Rational numbers, such as fractions and decimals, are harder to understand than natural numbers. Moreover, individuals struggle with fractions more than with decimals. The present study sought to disentangle the extent to which two potential sources of difficulty affect secondary-school students' numerical magnitude understanding: number type…

This paper presents an analysis of fractions errors displayed by learners due to deficient mastery of prerequisite concepts. Fractions continue to pose a critical challenge for learners. Fractions can be a tricky concept for learners although they often use the concept of sharing in their daily lives. 30 purposefully sampled learners participated…

Educational research assumes that error reflections are efficient if they include the rationale behind the own error instead of just correcting the error. However, thus far there is a lack of empirical evidence regarding this aspect. Thus, we conducted a field experiment with pre-post-follow-up design and with 7th and 8th grade students (N = 174).…

Common mistakes pupils make when adding fractions are categorized and analyzed. (MP)

The author mentions several broad types of student elementary algebra errors, including incorrect cancellation and cross-multiplication, notes confusing terms and factors, and gives several suggestions to help students avoid these. (MN)

This is a report of an application of the interpretation of errors and springboards in a real-life situation. If and why we need to reduce fractions is considered. (MNS)

A common mistake in adding fractions involves the confusion betwen the concepts of fraction and ratio. A coherent system to operate with ratios is developed. (MNS)

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)

A brief overview is given of a research project funded to investigate the cause and cure of errors in ratio and proportion, algebra, and fractions. Choosing pertinent information, interviewing students, listing significant features, developing lessons, and testing the materials are considered. (MNS)

Illustrated first is the case in which a wrong procedure (with fractions) leads to a correct result. Trying to justify why it works in this case and looking for similar patterns involved interesting algebraic considerations as well as use of computers. (MNS)

Findings on ratio and on fractions from a research project on strategies and errors in secondary mathematics are discussed, with typical errors described. Pupils seemed to learn rules without understanding. (MNS)

The process of transition from a novice's state to that of an expert, in the domain of decimals, is described in terms of explicit, intermediate, and transitional rules which are consistent yet erroneous. Data from students in grades 6-9 are included. (MNS)

The Concepts in Secondary Mathematics and Science (CSMS) and Strategies and Errors in Secondary Mathematics (SESM) research projects based at Chelsa College, England, have shown the marked reluctance of secondary school students to use fractions when solving mathematical problems, even though they have been taught the topic for a number of years.…