The Effect of Two Approaches Creative Reasoning and Algorithmic Reasoning in Learning
Subject Areas : Educational ScienceZohreh Rashidiyan 1 , Majid Haghverdi 2
1 - Educational Department, Arak Branch, Islamic Azad University, Arak, Iran
2 - گروه ریاضی و آمار، واحد اراک ، دانشگاه آزاد اسلامی واحد ، اراک، ایران
Keywords: : Mathematical Reasoning, Creative Reasoning, Algorithmic Reasoning, Rote Learning, ,
Abstract :
Drawing upon the theoretical framework of Lithner (2008), this study investigates the impact of two different reasoning approaches on mathematics learning: Algorithmic Reasoning (AR) and Creative Mathematically-founded Reasoning (CMR). Lithner's framework explains the origins and consequences of different types of reasoning by connecting them to thought processes, student capabilities, and the learning environment.[2] The primary objective of this research is to examine the hypothesis that mathematics learning can be more efficient and sustainable when students utilize creative reasoning, as opposed to solely using algorithmic reasoning where they are only provided with predetermined solution procedures. In this experimental study, 91 ninth-grade students were divided into two groups: the AR group (n=48), which was taught using predetermined formulas, and the CMR group (n=43), where students discovered and generated solutions without direct guidance. The tasks in the present study were based on a methodology previously developed and used by Boesen, Lithner, and Palm (2010) and Palm et al. (2011). The results of this study indicated that although the AR group performed better during the practice session (p < .0001, r=0.77), the CMR group was significantly superior in the test administered one week later (p = .001, d = 0.7). A correlational analysis revealed a strong relationship between practice and test performance for the CMR group (r = .81, p < .0001), while this correlation was not significant for the AR group.
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