Promoting middle school students’ proportional reasoning skills through an ongoing professional development programme for teachers

Abstract

Promoting students' proportional reasoning skills through an ongoing professional development programme for teachers Proportional reasoning is mathematical reasoning involving a sense of co-variation and the ability to make multiple comparisons in relative terms (Fielding-Wells, Dole, & Makar, 2014; Lesh, Post, & Behr, 1988). The skills needed for proportional reasoning include multiplicative and relational thinking; a highly developed understanding of foundational concepts, including fractions, decimals, multiplication, and division; and scale (Boyer & Levine, 2012; Lamon 2005; Lo & Watanabe, 1997). Multiplicative thinking contrasts with additive thinking, which involves considering sums or differences between quantities (Bright, Joyner, & Wallis, 2003). Research suggests that proportional reasoning skills do not develop naturally (Sowder et al., 1998) and many students tend to use additive thinking, find it difficult to distinguish situations of proportion from those of non-proportion, or over-rely on multiplicative thinking in situations where it is inappropriate (Van Dooren, De Bock, Hessels, Janssens, & Verschaffel, 2005). Proportional reasoning has been described as the cornerstone of many higher-level mathematics topics, including algebra, and the capstone of elementary school topics, such as number and measurement (Lesh et al., 1988). It is essential in many subjects beyond mathematics, including science, economics, and geography (Akatugba & Wallace 2009; Boyer, Levine, & Huttenlocher, 2008; Howe, Nunes, & Bryant, 2011); is one of the most commonly used applications of mathematics in everyday life; and is essential in many professions, for example, architecture, nursing, and pharmacy. Ahl, Moore, and Dixon (1992) described proportional reasoning as a "pervasive activity that transcends topical barriers in adult life" (p.

Semiotic Conflicts in the Learning of Proportionality: Analysis of a Teaching Experience in Primary Education

“…Developing proportional reasoning since its beginning in primary education and its continuity in secondary education has been the subject of intense attention by mathematics education researchers (Fernández & Llinares, 2012;Fielding-Wells, Dole & Makar, 2014;Hilton, Hilton, Dole & Goos, 2016;Karplus, Pulos & Stage, 1983;Lamon, 2007;Lesh, Post & Behr, 1988;Modestou & Gagatsis, 2010;Sánchez, 2013). Authors agree with the idea that proportional reasoning implies mathematical knowledge to solve specific types of problems, involving both the understanding of mathematical objects at stake and the justification of the properties and procedures required.…”

Kinds of Mathematical Reasoning Addressed in Empirical Research in Mathematics Education: A Systematic Review

“…Proportional reasoning also involves co-variation in a sense that the students have to be able to make comparisons between different entities. The students need to acquire multiple skills, including relational thinking, to be able to reason proportionally [54].…”

Model Penilaian Kemampuan Penalaran Proporsional pada Mahasiswa Calon Guru Anak Usia 6-7 Tahun

“…Penelitian yang dilakukan oleh Annette, Geoff, Shelley dan Merrylyn dengan judul Promoting middle school students proportional reasoning skills through an ongoing professional development programme for teachers menjelaskan bahwa penalaran proporsional dalam hal menggunakan rasio dalam situasi yang melibatkan perbandingan jumlah sangat penting untuk kompetensi matematika, terutama di tahun sekolah menengah dan merupakan penentu penting keberhasilan di luar sekolah. Penalaran proporsional tidak selalu berkembang secara alami, namun dari beberapa penelitian menunjukkan bahwa dengan pengajaran yang ditargetkan, kemampuan penalaran proporsional dapat dikembangkan (Hilton, Hilton, Dole, & Hilton, 2016).…”