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The dimensions of prospective elementary and middle school teachers’ problem posing for integer addition and subtraction
Journal of Mathematics Teacher Education ( IF 2.1 ) Pub Date : 2020-09-04 , DOI: 10.1007/s10857-020-09477-x
Nicole M. Wessman-Enzinger , Jennifer M. Tobias

Elementary and middle school prospective teachers participated in semi-structured problem posing for integer addition and subtraction. The prospective teachers (n = 98) posed a variety of different stories, but this paper focuses on the temperature stories they posed. Results include descriptions of their posed temperature stories through the lens of the various dimensions (i.e., problem types, realism, consistency, correctness). Prospective teachers posed mainly state-translation-state problem types and rarely posed state-state-distance, state-state-translation, or translation-translation-translation problem types. They often changed the structure of their number sentences. Although they posed mostly realistic and mathematically correct temperature stories, the stories compromised realism or consistency in order to use state-translation-state problem types. Coordinating of the various dimensions (e.g., problem types, consistency) when problem posing requires flexibility with problem types. This work highlights the complexity of posing temperature stories, and coordinating the various dimensions highlights the need for prospective teachers to experience problem posing. Implications for problem posing with integers and temperature are extended to all contexts that inherently support translation and relativity. In the discussion, we coordinate the different problem types with various number sentences and dimensions. Unpacking the various dimensions illuminates prospective teachers’ thinking and offers a way of considering integers and contexts.



中文翻译:

整数加减法构成中小学教师预期问题的维度

中小学的准教师参加了半结构化问题的整数加减运算。准教师(n = 98)提出了各种不同的故事,但本文着重于他们提出的温度故事。结果包括通过各个维度(即问题类型,现实性,一致性,正确性)的镜头描述它们所构成的温度故事。准教师主要提出状态-翻译-状态问题类型,很少提出状态-状态-距离,状态-状态-翻译或翻译-翻译-翻译问题类型。他们经常改变数字句子的结构。尽管它们构成了大多数逼真的且数学上正确的温度故事,但这些故事为了使用状态转换状态问题类型而损害了真实性或一致性。当提出问题时需要协调各种维度(例如,问题类型,一致性),以灵活解决问题类型。这项工作凸显了摆出温度故事的复杂性,协调各个方面凸显了准教师体验问题摆姿势的必要性。有关整数和温度构成问题的含义已扩展到所有固有支持平移和相对性的上下文。在讨论中,我们通过不同的数字句子和维度来协调不同的问题类型。拆开各个维度可以阐明潜在教师的思维,并提供一种考虑整数和上下文的方法。有关整数和温度构成问题的含义已扩展到所有固有支持平移和相对性的上下文。在讨论中,我们通过不同的数字句子和维度来协调不同的问题类型。拆开各个维度可以阐明潜在教师的思维,并提供一种考虑整数和上下文的方法。有关整数和温度构成问题的含义已扩展到所有固有支持平移和相对性的上下文。在讨论中,我们通过不同的数字句子和维度来协调不同的问题类型。拆开各个维度可以阐明潜在教师的思维,并提供一种考虑整数和上下文的方法。

更新日期:2020-09-04
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