This paper presents an updated WWC (What Works Clearinghouse) Review of the Article "Culture and the Interaction of Student Ethnicity with Reward Structure in Group Learning". The study examined the effects of different reward systems used in group learning situations on the math skills of African-American and White students. The…

The purpose of this study was to investigate prospective mathematics teachers' knowledge of common conceptions and misconceptions that sixth and seventh grade students had about multiplication of fractions. In addition, prospective teachers' knowledge of the sources of these misconceptions and strategies they knew to overcome these misconceptions…

Many high-school mathematics teachers have likely been asked by a student, "Why does the cross-multiplication algorithm work?" It is a commonly used algorithm when dealing with proportion problems, conversion of units, or fractional linear equations. For most teachers, the explanation usually involves the idea of finding a common denominator--one…

This study addressed the problem of why students with learning disabilities in mathematics too often fail to develop multiplicative and divisional concepts/operations. We conducted a constructivist teaching experiment with 12 students (nine 5th and three 4th graders). This report focuses on three students' conceptual progress, particularly on…

When solving basic number fact problems (e.g., 4x5=20), students with mathematical learning disabilities (MLDs) make qualitatively different kinds of errors than both typically achieving and low-achieving students. This study explores the origin of these qualitative differences through a detailed analysis of one student with an MLD. Data were…

This article reports challenges faced by prospective elementary teachers as they revisited whole number multiplication through a sequence of tasks that required them to develop and justify reasoning strategies for multiplication. Classroom episodes and student work are used both to illustrate these challenges, as well as to demonstrate growth over…

The purpose of the present study was to evaluate the effects of Direct Instruction (DI) flashcard procedure, combined with strategies and rewards on multiplication fact accuracy of two elementary school-age students. A single subject replication design across three and four sets of multiplication facts was used to evaluate outcomes. The results…

As education continues to progress schools are constantly seeking innovative ways to cultivate and enhance achievement for all students. As a result many public schools are pushing toward the inclusion model. This model includes co-taught instruction to meet the many needs of special education students. This research study was implemented to…

The authors investigated the performance on simple multiplication and division problems of 8-year-old children longitudinally to determine the developmental trajectories of both operations. Twice a year, during 2 consecutive school years, children performed a multiplication and division verification task and a number-matching task. All effects…

The North Carolina Standard Course of Study 2003 mathematics standards call for third-grade students to develop fluency in solving problems that involve multiplication and division. Released test items from the statewide standards-based assessment include multiplication and division tasks that require students to read the problem, identify the…

In the transition years, Grades 7 to 9, the shift from natural numbers to rational numbers and the associated multiplicative concepts prove challenging for many learners. The new concepts, operations and notation must be mastered if the student is to thereafter rise to meet the challenges of algebra and more advanced and powerful mathematics. The…

Many arithmetic problems can be solved in two ways: by a calculation involving several steps, and by direct retrieval of the answer. With practice on particular problems, memory retrieval tends to supplant calculation--an important aspect of skill learning. We asked how the distribution of practice on particular problems affects this kind of…

Contemporary teachers need instructional practices that are (a) powerful enough to meet the needs of a rapidly diversifying student population, (b) feasible to implement on a classwide basis, and (c) socially acceptable to them and their pupils. Classwide peer tutoring (CWPT) is one such instructional practice. In addition to describing CWPT, its…

The "Census in Schools Educator Update" is sent to educators and educational organizations periodically to keep them informed about current and upcoming census data and to provide ideas about how to use data in the classroom. This issue of the "Census in Schools Educator Update" newsletter focuses on the following topics: (1) Census in Schools is…

Researchers have documented the positive effects of classwide peer tutoring on academic performance, engagement, and other social behaviors of students with and without disabilities. Commonly, in classwide peer tutoring, students are paired and the class is divided in half. Points are awarded for tutoring behavior and academic responding during…