The COVID-19 pandemic revealed that many countries have failed to provide the general population with the cognitive tools to thoroughly understand and cope with a global health crisis. While scientists and leaders worldwide have struggled to discover ways to contain the spread of the virus, this difficult task has become overwhelming due to the…

The intent of this commentary is to identify elements of fraction sense and note how the research studies provided in this special issue, in related but somewhat different ways, validate the importance of such understandings. Proficiency with fractions serves as a prerequisite for student success in higher level mathematics, as well as serving as…

The three target articles presented in this special issue converged on an emerging theme: the importance of spatial proportional reasoning. They suggest that the ability to map between symbolic fractions (like 1/5) and nonsymbolic, spatial representations of their sizes or "magnitudes" may be especially important for building robust…

This commentary summarizes emerging research into fractions instruction for students who are at risk for failure. Each of the three articles emphasizes a measure conception of fractions. Teaching fractions as measurement helps students learn the magnitude of rational numbers. However, measurement is only part of the way that students should…

Discussed are the difficulties that entering college freshmen seem to have with mathematics, particularly with fractional forms. A success-oriented program is suggested in which all students are successful. To obtain this goal, a number of alternative routes are discussed such as presenting decimals before fractional forms and the use of the…

Argues that fractions should still be taught, even though they have been replaced by decimals in most real-world applications. (SJL)

Curricular placement of and emphasis on common and decimal fractions are discussed. Suggestions include: retaining common fractions in the curriculum, teaching decimal concepts and notation earlier, reducing fraction computation complexity, and moving fraction computation upward in the curriculum. (MK)

Discusses a strategy for clarifying students' understanding of decimals, improving their ability to read decimals, and increasing retention of decimal skills. (YP)

The mechanisms, images, and language needed for the development of rational-number ideas are briefly discussed. Such ideas are sophisticated and different from natural-numbers ideas. (MNS)

Argues the importance of teaching fractions and discusses examples of fundamental problems in students' conceptualization of common fractions and decimal fractions. (SS)

Many elementary and junior high school students do not become proficient with common and decimal fractions because they have established few connections between the form they learn in the classroom and understandings they already have. (Author/GC)

Examining how students reconstruct stories they've heard can give insights into why students often have difficulty understanding and retaining mathematics. Behavioral psychologists refer to the phenomenon of piecing together a series of events as "chaining." This paper argues that the cognitive capacity to reconstruct a whole contextual…

It is suggested that elementary school students find rational numbers troublesome because some teachers have an inadequate understanding of rational number concepts and poor facility with rational numbers skills. How to help them overcome difficulties, develop concepts, and know what topics to emphasize are discussed. (MNS)

The first in a series of three articles, successful instructional materials from a 15-year software development effort are analyzed and characterized with special attention given to educational experiences intended to shape students' perceptions of the fundamental nature, interconnectedness, and usefulness of mathematics. The software programs…

Suggests that a superior way of teaching fractions is to assist learners to conceptualize fractions, especially to grasp the varied meaning of fractions. Advocates using hands-on procedures, gives three different meanings of the concept "fraction," and explains how to teach children the deeper meaning of numberline subunits, fractions as division,…