Background/purpose: This study investigates the effectiveness of Problem-Based Learning (PBL) integrated with scaffolding in enhancing problem-solving skills among students with varying levels of prior knowledge. The main objective is to determine how scaffolding, when combined with PBL, can support students in developing stronger problem-solving…

New perspectives on executive functions propose a greater involvement of context. These perspectives have implications for research in mathematical cognition. We tackle the problem that although individuals clearly exercise inhibitory control in mathematical contexts, researchers find that the relations between inhibitory control and mathematics…

Task design is an important element of effective mathematics teaching and learning. Past research in mathematics education has investigated task design in mathematics education from different perspectives (e.g., cognitive and cultural) and offered a number of (theoretical) frameworks and sets of principles. In this study, through a narrative…

The degree of element interactivity determines the complexity and therefore the intrinsic cognitive load of linear equations. The unpacking of linear equations at the level of operational and relational lines allows the classification of linear equations in a hierarchical level of complexity. Mapping similar operational and relational lines across…

This study investigated the attributes of 297 instances of student mathematical thinking during whole-class interactions that were identified as having the potential to foster learners' understanding of important mathematical ideas (MOSTs). Attributes included the form of the thinking (e.g., question vs. declarative statement), whether the…

We synthesize ideas from the foregoing articles in this special issue and from the broader literature on transfer to explore several themes. In many ordinary life circumstances, transfer proceeds easily, but formal learning often shows much less transfer than educators would like, making failure to transfer a focus of investigation. Transfer, like…

I investigate how and whether a heterogeneous group of first-year university mathematics students in South Africa harness the potential power of a computer algebra system (CAS) when doing a specific mathematics task. In order to do this, I develop a framework for deconstructing a mathematics task requiring the use of CAS, into its primary…

One fifth grade student, Martha, was encouraged to develop her informal ratio and proportion strategies during a 6-month teaching experiment. The challenges Martha faced during the teaching experiment are described. The current study supports the claim made by Kaput and West (1994) that initial instruction on ratio and proportion based on…

Many researchers agree that children's difficulty with fraction and rational numbers is associated with their whole number knowledge, but they disagree on the origin of the whole number bias. This article reviews three explanations of the nature of the bias. These accounts diverge on the questions of whether or not early quantitative…

Various researchers have associated meaningful problem solving with methods guided directly by a conceptual knowledge base. By contast, a meaningless solving course, or sequence of operations, is essentially independent of the solver's conceptual understanding of the problem under consideration. This paper is the first to document a meaningless,…

The two purposes of this study were: (1) to determine the extent to which previous knowledge, on-going motivation and current social support influence performance in a college introductory statistics courses; and (2) to identify the thought processes used in statistics learning by students who preform well and perform well and poorly,…

The 7th International Conference on Education Data Mining held on July 4th-7th, 2014, at the Institute of Education, London, UK is the leading international forum for high-quality research that mines large data sets in order to answer educational research questions that shed light on the learning process. These data sets may come from the traces…

This is a record of the proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia (MERGA). The theme of the conference is "Mathematics: Essential research, essential practice." The theme draws attention to the importance of developing and maintaining links between research and practice and…