数学应用题解决表征研究中变量选择的现状与分析

数学应用题解决是当前知识丰富领域问题解决研究的热点,问题表征是应用题解决起始阶段的核心环节,本文从实验心理学的三个基本研究要素出发,举例分析并讨论了数学应用题解决的表征研究中变量选取的特点、不足及趋势。     

How do students coordinate context-based information and elements of their own knowledge? An analysis of students’ context-based problem-solving in thermodynamics

ABSTRACT

In science education, context-based learning is mostly based on problem-oriented tasks [Gilbert, J. K. (2006). On the nature of “context” in chemical education. International Journal of Science Education, 28(9), 957–976]. Therefore, a relevant question is, how do students integrate the information given in the task into their problem-solving process? The basic assumption is that there is a transition from the situation described in the task to a science model needed to solve the problem [Mestre, J. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. Journal of Applied Developmental Psychology, 23(1), 9–50]. The transition needs to be described by parameters of the situation, the science model and the transition process itself. This investigation focuses on the influence of these three elements on the problem-solving process to understand variations in performance [Bennett, J., Lubben, F., & Hogarth, S. (2007). Bringing science to life: A synthesis of the research evidence on the effects of context-based and STS approaches to science teaching. Science Education, 91(3), 347–370]) and the interaction with interest. Despite the large body of research on the mutual influence of context-based problem-solving and interest, research attempting to examine their interplay regarding performance is still lacking. We conducted a hierarchical regression analysis with 178 participants from German high-track schools to investigate three parameters with regard to their influence on affective variables and successful problem-solving: contextualisation of the situation described in the task; the complexity of the scientific model underlying the task; and transparency, which assesses whether and how the learner can identify this model [Löffler, P., & Kauertz, A. (2015). Modellanwendung in kontextualisierten Problemlöseaufgaben [Applying models in contextualised problem solving tasks]. In S. Bernholt (Ed.), Heterogenität und Diversität - Vielfalt der Voraussetzungen im naturwissenschaftlichen Unterricht (Vol. 35, pp. 648–650). Kiel: IPN; Durik, A., & Harackiewicz, J. (2007). Different strokes for different folks: How individual interest moderates the effects of situational factors on task interest. Journal of Educational Psychology, 99(3), 597–610)]. Our findings suggest that these parameters have different effects on how interest is triggered and maintained. Aspects of transparency exhibit small effects on successful problem-solving processes. The results support the assumption that the transition process is the main aspect of context-based problem-solving and can therefore be operationalised as the use of elements of the scientific model in students’ statements. Surprisingly, the usage of such elements cannot be sufficiently explained by pre-knowledge or cognitive abilities.     

探讨高考中涉及二项式定理的试题的解法

针对高考涉及二项式定理的试题题型介绍了四种解题方法.