In this article, we present a mathematical analysis that distinguishes two distinct quantitative perspectives on ratios and proportional relationships: variable number of fixed quantities and fixed numbers of variable parts. This parallels the distinction between measurement and partitive meanings for division and between two meanings for…

Although approximately 5-8% of students have a mathematical learning disability (MLD), researchers have yet to develop a consensus operational definition. To examine how MLD has been identified and what mathematics topics have been explored, the authors conducted a systematic review of 165 studies on MLD published between 1974 and 2013. To move…

This study evaluated the effects of a mathematics software program, the Building Blocks software suite, on young children's mathematics performance. Participants included 247 Kindergartners from 37 classrooms in 9 schools located in low-income communities. Children within classrooms were randomly assigned to receive 21 weeks of computer-assisted…

Teaching experiments have generated several hypotheses concerning the construction of fraction schemes and operations and relationships among them. In particular, researchers have hypothesized that children's construction of splitting operations is crucial to their construction of more advanced fractions concepts (Steffe, 2002). The authors…

This article presents the results of a 7th-grade classroom teaching experiment that supported students' understanding of integer addition and subtraction. The experiment was conducted to test and revise a hypothetical learning trajectory so as to propose a potential instructional theory for integer addition and subtraction. The instructional…

The author clarifies his position regarding what features of the examples used by Kaminski, Sloutsky, and Heckler (2008a) constitute substantive differences affecting performance. I also reiterate my hesitancy to extrapolate their findings to the broader realm of mathematics.

The purpose of this study was to investigate children's construction of 10s out of the 1s they have already constructed. It was found that, for many younger children, a dime was something different from 10 pennies even though they could say with confidence that a dime was worth 10 cents. As the children grew older, their performance improved.…

The purpose of this study was to examine the effects of a schema-based instructional strategy that emphasizes prealgebraic conceptualization of multiplicative relations on solving arithmetic word problems with elementary students with learning disabilities or problems (LP). Introducing symbolic representation and algebraic thinking in earlier…

The performance of students from three intelligence levels at grades 4, 5, 6, and 7 on certain discovery tasks in arithmetics are examined. Results indicate that students should be given from 3 to 6 instances to make discoveries of the type tested and that students of lower intelligence levels can form generalizations. (FL)

Examined the potential of using repeated rate-of-response measures to identify students exhibiting difficulties in arithmetic. Second-grade students (N=30) were followed over two years. Pearson product-moment correlations were computed to determine the ability of rate-of-response measures to predict arithmetic achievement. Results indicate that…

Explored is young children's ability to estimate set sizes and use reference points such as 10. Results indicated that many children could accurately place sets somewhat smaller than a reference point but had difficulty placing sets somewhat larger than a reference point. (CW)

The author describes the structure, content, and standardization of the Stanford Mental Arithmetic Test (SMAT), which was developed at Stanford University from 1973 to 1975. (MN)

Twenty student tutors were each matched with two elementary school children, one judged to be compatible and one incompatible on the basis of a test of interpersonal relations. After nine one-hour weekly tutoring sessions (in remedial arithmetic) no significant relations were found between student achievement and either compatibility or tutor…