Adidactical problem-posing as captured by scripting journeys: Investigating sums of consecutive integers

IF 1 Q3 EDUCATION & EDUCATIONAL RESEARCH
Andrew Kercher , Canan Güneş , Rina Zazkis
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引用次数: 0

Abstract

Research has demonstrated that problem-posing and problem-solving mutually affect one another. However, the exact nature and full extent of this relationship requires detailed elaboration. This is especially true when problem-posing arises in order to facilitate problem-solving, such as during the investigation of an unfamiliar mathematical property or phenomenon. In this study, groups of participants used scripting to record their mathematical activity as they made conjectures and justified conclusions about sums of consecutive integers. We analyze the unprompted problem-posing found within these scripting journeys using three facets of a problem-posing framework: mathematical knowledge base, problem-posing heuristics, and individual considerations of aptness. Our analysis reveals how these aspects of problem-posing emerge within a mathematical investigation, how they are related to surrounding problem-solving, and the kinds of mathematical insights and realizations that act as catalysts to promote further problem-posing activity.

通过脚本旅程捕捉交互式问题:探究连续整数之和
研究表明,提出问题和解决问题是相互影响的。然而,这种关系的确切性质和充分程度还需要详细的阐述。当提出问题是为了促进问题的解决时,如在探究一个陌生的数学性质或现象时,情况尤其如此。在本研究中,各组参与者在对连续整数之和进行猜想并证明结论的合理性时,使用脚本记录他们的数学活动。我们使用问题提出框架的三个方面:数学知识基础、问题提出启发式方法和个人能力考量,对这些脚本旅程中发现的无提示问题提出进行了分析。我们的分析揭示了提出问题的这些方面是如何在数学探究中出现的,它们是如何与周围的问题解决相关联的,以及作为催化剂促进进一步提出问题活动的数学见解和认识的种类。
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来源期刊
Journal of Mathematical Behavior
Journal of Mathematical Behavior EDUCATION & EDUCATIONAL RESEARCH-
CiteScore
2.70
自引率
17.60%
发文量
69
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.
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