In this study, we investigated how secondary students interpret algebraic expressions that contain literal symbols to stand for variables. We hypothesized that the natural number bias (i.e., the tendency to over-rely on knowledge and experiences based on natural numbers) would affect students to think that the literal symbols stand for natural…

We examined the development of numerical magnitude representations of fractions and decimals from fourth to 12th grade. In Experiment 1, we assessed the rational number magnitude knowledge of 200 Chinese fourth, fifth, sixth, eighth, and 12th graders (92 girls and 108 boys) by presenting fraction and decimal magnitude comparison tasks as well as…

One of the attributes of rational numbers that make them different from integers are the different symbolic modes (fraction, decimal and percentage) to which an identical number can be attributed (e.g. 1/4, 0.25 and 25%). Some research has identified students' difficulty in mental calculations with rational numbers as has also the switching to…

The mission of German special schools is to enhance the education of students with Special Educational Needs in the area of Learning (SEN-L). However, recent studies indicate that students with SEN-L from special schools show difficulties in basic arithmetical operations, and the development of basic mathematical skills during secondary special…

We examined developmental and individual differences in 6th and 8th graders' fraction arithmetic and overall mathematics achievement and related them to differences in understanding of fraction magnitudes, whole number division, executive functioning, and metacognitive judgments within a crosssectional design. Results indicated that the difference…

This research documents Kuwaiti eighth grade students' performance in recognizing reasonable answers and the strategies they used to determine reasonableness. The results from over 200 eighth grade students show they were generally unable to recognize reasonable answers. Students' performance was consistently low across all three number domains…

"The Zeroing in on Number and Operations" series, which aligns with the Common Core State Standards and the NCTM Standards and Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained in decades of mathematics teaching and research,…

Appropriate concrete and pictorial models allow students to construct meaning for rational numbers and operations with the numbers. To develop deep understanding of rational number, sixth through eighth graders must experience a variety of models (NCTM 2000). Since 1979, personnel from the Rational Number Project (RNP), a cooperative research and…

These item specifications were developed as a part of the Arkansas "Minimum Performance Testing Program" (MPT). There is one item specification for each instructional objective included in the MPT. The purpose of an item specification is to provide an overview of the general content and format of test items used to measure an…

Seventh and eighth grade students identified as holding an incomplete fraction conception of decimals were tested on related fraction knowledge. Most of these students (78%) had a problem in coordinating the size of the parts and the number of parts in comparing fractions. These students underwent several instructional sessions. Half of them…

A modern approach to the study of mathematical structure in the fifth class (grade eight) of French schools is described. Students make a number of experiments with various mathematical concepts in an attempt to discover interesting properties. (FL)

This article focuses on the kinds of conceptual changes that occur when students have to deal with negative numbers in elementary algebraic operations. Interviews were carried out with twelve 8th-grade level students who were selected on the basis of their results in a test where they were required to reduce polynomials. The questions applied to…

The contemporary mathematics program set forth in this publication developed as a result of experimentation and evaluation in classroom situations. This is Part 2 of "Mathematics: 8th Year." Part 1, a separate bulletin, was published during the school year 1967-68. The materials in this bulletin are intended to serve as guidelines for…

The materials in this bulletin consist of a series of daily lesson plans for use by teachers in presenting a modern program of eighth year mathematics. There is an emphasis on (1) an understanding of mathematical structure, (2) growth of a number system, (3) relations and operations in a number system, (4) a development of mathematical skills…

Middle school students consolidate their understanding of integers and rational numbers, increasing their facility with fractions, decimals, and percents and encountering proportionality. This book shows how students can explore these important ideas in such diverse activities as exchanging currency and using area models to develop algorithms for…