Evolving Communities of Mind-In Which Development Involves Several Interacting and Simultaneously Developing Strands
Evolving Communities of Mind-In Which Development Involves Several Interacting and Simultaneously Developing Strands
复制标题
不断发展的心灵社区——其中的发展涉及多个相互作用和同时发展的分支
DOI：
10.1207/s15327833mtl0602_7
复制
发表时间：
2004
影响因子：
1.6
通讯作者：
Caroline Yoon
中科院分区：
文献类型：
--
作者：
R. Lesh;Caroline Yoon
如果课程开发者的目标是创建一个单一的线性任务序列，从而导致一些重要数学概念的发展，那么一些研究人员建议，这些序列应该遵循类似于皮亚杰式相关概念研究中已确定的发展阶段的进展。这些基于研究的序列被称为学习轨迹。其他研究人员强调，概念发展可能涉及使用各种代表性媒体表达的想法之间的相互作用，并且可以沿着各种“维度”发生，例如具体-抽象、简单-复杂或情境-去情境化。因此，不同的路径可能适合不同的学生，而尝试沿着任何单一的发展路径集中发展可能对某些学生来说是不合适的。这些研究人员经常将轨迹设想为描绘可能性空间的分支树图中的特定路径。本文强调第三种情况，称为模型引发活动（Lesh、Hoover、Hole、Kelly 和 Post，2000）。它们是解决问题的情况，其中目标包括开发更强大的结构或概念系统。因此，显着的概念发展之所以发生，是因为学生面临着反复表达、测试和修改自己当前思维方式的挑战，而不是因为他们被引导沿着狭窄的概念路径走向老师的思维方式（理想化版本）。也就是说，发展看起来不太像沿着一条路径的进步，而更像是一棵倒置的基因遗传树，其中曾孙从同时且交互发展的多个谱系中追踪其进化。
If a curriculum developer's goal is to create a single linear sequence of tasks that lead to the development of some important mathematical concept, then some researchers have suggested that these sequences should follow progressions similar to stages of development that have been identified in Piaget-like research on the relevant concept(s). These research-based sequences are referred to as learning trajectories. Other researchers emphasize that conceptual development can involve interactions among ideas expressed using a variety of representational media and can occur along a variety of "dimensions" such as concrete-abstract, simple-complex, or situated-decontextualized. Therefore, different paths can be appropriate for different students, and trying to funnel development along any single developmental path can be inappropriate for some students. These researchers often envision trajectories to be specific paths within a branching tree diagram that portrays the space of possibilities. This article emphasizes a third type of situation called model-eliciting activities (Lesh, Hoover, Hole, Kelly, & Post, 2000). They are problem-solving situations in which goals include developing more powerful constructs or conceptual systems. Therefore, significant conceptual developments occur because students are challenged to repeatedly express, test, and revise their own current ways thinking-not because they were guided along a narrow conceptual path toward (idealized versions of) their teacher's ways of thinking. That is, development looks less like progress along a path, and it looks more like an inverted genetic inheritance tree in which great grandchildren trace their evolution from multiple lineages that develop simultaneously and interactively.