Concreteness Fading Strategy: A Promising and Sustainable Instructional Model in Mathematics Classrooms

Abstract

Conceptual understanding has been emphasized in the national curriculum and principles and standards across nations as it is the key in mathematical learning. However, mathematics instruction in classrooms often relies on rote memorization of mathematical rules and formulae without conceptual connections. This study considers the concreteness fading instruction strategy—starting with physical activities with manipulatives and gradually fading concreteness to access abstract concepts and representations—as a promising and sustainable instructional model for supporting students in accessing conceptual understanding in mathematics classrooms. The results from the case study support the validity of the concreteness fading framework in providing specific instructional strategies in each phase of concept development. This study implies the development of sustainable teacher education and professional development by providing specific instructional strategies for conceptual understanding.

The Development of Sustainable Assessment during the COVID-19 Pandemic: The Case of the English Language Program in South Korea

“…Despite the successful adaptation to the new sustainable language assessment examined herein, additional research on equipping language instructors with tools and guidelines for alternative and sustainable language assessment could act to enhance their collective ability to align learning with assessment. In order words, it is important to provide language instructors with adequate training and afford them with appropriate professional development so that they can equip themselves with the skills needed to develop sustainable language assessment (c.f., Kim [41]; and Lee et al [42]). As previous research on online learning has pointed out, the high dropout rate and students' inconsistent engagement in learning has been of a concern to practitioners and administrators (Friedman and Friedman [43]; Lee, Choi and Kim [44]; and Park and Choi [45]).…”

Teachers’ Perspectives on Addressing Linguistic Factors Affecting Visualisation of Mathematics Word Problems

“…According to Klerkx et al (2014), there is a need for more research to be conducted on visualisation to improve mathematics problem solving. Echoing the same sentiment, Kim (2020) stresses the need for visualisation as one of the features of the new approach to teaching mathematics to be embraced as a promising and sustainable instructional model for supporting learners in terms of accessing conceptual understanding in mathematics classrooms. Ziemkiewicz et al (2012) as well recommend that more research on visualisation in mathematics teaching and problem solving should be conducted in order to identify which individual factors are relevant to visualisation with the motive to confirm the factors already found and to investigate new factors.…”

Student Development in Logical Reasoning: Results of an Intervention Guiding Students Through Different Modes of Visual and Formal Representation

“…Bruner's model has been translated into the Concrete Representational Abstract (CRA) instruction framework, commonly used in the USA (Butler et al, 2003), or the Concrete Pictorial Abstract (CPA) framework as adopted in, for example, Singapore (Kim, 2020). Although the description of the different modes in the CRA and CPA frameworks is similar to the stages in CF, we will use the terminology of CF because it explicitly focuses on consecutively establishing the links between the three stages.…”

“…Fyfe et al, 2015) and the fact that many textbooks in middle and higher secondary school do not address the sequence correctly (Witzel et al, 2008, p. 272), there are some studies that show positive effects of CF in comparison with other approaches within mathematics education at other levels (e.g. Kim, 2020;McNeil & Fyfe, 2012;Ottmar & Landy, 2017). The different stages of this model and the focus on successful transitions between the different stages guide the activities in our intervention.…”