For teachers to provide students with meaningful instruction in area measurement, teachers need robust understandings of area. Here, I describe two cycles of a "lesson experiment" used to investigate prospective teachers' understandings of area units in an undergraduate mathematics class. For each cycle, I collected and analyzed the…

A mental model is a concept that exists in students' minds and is used to describe and explain a phenomenon. This study aims to describe the transition-attempting mental model of students in understanding the concept of integers. This study uses a qualitative approach and the type of research conducted is descriptive. The subjects of this study…

This article presents a networking of two theories, the Extended Theory of Mathematical Connections (ETC) and the Onto-semiotic Approach (OSA). In particular, concordances and complementarities are identified in the respective conceptions of mathematical connections, as a result of applying these theoretical frameworks to a student's response…

Although there has been intense criticism of NAPLAN in educational policy debates in Australia, little scholarly efforts have been made to understand the underlying cognitive mechanisms that contribute to the public narrative about the national testing program. We aim to provide tentative evidence about the way public perceptions about NAPLAN may…

Self-regulated learning (SRL) has been linked to improved learning and corresponding learning outcomes. However, there is a need for more precise insights into how SRL during learning contributes to specific learning outcomes. We operationalised four learning outcomes that varied on two dimensions: structure/connectedness and level/deepness of…

Object-oriented programming distinguishes between instance attributes and methods and class attributes and methods, annotated by the "static" modifier. Novices encounter difficulty understanding the means and implications of "static" attributes and methods. The paper has two outcomes: (a) a detailed classification of aspects of…

Intuitive conceptions based on cognitive biases (teleology, anthropomorphism, and essentialism) often prove helpful in everyday life while simultaneously being problematic in scientific contexts. Nonetheless, students often have intuitive conceptions of scientific topics such as evolution. As potential approaches to enable students to…

Research Findings: The present study analyzes whether child factors are linked to variations in teacher cognitive activation (CA) among individual children in math-related activities within Chinese kindergarten classrooms. The findings show that teachers tend to provide direct CA with high concreteness and that child engagement with tasks is…

Even after research-based instruction, students who demonstrate the ability to assemble relevant conceptual knowledge on one physics question may have difficulty assembling that same knowledge on a closely related problem. Recent research has suggested that reflexive, bottom-up reasoning processes seemingly unrelated to the physics concepts…

In cognitive load theory, the superiority of the Example-Problem sequence over the Problem-Example sequence has become a classic paradigm. The comparative effectiveness of these sequences, however, is subject to the influence of the factors of element interactivity and prior knowledge, and studies have examined these influences focused mostly on…

The purpose of this article is to share how one teacher implemented exploratory writing within a mathematics lesson to support her third graders in making sense of fractions and communicating their mathematical ideas. The author defines exploratory writing, then describes the teacher's lesson while also presenting a general overview about how to…

Numerical thinking is needed to recognize, interpret, determine patterns, and solve problems that contain the context of life. Self-efficacy is one aspect that supports the numerical thinking process. This study aims to obtain a numerical thinking profile of Mathematics pre-service teachers based on self-efficacy. This study used descriptive…

The overall purpose of this study was to investigate the role of personal relevance in conceptual change. First, we used an experimental design to investigate the role of augmented activation--which directly implicated teachers' personal prior beliefs about mathematics learning and instruction--and refutational text manipulations on short and…

Literature suggests that students need to be exposed to cognitively demanding tasks (CDT). In this qualitative study, we examined in-service secondary school teachers' challenges in understanding (e.g. recognizing, solving, and designing) and implementing cognitively demanding tasks in mathematics classrooms. Purposive sampling consisted of eleven…

Repeated study typically improves episodic memory performance. Two different types of explanations of this phenomenon have been put forward: (1) reactivating the same representations strengthens and stabilizes memories, or (2) greater encoding variability benefits memory by promoting richer traces. The present experiment directly compared these…