Recent studies of eye movements in reading and other information processing tasks, such as music reading, typing, visual search, and scene perception, are reviewed. The major emphasis of the review is on reading as a specific example of cognitive processing. Basic topics discussed with respect to reading are (a) the characteristics of eye movements, (b) the perceptual span, (c) integration of information across saccades, (d) eye movement control, and (e) individual differences (including dyslexia). Similar topics are discussed with respect to the other tasks examined. The basic theme of the review is that eye movement data reflect moment-to-moment cognitive processes in the various tasks examined. Theoretical and practical considerations concerning the use of eye movement data are also discussed.

/pdf/eye-movements-in-reading-and-information-processing-20-years-3z5ay8hdwc.pdf

Eye movements in reading and information processing: 20 years of research.

How we Think

The goals of this chapter are (1) to outline and substantiate a broad conceptualization of what it means to think mathematically, (2) to summarize the literature relevant to understanding mathematical thinking and problem solving, and (3) to point to new directions in research, development, and assessment consonant with an emerging understanding of mathematical thinking and the goals for instruction outlined here. The use of the phrase “learning to think mathematically” in this chapter’s title is deliberately broad. Although the original charter for this chapter was to review the literature on problem solving and metacognition, the literature itself is somewhat ill defined and poorly grounded. As the literature summary will make clear, problem solving has been used with multiple meanings that range from “working rote exercises” to “doing mathematics as a professional”; metacognition has multiple and almost disjoint meanings (from knowledge about one’s thought processes to self-regulation during problem solving) that make it difficult to use as a concept. This chapter outlines the various meanings that have been ascribed to these terms and discusses their role in mathematical thinking. The discussion will not have the character of a classic literature review, which is typically encyclopedic in its references and telegraphic in its discussions of individual papers or results. It will, instead, be selective and illustrative, with main points illustrated by extended discussions of pertinent examples. Problem solving has, as predicted in the 1980 Yearbook of the National Council of Teachers of Mathematics (Krulik, 1980, p. xiv), been the theme of the 1980s. The decade began with NCTM’s widely heralded statement, in its Agenda for Action, that “problem solving must be the focus of school mathematics” (NCTM, 1980, p. 1). It concluded with the publication of Everybody Counts (National Research Council, 1989) and the Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989), both of which emphasize problem solving. One might infer, then, that there is general acceptance of the idea that the primary goal of mathematics instruction should be to have students become competent problem solvers. Yet, given the multiple interpretations of the term, the goal is hardly clear. Equally unclear is the role that problem solving, once adequately characterized, should play in the larger context of school mathematics. What are the goals for mathematics instruction, and how does problem solving fit within those goals? Such questions are complex. Goals for mathematics instruction depend on one’s conceptualization of what mathematics is, and what it means to understand mathematics. Such conceptualizations vary widely. At one end of the spectrum, mathematical knowledge is seen as a body of facts and procedures dealing with quantities, magnitudes, and forms, and the relationships among them; knowing mathematics is seen as having mastered these facts and procedures. At the other end of the spectrum, mathematics is conceptualized as the “science of patterns,” an (almost) empirical discipline closely akin to the sciences in its emphasis on pattern-seeking on the basis of empirical evidence. The author’s view is that the former perspective trivializes mathematics; that a curriculum based on mastering a corpus of mathematical facts and procedures is severely impoverished—in much the same way that an English curriculum would be considered impoverished if it focused largely, if not exclusively, on issues of grammar. The author characterizes the mathematical enterprise as follows:

Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics (Reprint):

Life-span developmental psychology involves the study of constancy and change in behavior throughout the life course. One aspect of life-span research has been the advancement of a more general, metatheoretical view on the nature of development. The family of theoretical perspectives associated with this metatheoretical view of life-span developmental psychology includes the recognition of multidirectionality in ontogenetic change, consideration of both age-connected and disconnected developmental factors, a focus on the dynamic and continuous interplay between growth (gain) and decline (loss), emphasis on historical embeddedness and other structural contextual factors, and the study of the range of plasticity in development. Application of the family of perspectives associated with life-span developmental psychology is illustrated for the domain of intellectual development. Two recently emerging perspectives of the family of beliefs are given particular attention. The first proposition is methodological and suggests that plasticity can best be studied with a research strategy called testing-the-limits. The second proposition is theoretical and proffers that any developmental change includes the joint occurrence of gain (growth) and loss (decline) in adaptive capacity. To assess the pattern of positive (gains) and negative (losses) consequences resulting from development, it is necessary to know the criterion demands posed by the individual and the environment during the lifelong process of adaptation. The study of life-span development is not a homogeneous field. It comes in two major interrelated modes. The first mode is the extension of developmental studies across the life course without a major effort at the construction of metatheory that emanates from life-span work. The second mode includes the endeavor to explore whether life-span research has specific implications for the general nature of developmental theory. The second approach represents the topic of this article. Specifically, the purpose of this article is twofold. First, after a brief introduction to the field of life-span developmental psychology, some "prototypical" features of the life-span approach in developmental psychology are presented. Second, these features are illustrated by work in one domain: intellectual development. Although the focus of this paper is on life-span developmental psychology and its theoretical thrust, it is important to recognize at the outset that similar perspectives on developmental theory have been advanced in other quarters of developmental scholarship as well (Hetherington & Baltes, in press; Scan; 1986). There is, however, a major difference in the "gestalt" in which the features of the theoretical perspective of life-span psychology are organized.

