专家型学生在处理数学中结构不严谨的问题时会获得哪些类型的洞察力？

IF 1 Q3 EDUCATION & EDUCATIONAL RESEARCH

Journal of Mathematical Behavior Pub Date : 2024-10-21 DOI:10.1016/j.jmathb.2024.101199

Eirin Stenberg , Per Haavold , Bharath Sriraman

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引用次数: 0

摘要

在我们的研究中，我们探讨了两名数学成绩优秀的学生是如何在处理结构混乱的问题时获得洞察力的。我们通过基于任务的访谈跟踪了他们的解题过程，并观察到这两名学生在解题过程中获得洞察力的相似顺序--(1) 自发洞察力，(2) 被动渐进洞察力，(3) 突发性洞察力，(4) 主动渐进洞察力。在第二次和第三次洞察之间出现了僵局，这似乎加快了解决问题的进程。在这一洞察过程中，我们观察到情绪的转变似乎对这一过程产生了有益的影响，特别是参与者将与僵局有关的不确定性解释为一种挑战和启发。未来的研究需要在更大的数据集和更广泛的问题解决者中研究观察到的洞察力序列和相关影响。

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What types of insight do expert students gain during work with ill-structured problems in mathematics?

In our study, we explored how two high-performing mathematics students gained insight while working on ill-structured problems. We followed their problem-solving process through task-based interviews and observed a similar sequence of insights in both participants’ work- (1) Spontaneous insight, (2) Passive gradual insight, (3) Sudden insight, and (4) Active gradual insight. An impasse occurred in the intersection between the second and third insight and seemed to accelerate the progression toward solution. During this insight sequence, we observed emotional transitions that appeared to impact the process in a useful manner, especially due to the participant’s interpretation of uncertainty related to the impasse as a challenge and an inspiration. Future research is needed to study the observed sequence of insights and related affects in a larger data set and in a broader spectrum of problem solvers.

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来源期刊

Journal of Mathematical Behavior EDUCATION & EDUCATIONAL RESEARCH-

CiteScore

2.70

自引率

17.60%

发文量

期刊介绍： The Journal of Mathematical Behavior solicits original research on the learning and teaching of mathematics. We are interested especially in basic research, research that aims to clarify, in detail and depth, how mathematical ideas develop in learners. Over three decades, our experience confirms a founding premise of this journal: that mathematical thinking, hence mathematics learning as a social enterprise, is special. It is special because mathematics is special, both logically and psychologically. Logically, through the way that mathematical ideas and methods have been built, refined and organized for centuries across a range of cultures; and psychologically, through the variety of ways people today, in many walks of life, make sense of mathematics, develop it, make it their own.