In studies over recent years, there has been an increasing interest in teachers' predicting middle school students' thinking processes. However, as far as we are aware, there are no studies examining students' thinking in terms of mathematical thinking components. This study primarily aimed to determine the mathematical thinking of middle school…

In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to…

A prevailing theory of mathematical problem solving predicts that children will be less accurate solving a + b = c + __ problems versus a + b = __ + c. However, this has never been tested directly. Because of low base rates, information combined from multiple studies can help improve estimation accuracy and precision. This study compared…

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…

In Intelligent Tutoring Systems (ITS), methods to choose the next exercise for a student are inspired from generic recommender systems, used, for instance, in online shopping or multimedia recommendation. As such, collaborative filtering, especially matrix factorization, is often included as a part of recommendation algorithms in ITS. One notable…

This study aimed to investigate the effect of instruction based on metacognitive strategies on geometrical problem-solving performance of mathematics preservice teachers. Geometrical problem-solving tests developed by the researchers were applied as pre-test and post-test before and after the experimental instruction. Preservice teachers predicted…

Much of our real-life decision making is bounded by uncertain information, limitations in cognitive resources, and a lack of time to allocate to the decision process. It is thought that humans overcome these limitations through "satisficing," fast but "good-enough" heuristic decision making that prioritizes some sources of…

STEM-oriented engineering design practice has become recognized increasingly by technology education professionals in Taiwan. This study sought to examine the effectiveness of the application of an integrative STEM approach within engineering design practices in high school technology education in Taiwan. A quasi-experimental study was conducted…

Understanding an arithmetic operation implies, at minimum, knowing the direction of effects that the operation produces. However, many children and adults, even those who execute arithmetic procedures correctly, may lack this knowledge on some operations and types of numbers. To test this hypothesis, we presented preservice teachers (Study 1),…

Although traditional methods to collect similarity data (for multidimensional scaling [MDS]) are robust, they share a key shortcoming. Specifically, the possible pairwise comparisons in any set of objects grow rapidly as a function of set size. This leads to lengthy experimental protocols, or procedures that involve scaling stimulus subsets. We…

The present study evaluated the utility of brief experimental analysis (BEA) in predicting effective interventions for increasing the math fluency of 3 elementary students identified as having math skill deficits. Baseline data were collected followed by implementation of a BEA consisting of the following interventions: cover, copy, and compare,…

An analytic cognitive style denotes a propensity to set aside highly salient intuitions when engaging in problem solving. We assess the hypothesis that an analytic cognitive style is associated with a history of questioning, altering, and rejecting (i.e., unbelieving) supernatural claims, both religious and paranormal. In two studies, we examined…

This article discusses five generally accepted reasons to use data as a part of an educator's ongoing professional practice. Of course, there are many other more specific reasons one might look at data, but these five cover the overarching need in an educational setting. The five major purposes for using data are: (1) To enhance understanding and…

Many college students struggle with first-semester general chemistry. Prior studies have shown that a student's prior knowledge of chemistry, a cognitive factor, does not account for the total variance when measured by examination scores. This study explored the role of self-regulated learning (SRL) to identify the degree of success or failure of…

Investigating students' perceptions of their classroom environment is one of the ways researchers and educators can effectively determine what factors may benefit students' learning. Student Perceptions of Classroom Quality (SPOCQ; Gentry & Owen, 2004) was used with a group of Chinese gifted and general secondary students in the study. SPOCQ…