thought the place they deserve in the educational process.

中文翻译：

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数学教师候选人在几何学中使用拓扑的方法

当我们查看三种几何类型之间的理论关系时，我们发现最原始的类型是拓扑，而欧几里得几何和射影几何都从该较早的类型派生而来。因此，伯爵将理解几何的第一阶段或层次描述为拓扑理解。在这项研究中，研究了数学教师候选人的几何思维条件，并通过调查他们对本科课程的看法来确定他们对拓扑课程的看法。该研究的参与者包括36名在土耳其一所大学附属的理学院数学系学习的教师候选人。研究结果表明，没有一个教师候选人使用拓扑思维来解决数据收集工具中的问题。那些将拓扑视为抽象课程的候选人没有将拓扑与几何相关联。对拓扑和拓扑思想的含义有透彻的了解，对于年幼的孩子和大学生都是有利的；改进有关该主题的数学课程，尤其是在研究生水平上，将确保所有未来的教师都受到适当的培训，以承担他们未来教育他人的责任。我们认为有必要在教育过程中给予拓扑和拓扑思想应有的地位。对拓扑和拓扑思想的含义有透彻的了解，对于年幼的孩子和大学生都是有利的；改进有关该主题的数学课程，尤其是在研究生水平上，将确保所有未来的教师都受到适当的培训，以承担他们未来教育他人的责任。我们认为有必要在教育过程中给予拓扑和拓扑思想应有的地位。对拓扑和拓扑思想的含义有透彻的了解，对于年幼的孩子和大学生都是有利的；改进有关该主题的数学课程，尤其是在研究生方面，将确保所有未来的教师都受到适当的培训，以承担其未来教育他人的责任。我们认为有必要在教育过程中给予拓扑和拓扑思想应有的地位。