This paper presents results of a study aimed at describing and discussing evidence/features of advanced algebraic thinking processes. To achieve these objectives, we analysed the written production of students enrolled in engineering courses working on mathematical modelling tasks related to differential equations. Our guiding question was as…

In the subject matter of functional relationships, a student's ability to translate from one form of representation to another is seen as a central competence. In the course of the HEUREKO project (heuristic work with representations of functional relationships and the diagnosis of mathematical competencies of students), a theoretical competence…

A recent discussion involves the elaboration on possible design principles for sequences of tasks. This paper builds on three principles, as described by Bokhove and Drijvers (2012a). A model with ingredients of crises, feedback and fading of sequences with near-similar tasks can be used to address both procedural fluency and conceptual…

The article first summarizes the assumptions of Luce (2004, 2008) for inherently binary (2-D) stimuli (e.g., the ears and eyes) that lead to a "p-additive," order-preserving psychophysical representation. Next, a somewhat parallel theory for unary (1-D) signals is developed for intensity attributes such as linear extent, vibration to finger, and…

The white picket fence is an integral component of the iconic American townscape. But, for mathematics students, it can be a mathematical challenge. Picket fences in a variety of styles serve as excellent sources to model constant, step, absolute value, and sinusoidal functions. "Principles and Standards for School Mathematics" (NCTM 2000)…

A decision field theory is proposed and used to explain motivational and cognitive mechanisms that guide the deliberation process involved in decisions made under uncertainty. Decision theories are extended into the stochastic-dynamic category. The proposed theory is compared with four other theories of decision making under uncertainty. (SLD)

It is argued that human memory is adaptively designed and that much can be learned by understanding its adaptiveness. The information-retrieval problem is framed, and optimal memory behavior is derived. Applying this framework to the classic free-recall paradigm is discussed. (SLD)

A large body of data is reviewed to support a new theory of motion perception described by S. Grossberg and M. E. Rudd (1989). The Motion Boundary Contour System is used to explain classical and recent data about motion perception that have not been explained by other models. (SLD)

Diagnosing cognitive errors possessed by examinees can be considered as a pattern classification problem that is designed to classify a sequential input of stimuli into one of several predetermined groups. The sequential inputs in this paper's context are item responses, and the predetermined groups are various states of knowledge resulting from…

Multinomial modeling--a methodology that can be used to measure and study cognitive processes--is discussed, and applications are presented. This statistically based technique involves estimating hypothetical parameters that represent the probabilities of unobservable cognitive events and is compatible with computational theories of cognition.…

Mental-rotation task response times from 12 studies involving 505 adults--251 males and 254 females--were used to evaluate 5 hypotheses concerning sex differences derived from an X-linked genetic model. The model assumes that task facilitation in speed of mental rotation is mediated by a recessive gene. Four hypotheses derived from the model were…

A theory of the updating of beliefs over time is presented that explicitly accounts for order-effect phenomena as arising from the interaction of information-processing strategies and task characteristics. The belief-adjustment model is supported by 5 experiments involving 192 adult subjects. (SLD)

When learning is taking place, students test their hypotheses and evaluate them, and modify their current theories on the basis of new information. This phenomenon is known as "hypothesis testing view" or "theory changes." Many students change their rules to another while they are taking a test. This study introduced a new…

The cognitive structure of an algebra test was defined and validated using the linear test model (LLTM) and quadratic assignment (QA) techniques. The LLTM is an extension of the Rasch model with a linear constraint that describes item difficulty in terms of the cognitive operations required to solve the item. The model permits the specification of…

This document contains the fourth volume of the proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 59 research reports by presenters with last names beginning between Kun and…