The equipartitioning learning trajectory (Confrey, Maloney, Nguyen, Mojica & Myers, 2009) has been hypothesized and the proficiency levels have been validated through much prior work. This study solidifies understanding of the upper level of co-splitting, which has been redefined through further clinical interview work (Corley, Confrey &…

The purpose of this study was to document and trace how students' understanding of situations that involve finding a fractional part of a fraction developed during a course of instruction in which students explored and represented various kinds of situations using each of the five representational systems. A class of 5th grade students (n=22)…

The study investigated the effectiveness of a constant time delay procedure in teaching multiplication facts to four fifth- and sixth-grade students identified as learning disabled, behavior disordered, or educable mentally retarded. Results indicated that the learning procedure was effective and near errorless. (Author/DB)

This six month study investigated the similarities and differences between 137 fourth graders' understanding of and reasoning about multiplication, division, and proportion tasks. All students were administered a pretest mid-year and a posttest at the end of year. A sample of 18 students was interviewed individually on tasks involving reasoning…

Offers suggestions for presenting multiplication to elementary students at the primary and intermediate levels. At the primary level, the emphasis is on introducing the concept of multiplication; at the intermediate level, the focus is on numeration and place value (using grids and a place value game). (SM)

Described is a multiplication unit for intermediate aged emotionally disturbed boys which used citizen band radio terms and a drawing of a road to record individual progress. (CL)

It is not complex to teach the algorithm for multiplying fractions so that children can multiply numerators and denominators to arrive at correct answers. However, it is a challenge to teach so that students build understanding of multiplication of fractions, extending what they have already learned about fractions and about multiplication of…

A Copy/Cover/Compare method of teaching multiplication facts to a sixth grade student with learning disabilities was evaluated. Results indicated that the Copy/Cover/Compare method was effective in increasing percent correct for the targeted multiplication facts. Practical implications of employing this drill and practice procedure in the…

This study investigated the processes by which variation in format for presenting multiplication problems influenced children's motivation and achievement. The three multiplication drill and practice instructional methods were: (1) computer-assisted instruction (CAI) with a reward game, (2) computer-assisted instruction without a reward game, and…

This study evaluated the effectiveness of teaching multiplication facts and related word problems using the concrete-representational-abstract teaching sequence and strategy instruction to three middle school students with mental retardation. Evaluation of the 21 scripted lessons given each student found only four occurrences (out of 63 lessons)…

Two experiments involving 90 primary and intermediate-grade students studied how the COPPERS computer-based mathematical learning environment advances children's understanding that multiplication problems have many different correct solutions. Factors affecting learning and theoretical implications are discussed in terms of scaffolding learning.…

Activities and teaching methods for developing an understanding of fractions are presented. The activities, which use mathematical models (visual representations of fractions), are divided into three sections: (1) equivalent fraction circles; (2) fraction bars; and (3) multiplication of fractional numbers using squares. Each section includes the…

This study focused on the way mathematics was taught in selected primary school classrooms. The study involved the observation of 21 fourth-grade classes in eight schools over a two-week period. Results indicated a hiatus between what was taught and what should be taught and between how mathematics is taught and how it should be taught.…

A Copy, Cover, and Compare procedure was found to produce large improvements in the accuracy of the multiplication facts of two middle school students with attention deficit disorder or attention deficit-hyperactivity disorder. The addition of a token economy program produced only small improvements in performance. (Author/PB)

Assessed the achievement in addition, subtraction, multiplication, and division of 93 fourth graders before and after they received either computer or traditional classroom drill-and-practice instruction. Students who received computer instruction showed greater increases in achievement scores in subtraction and multiplication than did students…