Fraction mapping and fraction comparison skills among grade 4 Chinese students: An error analysis

Abstract

Background: Mapping fraction symbols to magnitudes is easier for students to master than comparing fraction magnitudes. Fraction mapping assesses students' understanding of part-whole interpretations of fractions; fractions represent the parts of an object or set of objects. Fraction comparison assesses students' understanding of measurement interpretations of fractions; a fraction is a single numerical quantity, not a combination of two whole numbers. Aim: To examine and compare the types of errors made by emergent fraction learners on fraction mapping and comparison tasks. Sample: Grade 4 Chinese students (N = 1036; 577 boys; M age = 9.9 years). Method: We examined performance and identified errors on fraction mapping and comparison tasks. For mapping, students converted pictorial representations into fraction notation. For comparison, they chose the larger of two symbolic fractions. Results: Consistent with curriculum expectations, most students successfully mapped pictorial representations to fraction notation. In contrast, few students were able to accurately compare fraction magnitudes. Within each task, students' errors were consistent across trials, suggesting that they applied systematic but incorrect procedures. However, errors were not consistent between tasks and the correlation between mapping and comparison performance was weak. Conclusion: Emergent fraction learners can acquire part-whole knowledge of fractions without acquiring

Beyond linearity: Using IRT‐scaled level models to describe the relation between prior proportional reasoning skills and fraction learning outcomes

“…These approaches are promising to illustrate the rationale behind the arithmetic fraction operations such as addition and subtraction, multiplication and division, but also expanding and reducing fractions. Not only established models of fraction knowledge and skills (e.g., Behr et al, 1983) build on this perspective but also research focusing on the role of concrete models and manipulatives for fraction learning (Carbonneau et al, 2013; Cramer & Wyberg, 2009; Di Lonardo Burr et al, 2022; Fyfe et al, 2014; Jiang et al, 2021; Mix & Paik, 2008).…”

Epistemisk pendling mellan del och helhet i historieundervisning

“…Forskning om del och helhet i ett kunskapsinnehåll är mångfacetterad (jfr. Park et al, 2012;Di Lonardo Burr et al, 2022;Gadamer, 1989). Epistemologiskt handlar det, som redan nämnts i inledningen, om hur kunskap kan förstås och organiseras (VanSledright & Reddy, 2014).…”

“…Även inom naturvetenskapliga ämnen, matematik och språk har del och helhet undersökts som didaktiska modeller i relation till undervisning. Bland annat inom matematikundervisningen har det undersökts hur del och helhet kan underlätta elevers förståelse av matematiska processer (Marton & Booth, 1997;Cheng, 2012;Di Lonardo Burr et al, 2022). Inom läsundervisning har del och helhet också använts som didaktisk modell för att främja elevers läsförståelse (Cunningham, 1993).…”