Fraction and decimal arithmetic pose large difficulties for many children and adults. This is a serious problem, because proficiency with these skills is crucial for learning more advanced mathematics and science and for success in many occupations. This review identifies two main classes of difficulties that underlie poor understanding of…

This paper is a translation of a report on two Swedish investigations concerning children's lack of understanding of the quantitative value of numbers (specifically, decimals and fractions). (MN)

This report describes the test performances of 26 students who displayed a variety of erroneous rules in completing a 48-item test of fraction addition problems, constructed to diagnose at least 88 projected erroneous rules. Cases were selected for their potential usefulness in designing and implementing an error-diagnostic testing system and in…

A few examples, relating specifically to fractions, of the many possible intriguing and substantial ideas to be found in remedial mathematics are given. (MN)

Results of the 1974 mathematics section of the London board's Ordinary level examination are presented in the context of item-correctness differences between boys and girls. Implications are made that insecurity with concepts such as fractions and proportionality may explain why girls seem to have trouble with quantification and spatial…

Research on the conceptual notions of fractions held by students at various levels of schooling is discussed. A method of approach to instructing students on fractions that seems to hold considerable promise is also covered in detail. (MP)

Students recognized as less successful individuals in mathematics are tested for their understanding of fractions. The data reveals that most were only able to apply remembered rules to problems without actually knowing if the rule worked for the given situation. (MP)

This report illustrates procedures of item construction for addition and subtraction examples involving decimal fractions. Using a procedural network of skills required to solve such examples, an item characteristic matrix of skills analysis was developed to describe the characteristics of the content domain by projected student difficulties. Then…

The ideas and techniques involved in learning about fractions were investigated with students in grades 1-12, in the first 3 years of colleges, in community college mathematics courses, and in graduate school. Also included were some high school mathematics teachers, some mathematicians, and some retired persons. Part I provides the rationale and…

Thirty-five secondary school children were interviewed on a one-to-one basis using questions which involved concepts considered as basic to the notion of ratio. One implication of the study is that a doubling ability is no indication of the ability to tackle other ratio questions. (MN)