Generalization and Justification: The Challenge of Introducing Algebraic Reasoning Through Patterning Activities
Generalization and Justification: The Challenge of Introducing Algebraic Reasoning Through Patterning Activities
复制标题
泛化和论证：通过模式化活动引入代数推理的挑战
DOI：
10.1207/s15327833mtl0703_3
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发表时间：
2005
影响因子：
1.6
通讯作者：
J. Lannin
中科院分区：
文献类型：
--
作者：
J. Lannin
期望学生被介绍给代数思想在较早的年级水平的地方增加了课堂教师的负担，以帮助学生构建和证明概括。本研究提供了深入了解25个六年级学生的推理，因为他们接近模式化的任务，他们被要求开发和证明概括，同时使用计算机电子表格作为教学工具。学生们展示了这些活动的潜力和陷阱。在全班讨论中，学生通常能够提供适当的概括，并使用通用的例子来证明。使用几何方案的学生在提供一般性论点和有效的理由方面更成功。然而，在小组讨论中，学生们很少证明他们的概括是正确的，有些学生更关注特定的价值观，而不是一般的关系。建议将各种学生策略和理由带到课堂讨论的最前沿，以便学生可以检查学生通常介绍的各种策略和理由的数学能力和有效性。
The expectation that students be introduced to algebraic ideas at earlier grade levels places an increased burden on the classroom teacher to help students construct and justify generalizations. This study provides insight into the reasoning of 25 sixth-grade students as they approached patterning tasks in which they were required to develop and justify generalizations while using computer spreadsheets as an instructional tool. The students demonstrated both the potential and pitfalls of such activities. During whole-class discussions, students were generally able to provide appropriate generalizations and justify using generic examples. Students who used geometric schemes were more successful in providing general arguments and valid justifications. However, during small-group discussions, the students rarely justified their generalizations, with some students focusing more on particular values than on general relations. It is recommended that the various student strategies and justifications be brought to the forefront of classroom discussions so that students can examine the mathematical power and validity of the various strategies and justifications typically introduced by students.