组合数学和推理：表示、证明和构建同构是基于一组从一年级到高中及以后的学习者的成就，他们专注于一组组合数学任务。通过对这些学生的研究，编辑们深入了解了证明构建的基础、建立联系所需的工具和环境、扩展和推广组合学习的活动，甚至探索了这种学习在本科水平上的意义。
这本书强调了在建立论点时注意基本思想的力量；它表明了为学习者群体共同构建知识提供机会的重要性；它还展示了精心构建适当任务的价值。此外，它还记录了以证据形式进行的推理是如何与幼儿一起发展的，并讨论了支持学生推理的条件。
Combinatorics and Reasoning: Representing, Justifying and Building Isomorphisms
Combinatorics and Reasoning: Representing, Justifying and Building Isomorphisms is based on the accomplishments of a cohort group of learners from first grade through high school and beyond, concentrating on their work on a set of combinatorics tasks. By studying these students, the Editors gain insight into the foundations of proof building, the tools and environments necessary to make connections, activities to extend and generalize combinatoric learning, and even explore implications of this learning on the undergraduate level.
This volume underscores the power of attending to basic ideas in building arguments; it shows the importance of providing opportunities for the co-construction of knowledge by groups of learners; and it demonstrates the value of careful construction of appropriate tasks. Moreover, it documents how reasoning that takes the form of proof evolves with young children and discusses the conditions for supporting student reasoning.
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