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The development of relational thinking: a study of Measure Up first-grade students’ thinking and their symbolic understandings
Educational Studies in Mathematics ( IF 3.4 ) Pub Date : 2021-01-04 , DOI: 10.1007/s10649-020-10014-z
Linda C. H. Venenciano , Seanyelle L. Yagi , Fay K. Zenigami

This study is focused on the relational thinking of first-grade students following their first 3 months of instruction from the Measure Up (MU) curriculum, an adaptation of the El’konin-Davydov curriculum. Following Davydov’s outline of instructional material, the MU first-grade materials were designed to have students identify the quantitative attributes of objects, learn to designate the properties using certain symbols, and carry out elementary analyses of the relationships. Additionally, MU emphasized the use of specific, multiple concurrent representations so students could use concrete, diagrammatic, and symbolic ways to analyze comparisons and convey their findings. Our research focused on the characteristics of MU first-grade students’ thinking about relations without numbers. Additionally, we were interested in the role symbols had in their ability to communicate their thinking. We analyzed video recordings and transcriptions of six semi-structured student interviews and then reanalyzed the data for specific evidence of symbolic understandings. Recognizing MU as a symbolically structured environment, we connected our data to this paradigm. Our findings show that students were able to make direct and indirect comparisons and that they relied on symbolizing to explain their thinking. These results show further support for Davydov’s hypothesis––a non-numeric introduction to relational symbols can develop children’s theoretical thinking abilities by going beyond empirical ways of knowing.

中文翻译:

关系思维的发展:Measure Up 一年级学生思维及其符号理解的研究

这项研究的重点是一年级学生在接受 Measure Up (MU) 课程(改编自 El'konin-Davydov 课程)的前 3 个月教学后的关系思维。按照达维多夫的教材大纲,MU一年级教材旨在让学生识别物体的数量属性,学习使用某些符号来指定属性,并进行关系的基本分析。此外,MU 强调使用特定的、多重并发表示,以便学生可以使用具体的、图解的和象征性的方式来分析比较并传达他们的发现。我们的研究侧重于MU一年级学生对没有数字的关系的思考特征。此外,我们对符号在传达其思想的能力中所扮演的角色很感兴趣。我们分析了六个半结构化学生访谈的视频记录和转录,然后重新分析数据以获得象征性理解的具体证据。将 MU 视为符号结构化环境,我们将数据连接到这种范式。我们的研究结果表明,学生能够进行直接和间接比较,并且他们依靠象征来解释他们的想法。这些结果进一步支持了达维多夫的假设——对关系符号的非数字介绍可以通过超越经验的认识方式来发展儿童的理论思维能力。我们分析了六个半结构化学生访谈的视频记录和转录,然后重新分析数据以获得象征性理解的具体证据。将 MU 视为符号结构化环境,我们将数据连接到这种范式。我们的研究结果表明,学生能够进行直接和间接比较,并且他们依靠象征来解释他们的想法。这些结果进一步支持了达维多夫的假设——对关系符号的非数字介绍可以通过超越经验的认识方式来发展儿童的理论思维能力。我们分析了六个半结构化学生访谈的视频记录和转录,然后重新分析数据以获得象征性理解的具体证据。将 MU 视为符号结构化环境,我们将数据连接到这种范式。我们的研究结果表明,学生能够进行直接和间接比较,并且他们依靠象征来解释他们的想法。这些结果进一步支持了达维多夫的假设——对关系符号的非数字介绍可以通过超越经验的认识方式来发展儿童的理论思维能力。我们的研究结果表明,学生能够进行直接和间接比较,并且他们依靠象征来解释他们的想法。这些结果进一步支持了达维多夫的假设——对关系符号的非数字介绍可以通过超越经验的认识方式来发展儿童的理论思维能力。我们的研究结果表明,学生能够进行直接和间接比较,并且他们依靠象征来解释他们的想法。这些结果进一步支持了达维多夫的假设——对关系符号的非数字介绍可以通过超越经验的认识方式来发展儿童的理论思维能力。
更新日期:2021-01-04
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