Recent laboratory experiments have shown that both infant and adult learners can acquire word-referent mappings using cross-situational statistics. The vast majority of the work on this topic has used unfamiliar objects presented on neutral backgrounds as the visual contexts for word learning. However, these laboratory contexts are much different…

Similarity is one of the most important relations humans perceive, arguably subserving category learning and categorization, generalization and discrimination, judgment and decision making, and other cognitive functions. Researchers have proposed a wide range of representations and metrics that could be at play in similarity judgment, yet have not…

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…

Computational activity is increasingly relevant in education and society, and researchers have investigated its role in students' mathematical thinking and activity. More work is needed within mathematics education to explore ways in which computational activity might afford development of mathematical practices. In this paper, we specifically…

How do people use information from others to solve complex problems? Prior work has addressed this question by placing people in social learning situations where the problems they were asked to solve required varying degrees of exploration. This past work uncovered important interactions between groups' "connectivity" and the problem's…

Generalization is critical to mathematical thought and to learning mathematics. However, students at all levels struggle to generalize. In this paper, I present a theoretical analysis connecting Piaget's assimilation and accommodation constructs to Harel and Tall's (1991) framework for generalization in advanced mathematics. I offer a theoretical…

This study aims to explore all the types of students' mental models of number patterns. The study used a qualitative approach with an explorative type. The subjects used to characterize the student's mental models in this study were 46 eighth grade students in Indonesia. To reveal the subjects' mental model, they were asked to solve the number…

A striking characteristic of human thought is that we form representations about abstract kinds (Giraffes have purple tongues), despite experiencing only particular individuals (This giraffe has a purple tongue). These generic generalizations have been hypothesized to be a cognitive default, that is, more basic and automatic than other forms of…

Building conceptual knowledge that generalizes to novel situations is a key function of human memory. Category-learning paradigms have long been used to understand the mechanisms of knowledge generalization. In the present study, we tested the conditions that promote formation of new concepts. Participants underwent 1 of 6 training conditions that…

There is much evidence showing that the prospect of performance-contingent reward increases the usage of cuing information and cognitive stability. In a recent study, we showed that participants under reward conditions even continued using cues even when they were no longer predictive of the required response rule, even at the expense of higher…

Algebraic thinking in children can bridge the cognitive gap between arithmetic and algebra. This quantitative study aimed to develop and test a cognitive model that examines the cognitive factors influencing algebraic thinking among Year Five pupils. A total of 720 Year Five pupils from randomly selected national schools in Malaysia participated…

This research aims to describe the expectations of prospective teachers for students' mathematical thinking processes in solving problem-based on the Polya model. This model is perceived by the theory of mathematical thought processes proposed by Mason. A descriptive method with a qualitative approach was used in this research. The research…

Generalization is a critical component of mathematical reasoning, with researchers recommending that it be central to education at all grade levels. However, research on students' generalizing reveals pervasive difficulties in creating and expressing general statements, which underscores the need to better understand the processes that can support…

Feedback on student answers and even during intermediate steps in their solutions to open-ended questions is an important element in math education. Such feedback can help students correct their errors and ultimately lead to improved learning outcomes. Most existing approaches for automated student solution analysis and feedback require manually…

Research has shown that the types of tasks assigned to students affect their learning. Various authors have described desirable features of mathematical tasks or of the activity they initiate. Others have suggested task taxonomies that might be used in classifying mathematical tasks. Drawing on this literature, we propose a set of task types that…