/pdf/theoretical-propositions-of-life-span-developmental-3pdj15vxom.pdf

Theoretical propositions of life-span developmental psychology : On the dynamics between growth and decline

http://academic.oup.com/milmed/article-pdf/146/7/506/24126715/milmed-146-7-506.pdf

Goodman and Gilman's The Pharmacological Basis of Therapeutics

The scanpath hypothesis as proposed by Noton and Stark is briefly reviewed and some of the difficulties in its theory and empirical investigation are mentioned. A distinction is proposed between “local scanpaths” in the sense of Stark et al. reflecting consistent patterns of successive fixations, and “global scanpaths” reflecting the distribution of fixations over a larger time scale irrespective of their immediate succession. It is assumed that local scanpaths are regulated by the momentary fixation and its peripheral information in a moment-to-moment control mode, and global scanpathsare regulated by the hypothesis or search plan of the subject and are assumed to operate in a top-down fashion. The data of a facial' inspection and recognition experiment are analysed and empirical evidence for both local and global scanpaths is found. Finally, the type of scanning behavior is set into relation with several performance measures.

Looking at Faces: Local and Global Aspects of Scanpaths

Library of Congress Cataloging in Publication Data Main entry under title: Methods of heuristics.

Methods of Heuristics

A review of recent experimental and theoretical findings is presented which relates the results of neurophysiological and psychological research on attention and eye movement to cognitive theorizing. With respect to the relation between shifts of attention and saccadic eye movements, several experiments have demonstrated that it is possible to dissociate the line of attention from the gaze direction. On the other hand, there is some indirect (although not yet conclusive) evidence that saccadic eye movements always produce a concomitant shift of attention. Another question is whether there is a moment-to-moment control of each consecutive saccade and latency or whether indirect control models (i.e. planning several saccades in advance) are more appropriate. The function of attentional processes which have to coordinate stimulus driven (bottom-up) and concept driven (top-down) mechanisms are discussed and related to some studies investigating local and global scanpaths.

Attention and eye movement control: an overview.

An experiment was conducted to examine the influence of luminance, contrast, and spatial frequency content on saccadic eye movements. 112 pictures of natural textures from Brodatz were low-pass filtered (0.04 – 0.76 cycles deg−1) and high-pass filtered (1.91 – 19.56 cycles deg−1) and varied in luminance (low and high) and contrast (low and high), resulting in eight images per texture. Circular clippings of the central parts of the images (approximately 15% of the whole image) were used as stimuli. In the condition of bottom - up processing, the eight stimuli derived from one texture were presented for 1500 ms in a circular arrangement around the fixation cross. They were followed by a briefly presented target stimulus in the centre, which in half the trials was identical to one of the eight test stimuli. Participants had to decide whether the target stimulus was identical to any of the preceding stimuli. During a trial, their eye movements were recorded by means of a Dual-Purkinje-Image eye tracker. In the top - down condition, the target stimulus was presented in each trial prior to the display of the test stimulus. It was assumed that the priming with a target produced a top - down processing of the test stimuli. The latency and landing site of the first saccade were computed and compared between the top - down and bottom - up conditions. It is hypothesised that stimulus characteristics (luminance, contrast, and spatial frequency) play a more prominent role in bottom - up processing, while top - down processing is adjusted to the particular characteristics of the prime.

Top-Down versus Bottom-up Control of Saccades in Texture Perception

https://webdocs.cs.ualberta.ca/~wfb/publications/J-1993-VR-Groner.pdf

Marina Groner

Papers

Looking at Faces: Local and Global Aspects of Scanpaths

Methods of Heuristics

Attention and eye movement control: an overview.

Top-Down versus Bottom-up Control of Saccades in Texture Perception

On the confounding effects of phosphor persistence in oscilloscopic displays.