The ability to perceive structures in sets and to use them to determine cardinality is one important basis for arithmetical learning. This study is based on a theoretical model that distinguishes between the two processes of perception and determination. A total of 95 5-year-old children were interviewed individually to find out whether and how…

The collection of articles in this special issue and related studies over the past decade provides a fine example of the substantial progress that has been made in our understanding and remediation of mathematical learning disabilities and difficulties since 1993 (Geary, 1993). The originally proposed procedural and retrieval deficits have been…

Geometry is required for many secondary school students, and is often learned, taught, and assessed more in a heuristic image-based manner, than as a formal axiomatic deductive system. Students are required to prove general theorems, but diagrams are usually used. It follows that understanding how students engage in perceiving and reasoning about…

This study investigated whether students' memory retention rate improved when they were provided with blue ink printed material. A pretest, treatment, posttest with control group design was used. The participants were 93 10th and 11th grade students in algebra and geometry courses, and there were 2 classes in each course. The treatment lasted for…

An awareness of negative effects of mind set is promoted, and ways to minimize harmful sets are suggested. Visual perception, Eistelung effect, and functional fixedness are discussed as categories of potentially negative mind sets, with several examples given of each. Fixation combinations are noted as well. (MP)

The role of visual-spatial operations in nonroutine mathematical problem solving in schoolchildren is investigated through a search of related literature. It is suggested that certain visual-spatial operations are concomitant with the mental processes necessary in problem solving. The following topics are discussed: (1) the importance of problem…

Defines visualization as the product and the process of creation, interpretation, and reflection upon pictures and images. Analyzes, exemplifies, and reflects upon the many different and rich roles that it can and should play in the learning and doing of mathematics. Discusses limitations and possible sources of difficulties visualization may pose…

Two authors introduce the topic of visualization in mathematics education. Fourteen articles are briefly described. (YP)

The aim of the 2018 International Association for Development of the Information Society (IADIS) Cognition and Exploratory Learning in the Digital Age (CELDA) conference was to address the main issues concerned with evolving learning processes and supporting pedagogies and applications in the digital age. There have been advances in both cognitive…

Describes the Agam program, a 36-unit curriculum program to introduce students to basic visual concepts and that applies visual abilities and visual thinking to learning tasks. Describes two units at the third grade level, "Ratio and Proportion" and "Numerical Intuition," and makes observations of the students' learning. (MDH)

Several studies that were directed towards examining the influence of cognitive factors in sex-related differences in mathematics achievement are reported. Specifically, two lines of research were pursued examining: (1) the relationship between different types of visual-spatial skill and mathematics achievement, and (2) the trainability of…