Magnitude understanding is critical for students to develop a deep understanding of fractions and more advanced mathematics curriculum. The research reports in this special issue underscore magnitude understanding for fractions and emphasize number lines as both an assessment and an instructional tool. In this commentary, we discuss how number…

In this commentary, I examine some of the distinctive, foundational difficulties in learning fractions and other types of rational numbers encountered by students with a mathematical learning disability and how these differ from the struggles experienced by students classified as low achieving in math. I discuss evidence indicating that students…

Learning fractions is difficult for children in general and especially difficult for children with mathematics difficulties (MD). Recent research on developmental and individual differences in fraction knowledge of children with MD and typically achieving (TA) children has demonstrated that U.S. children with MD start middle school behind their TA…

In this study, it was aimed to determine the errors and misunderstandings of 5th and 6th grade middle school students in fractions and operations with fractions. For this purpose, the case study model, which is a qualitative research design, was used in the research. In the study, maximum diversity sampling, which is a purposeful sampling method,…

By the time they reach middle school, all students have been taught to add fractions. However, not all have "learned" to add fractions. The common mistake in adding fractions is to report that a/b + c/d is equal to (a + c)/(b + d). It is certainly necessary to correct this mistake when a student makes it. However, this occasion also…

The SCOPE Mathematics Achievement Test booklet for grade 5 presents 11 mathematical concepts with instructions for students to take the test with little or no teacher direction. Testing items include: writing number words; reading and writing numerals in sequence from 0.001 to 100,000; adding and subtracting whole numbers; multiplying up to four…

This is volume one of a three-volume SMSG junior high school mathematics text. This volume contains units concerned with the structure of the number systems of arithmetic. Unit topics include: (1) numeration; (2) natural numbers and zero; (3) factoring and primes; (4) supplementary tests for divisibility and repeating decimals; (5) the…

This is volume one of a three-volume set for teachers using SMSG junior high school text materials. Each unit contains a commentary on the text, answers to all the exercises, a copy of the questionnaire used for evaluating the material, and a summary of comments by the teachers using the text. Unit topics include: (1) numeration; (2) natural…

Attempted to verify knowledge regarding decimal and rational numbers in children ages 10-14. Discusses how pupils can receive and assimilate extensions of the number system from natural numbers to decimals and fractions and later can integrate this extension into a single and coherent numerical structure. (Author/MKR)

The problem of getting a correct result when a fraction is reduced by cancelling a digit which appears in both the numerator and the denominator is extended from the base ten situation to any number base. (DT)

This study determined if overall mathematics performance of male and female students was: (1) different within each of six content areas; (2) differentially affected by ability grouping within each of the six content areas; and (3) differentially affected by the combination of ability grouping and grade level within each of the six content areas.…

Presents three algorithms for changing decimal fractions to basic five (quinary) fractions, or for any base to "b-ary fractions. (RP)

The topics discussed are, "Helping Students Understand the Distributive Property,""Converting from Base 10: Nonintegral Bases?,""Rapid Mental Squaring of Mixed Numbers," and "Some Nonstandard Binary Operations and their Properties." (JT)

A discussion of early Egyptian hieroglyphic numeration and calculation is presented. (SD)

The early use of the distributive law can aid students in learning addition of fractions and provide rapid approaches to computation involving other operations. (SD)