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The development and application of an interview structure on determining preservice mathematics teachers’ competence in proportional reasoning
Mathematics Education Research Journal Pub Date : 2021-05-27 , DOI: 10.1007/s13394-021-00388-5
Muhammet Arican

Determining preservice teachers’ competence in proportional reasoning is a very complex task, and existing research methods do not provide effective tools in doing that. This study describes an interview structure and application of it in determining preservice teachers’ competence in proportional reasoning. The interview structure consists of in-depth questioning and cognitive conflicts and is situated in the knowledge-in-pieces epistemological perspective. The preservice teachers’ competence in proportional reasoning was determined by examining the knowledge resources that they drew upon when reasoning about proportional and nonproportional situations. Semi-structured interviews were conducted with six preservice teachers to demonstrate the effectiveness of the interview structure. The case analysis indicated the preservice teachers’ attention to the various fine-grained knowledge resources. However, they mostly drew upon the qualitative relationships, cross-multiplication, and across-multiplication. The preservice teachers’ over-attention to these three knowledge resources hindered their ability to distinguish proportional relationships from nonproportional relationships. Furthermore, the productivity of knowledge resources was easily influenced by the relationships presented in problems and participants’ past learning experiences. Implications of the application of the interview structure in teacher education programs and further research suggestions are discussed.



中文翻译:

确定职前数学教师胜任比例推理能力的面试结构的开发与应用

确定职前教师在比例推理中的能力是一项非常复杂的任务,而现有的研究方法并不能提供有效的工具来做到这一点。这项研究描述了访谈结构及其在确定职前教师按比例推理能力方面的应用。采访结构由深入追问认知冲突,并坐落在知识的-件认识论的观点。通过检查知识资源来确定职前教师的比例推理能力他们在对比例和非比例情况进行推理时所借鉴的东西。与六名职前教师进行了半结构式访谈,以证明访谈结构的有效性。案例分析表明,职前教师对各种细粒度知识资源的关注。但是,他们大多利用定性关系交叉乘法交叉乘法。职前教师对这三种知识资源的过度关注阻碍了他们区分比例关系和非比例关系的能力。此外,知识资源的生产力很容易受到问题和参与者过去学习经历之间的关系的影响。讨论了面试结构在教师教育计划中的应用意义以及进一步的研究建议。

更新日期:2021-05-27
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