Conjecturing via reconceived classical analogy

Abstract

Analogical reasoning is believed to be an efficient means of problem solving and construction of knowledge during the search for and the analysis of new mathematical objects. However, there is growing concern that despite everyday usage, learners are unable to transfer analogical reasoning to learning situations. This study aims at facilitating analogy use for conjecturing in discourse-rich mathematics classrooms. We reconceptualized one of the traditional perspectives on analogical reasoning, called classical analogy, as a more dynamic one by providing learners with the opportunity to choose a target object and its property. While shifting attention to particular aspects of mathematical activity, we observed and analyzed how students became aware of hidden relational similarities and utilized them while weakening others to make conjectures. The detailed analysis of the constructs and processes of several similarity-making and conjecturing activities supports the significance of reconceived classical analogy use in mathematics classrooms.

How can Students Generalize the Chain Rule? The Roles of Abduction in Mathematical Modeling

“…For example, students directly applied "relationship between area and length of edge" and "differentiation rules of a polynomial" to a given problem situation (Episode 1). Although analogy is known to play a key role in knowledge construction, as Lee and Sriraman (2011) have emphasized, the students could not use analogy productively at the beginning of their inquiries. The students' uses of diagrammatic reasoning were also in the form of directly applying conventional rules to diagrams.…”

Penalaran Analogi Siswa SMA dalam Pengajuan Masalah Setelah Solusi

“…Penalaran analogi bergantung pada pengetahuan atau masalah yang sudah dipelajari sebelumnya (English, 2004). Penalaran analogi didefinisikan sebagai kemampuan mengamati, dan menemukan kemiripan antar struktur (Lee dan Sriraman, 2011), serta merujuk pada keterampilan kognitif yang menjadi dasar proses mempersepsikan kemiripan struktur antar masalah (Richland, 2016). Inti dari penalaran analogi adalah menemukan masalah sumber yang mirip dengan masalah target dan memetakan solusi dari masalah sumber ke masalah target (Lee, 1992).…”

Penguasaan Penalaran Analogi Dalam Pemecahan Masalah Unsur-Unsur Dan Luas Kubus

“…Karena, penalaran analogi dipergunakan dalam menilai kebenaran suatu argumen matematika (Shadic, 2004) dan mempermudah proses pemecahan masalah matematika (Lee & Sriraman, 2011); (Yıldırım & Ersözlü, 2013); (Bikić & Pikula, 2016); (Kristayulika, et al, 2018). Dalam proses pemecahan masalah matematika, analogi digunakan dalam menemukan atau menciptakan solusi masalah sulituntuk pembentukan penguasaan konsep baru dalam matematika (Sriraman & English, 2005).…”