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…

How does the visual system recognize images of a novel object after a single observation despite possible variations in the viewpoint of that object relative to the observer? One possibility is comparing the image with a prototype for invariance over a relevant transformation set (e.g., translations and dilations). However, invariance over…

The future of education is human expertise and artificial intelligence working in conjunction, a revolution that will change the education as we know it. The Intelligent Tutoring System is a key component of this future. A quantitative measurement of efficacies of practice to heterogeneous learners is the cornerstone of building an effective…

A focus of early mathematics education is to build fluency through practice. Several models of skill acquisition have sought to explain the increase in fluency because of practice by modeling both the learning mechanisms driving this speedup and the changes in cognitive processes involved in executing the skill (such as transitioning from…

In light of conceptual metaphor theory, historical mathematicians' and students' difficulty with negative numbers reveals that the collecting objects metaphor may be a cognitive obstacle to those first learning about negative numbers. Moreover, consistency of physical motions with targeted ideas is a factor of cognition. Thus, this…

This paper reports on an investigation into managing cognitive conflict in the context of student learning about decimal magnitude. The influence of prior constructs is examined through a brief review of the literature. A micro-genetic approach was used to capture detail of the teaching intervention used to facilitate development in student…

This study investigated a theoretical structure which attempts to explain the problem-solving strategies used by first-grade students who are successful in solving simple arithmetic story problems. The structure used describes the problem-solving procedure as consisting of a three-stage model building process: (1) comprehending the story, (2)…

Findings from prior research are drawn together to create a learning model for elementary school mathematics in the cognitive-constructivist tradition. A potential teaching/learning process consistent with the model was developed and applied in a longitudinal collaborative arrangement between university personnel and a local elementary school…

Ongoing work toward developing a learning environment that will perform real-time diagnoses of students' difficulties in solving mathematical word problems is described. The learning environment designed consists of a microworld and expert modules. The microworld (or toolbox) is a collection of mouse-driven interfaces that facilitate a transition…

A LEARNING MODEL TO IDENTIFY FACTORS CONTRIBUTING TO THE DIFFICULTY OF A PROBLEM ITEM WAS SUPPORTED EMPIRICALLY, AND INDICATED THAT THE NUMBER OF STEPS REQUIRED TO SOLVE A PROBLEM WAS THE MOST IMPORTANT VARIABLE IN PREDICTING BOTH ERROR PROBABILITY AND RESPONSE LATENCY. THE MODEL, IN ORDER TO ESTABLISH DIFFERENTIAL PREDICTIONS OF DIFFICULTY IN…

This document contains the third volume of the proceedings of the 28th Annual Conference of the International Group for the Psychology of Mathematics. Conference presentations are centered around the theme "Inclusion and Diversity". A total of 65 research reports are presented here: (1) A Teacher's Model of Students Algebraic Thinking…