教师根据中学代数教学中呈现的实例所做的数学工作

Carolina Henríquez-Rivas, Paula Verdugo-Hernández
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摘要

与学校代数教学相关的国际考试结果和科学证据都表明,有必要对课堂数学实践进行分析。在此背景下,我们制定了研究目标,即根据教师在中学代数领域内的专题教学中实施的实例,分析教师所偏爱的数学工作的特点。为此,本研究采用了工具性集体案例研究方法,将其置于解释性范式之中。研究设计选取了智利学校数学教师的两个代表性案例,目的是根据他们提供的实例,了解和描述他们在中学课堂上的数学工作。结果表明,第一位教师利用各种实例激活了不同形式的数学思维,促进了工具性和话语性创生的激活。相比之下,第二位教师采用了更为传统的方法,利用实例进行说明和激励,直接呈现知识,主要激活符号生成,其中缺乏数字和代数之间的过渡。最终,研究结果强调了在代数教学中深入考虑实例选择的重要性,以及这些实例如何影响学生的学习。此外,我们还为这一研究方向未来的工作提出了更多与在课堂上使用示例相关的想法。
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Teachers’ mathematical work based on examples presented in the teaching of algebra in secondary education
Both international examination results and scientific evidence related to the teaching and learning of school algebra point to the necessity for analyzing mathematical practice in the classroom. In this context, we have formulated the research objective of characterizing the mathematical work that teachers favor based on the examples that they implement in the teaching of topics within the domain of secondary school algebra. To this end, this study is situated within the interpretive paradigm utilizing an instrumental collective case study approach. The study design entails the selection of two representative cases of mathematics teachers in Chilean schools, with the objective of understanding and describing their mathematical work in the secondary school classroom based on the examples they present. The results show that the first teacher utilizes varied examples that activate distinct forms of mathematical thinking, promoting the activation of both instrumental and discursive genesis. In contrast, the second teacher follows a more traditional approach, with the use of examples to illustrate and motivate, and a direct presentation of knowledge, activating primarily semiotic genesis, in which a transition between the numerical and the algebraic is lacking. Ultimately, the results highlight the importance of deeper consideration of the choice of examples in the teaching of algebra and how these examples can influence students’ learning. Furthermore, additional ideas are put forward for future work in this line of research associated with the use of examples in the classroom.
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