The purpose of this study was to investigate the effects of the concrete-representational-abstract--integrated (CRA-I) sequence on students with learning disabilities' performance when learning fraction and decimal concepts. Three elementary-level students in Grades 4 and 6 participated in a single-case multiple probe across behaviors study. The…

In an attempt to further understand connections between children's proficiency and development with single- and multidigit addition, this study investigated the conceptualizations and solution strategies of 26 first-graders presented with several single-digit, multiple addend addition problems. The changes in students' solution strategies over the…

As young children make sense of mathematics, they begin to see with new eyes. What once was uncertain may now be determined. Objects become countable; fingers become tools; and numbers become more than just names. Educators revel in such developments--which mark significant progress toward more sophisticated understanding of number--and work…

This study examined the effect of training in math metacognition on fractional mathematics among primary school pupils, with a quasi-experimental design, specifically a post-test only control group design. Two intact classes were randomly selected and assigned to treatment and control conditions. Sixty primary six pupils constituted the sample…

The authors' goal was to evaluate the potential of Math Recovery (MR), a pullout, one-to-one tutoring program that has been designed to increase mathematics achievement among low-performing first graders, thereby closing the school-entry achievement gap and enabling participants to achieve at the level of their higher-performing peers in the…

The effectiveness of different concrete and pictorial models on students' understanding of the part-whole construct for fractions was investigated. Using interview data from fourth and fifth grade students from three different districts that adopted the "Mathematics Trailblazers" series, authors identified strengths and limitations of models used.…

At the heart of the recent focus on mathematics has been an increased emphasis on developing students' "number sense." Ironically, although growing as a force in the education literature, number sense has not been clearly defined for teachers. Teachers need specific support in understanding how to develop number sense in students, to…

The mixed method sequential nested study examines whether and how the cognitive type of teachers' content knowledge is associated with student achievement, and correlated with teaching practice. In the context of this study, the "cognitive type" refers to the kind of teacher content knowledge and thinking processes required to accomplish…

This article discusses large-scale assessment of change in student achievement and takes the study by Hickendorff, Heiser, Van Putten, and Verhelst (2009) as an example. This study compared the achievement of students in the Netherlands in 1997 and 2004 on written division problems. Based on this comparison, they claim that there is a performance…

Results supported the hypothesis that there was no significant difference in pupil performance on arithmetic problems presented in different forms. (Author)

Student attitudes towards learning arithmetic and student preferences for working independently were not changed by organized lessons based on the manipulation of physical models using a wide range of student participation. (AN)

This article explains how to teach long division using hands-on materials (skittles, base ten blocks, colored counters, numeral cards) and investigates reviewing division word problems with middle school students (N=27) with learning disabilities in mathematics by this approach compared to spending the same amount of time on the typical practices…

The effects of the combined use of a nonsimulation game and student teams in mathematics on student achievement were investigated. Ninety-six seventh grade students in two low- and two average-ability mathematics classes participated in the study. One low- and one average-ability class played the nonsimulation game Equations twice a week for nine…

Constructs a corrective learning system using the Socratic dialogue as a guide to correct mistakes in students' knowledge of subtraction. The Socratic dialog applies a dialectic method to present questions to the student and lets the student reconsider his or her own thinking. Results show that the Socratic-dialog approach is of great help to…