Competence with rational numbers is essential for mathematics proficiency in secondary mathematics. However, many students struggle with rational number concepts, and students with mathematics difficulties struggle even more. The purpose of this study was to examine the effects of an intervention that incorporated the use of explicit instruction…

Digital learning games are designed to foster both student learning and enjoyment. Given this goal, an interesting research topic is whether game mechanics that promote learning and those that promote enjoyment have different effects on students' experience and learning performance. We explored these questions in "Decimal Point," a…

This study aimed to address the need for a comprehensive assessment tool to evaluate the mathematical abilities of first-grade students through cognitive diagnostic assessment (CDA). The primary challenge involved in this endeavor was to delineate the specific cognitive skills and sub-skills pertinent to first-grade mathematics (FG-M) and to…

Arithmetic problem solving is a crucial part of mathematics education. However, existing problem solving theories do not fully account for the semantic constraints partaking in the encoding and recoding of arithmetic word problems. In this respect, the limitations of the main existing models in the literature are discussed. We then introduce the…

The development of mathematical reasoning is a key proficiency for mathematics within the Australian Curriculum. However, reasoning can be difficult for teachers to assess, particularly with pen and paper tests. In this study, interview tasks were designed across three curriculum areas at three different levels to assess student reasoning through…

Algebraic Thinking Skills (ATS) are one of the skills that students need to master in order to solve nonroutine problems. These skills are also necessary as a foundation for students preparing to enter university studies and fields of work that require logical and analytical thinking. However, Malaysian students' performance in solving algebraic…

Investigators often rely on the proportion of correct responses in an assessment when describing the impact of early mathematics interventions on child outcomes. Here, we propose a shift in focus to the relative sophistication of problem-solving strategies and offer methodological guidance to researchers interested in working with strategies. We…

In this article we aim to deepen our understanding of the content and nature of the early childhood teacher's knowledge, focusing on those aspects which might promote students' algebraic thinking. Approaching arithmetic from the viewpoint of algebra as an advanced perspective and considering the analytical model "Mathematics Teachers'…

In learning, errors are ubiquitous and inevitable. As these errors may signal otherwise latent cognitive processes, tutors--and students alike--can greatly benefit from the information they provide. In this paper, we introduce and evaluate the Systematic Error Tracing (SET) model that identifies the possible causes of systematically observed…

Several factors seem important to understand the nature of mathematical learning. Byrnes and Miller combined these factors into the Opportunity-Propensity model. In this study the model was used to predict the number-processing factor and the arithmetic fluency in grade 4 (n = 195) and grade 5 (n = 213). Gender, intelligence and affect (positive…

Knowledge tracing algorithms are embedded in Intelligent Tutoring Systems (ITS) to keep track of students' learning process. While knowledge tracing models have been extensively studied in offline settings, very little work has explored their use in online settings. This is primarily because conducting experiments to evaluate and select knowledge…

Number line models provide a visual aid for students to examine the relationship of integers with each other and facilitate learning of integers and integer operations. Such models are typically used when students are asked real-life problems. This study employs a qualitative case study design to perform an in-depth analysis of how middle grade…

A central issue in the mathematics curriculum is that we want students to make connections. This issue has been analysed in a series of curricula and instruction design and analysis studies. Moving towards mathematics connections--and away from treating mathematics as a body of isolated concepts and procedures--is an important goal of mathematics…

The strategy choice model (SCM) is a highly influential theory of human problem-solving. One strength of this theory is the allowance for both item and person variance to contribute to problem-solving outcomes, but this central tenet of the model has not been empirically tested. Explanatory item response theory (EIRT) provides an ideal approach to…

Despite decades of research on the close link between eye movements and human cognitive processes, the exact nature of the link between eye movements and deliberative thinking in problem-solving remains unknown. Thus, this study explored the critical eye-movement indicators of deliberative thinking and investigated whether visual behaviors could…