This conceptual paper discusses two frameworks, developed independently by the lead author, that will provide the conceptual foundation for the identification and evaluation of mental computation strategies students demonstrate during an upcoming research project entitled Mental Computation in Year 5. These frameworks will be used by the lead…

Abacus-based mental calculation (AMC) is a widely used educational tool for enhancing math learning, offering an accessible and cost-effective method for classroom implementation. Despite its universal appeal, the neurocognitive mechanisms that drive the efficacy of AMC training remain poorly understood. Notably, although abacus training relies…

In this article, we focus on the cognitive presence element of the Community of Inquiry (CoI) framework. Cognitive presence consists of four categories: Triggering Event, Exploration, Integration, and Resolution. These categories have been described as phases following an idealized logical sequence, although the phases should not be seen as…

Children with mathematical difficulties need to spend more time than typically achieving children on solving even simple equations. Since these tasks already require a larger share of their cognitive resources, additional demands imposed by the need to switch between tasks may lead to a greater decline of performance in children with mathematical…

Understanding students' behavior while solving tasks at various levels is essential for the support educators may provide to students. The current study reports on a large-scale exploration of students' activity in an online learning environment for mathematics, while comparing between lower-order thinking (LOT) and higher-order thinking (HOT)…

Algebraic thinking and strategy flexibility are essential to advanced mathematical thinking. Early algebra instruction uses 'missing-operand' problems (e.g., x - 7 = 2) solvable via two typical strategies: (1) direct retrieval of arithmetic facts (e.g., 9 - 7 = 2) and (2) performance of the inverse operation (e.g., 2 + 7 = 9). The current study…

Much of the research on the development of professional noticing expertise has focused on prospective teachers. We contend that we must investigate practicing teachers as well, and in particular practicing secondary teachers, because they bring with them years of teaching experience and are situated in unique contexts. Hence we studied the…

Depletion of limited working memory resources may occur following extensive mental effort resulting in decreased performance compared to conditions requiring less extensive mental effort. This "depletion effect" can be incorporated into cognitive load theory that is concerned with using the properties of human cognitive architecture,…

The author examined 2 distinctive aspects of emotion regulation in mathematics homework, including emotion management and cognitive reappraisal. Participants were 1,799 high school students from 46 classes in China. Two multilevel models were run, 1 with emotion management and another with cognitive reappraisal as the dependent variable. Both…

We used event-related potentials (ERPs) to determine the time course of mechanisms underlying strategy selection. Participants had to select the better strategy on multiplication problems (i.e., 51 × 27) to find approximate products. They could choose between rounding up and rounding down both operands to their nearest decades. Two types of…

Box plots are frequently used, but are often misinterpreted by students. Especially the area of the box in box plots is often misinterpreted as representing number or proportion of observations, while it actually represents their density. In a first study, reaction time evidence was used to test whether heuristic reasoning underlies this…

We describe the application of the Evidence-Centered Design (ECD) framework to measure the self-regulated learning (SRL) strategies of students' enrolled in an online mathematics course by using their trace logs captured by a Learning Management System (LMS). We found that the ECD framework was helpful in building evidentiary arguments for…

This study explores the effects of the "presence of external representations of a mathematical object" (ERs) on problem solving performance associated with short double-choice problems. The problems were borrowed from secondary school algebra and geometry, and the ERs were either formulas, graphs of functions, or drawings of geometric…

This study sought to understand how aspects of middle school mathematics teachers' knowledge and conceptions are related to their enactment of cognitively demanding tasks. I defined the enactment of cognitively demanding tasks to involve task selection and maintenance of the cognitive demand of high-level tasks and examined those two…

The present study investigated (a) whether the perceived cognitive load was different when geometry problems with various levels of configuration comprehension were solved and (b) whether eye movements in comprehending geometry problems showed sources of cognitive loads. In the first investigation, three characteristics of geometry configurations…