The introduction of negative numbers should mean that mathematics can be twice as much fun, but unfortunately they are a source of confusion for many students. Difficulties occur in moving from intuitive understandings to formal mathematical representations of operations with negative and positive integers. This paper describes a series of…

Recent findings suggest deficits in coherent motion sensitivity, an index of visual dorsal stream functioning, in children with poor mathematical skills or dyscalculia, a specific learning disability in mathematics. We extended these data using a longitudinal design to unravel whether visual dorsal stream functioning is able to "predict"…

Multiplicative reasoning is required in different contexts in mathematics: it is necessary to understand the concept of multipart units, involved in learning place value and measurement, and also to solve multiplication and division problems. Measures of hearing children's multiplicative reasoning at school entry are reliable and specific…

This study purposed to determine the effect of an endogenously designed instructional game on conceptual understanding of the associative and distributive properties of multiplication. Additional this study sought to investigate if performance on measures of conceptual understanding taken prior to and after game play could serve as predictors of…

The present study examined the effectiveness of an instructional package that included an adapted version of pegword mnemonics paired with a picture fading technique in teaching two students with moderate intellectual disabilities to recall 28 single-digit multiplication facts between 2 and 9. The instructional package was assessed using a…

Games can be a valuable tool for a mathematics teacher. Students who dislike mathematics and are not engaged in class never get to experience the exhilaration that accompanies hard work and real accomplishment in mathematics; they usually experience only the frustration that accompanies enforced and futile effort. Game playing is a way to engage…

Teachers' knowledge of mathematical content and children's mathematical thinking have been identified as critical elements related to teachers' ability to effectively teach mathematics (Fennema & Franke, 1992; Kazemi & Franke, 2001; Ma, 1999; Peterson, Carpenter, & Fennema, 1989). Literature on teachers' knowledge…

This paper describes a synthesis conducted to determine what research says regarding preservice teachers' understanding of fractions and identify the gaps in their existing knowledge basis. Specifically, this paper will address a smaller portion of the synthesis and report the findings from fraction multiplication and division topics. Results…

Third grade students at a Midwestern elementary school participated in a 9-week mobile learning intervention (MLI). Two classrooms used Everyday Math and daily practice using flashcards, etc., to learn multiplication. Two other classrooms used Everyday Math and web applications for the iPod touch for daily practice. MLI students outperformed…

Previous research has shown that time to name single-digit Arabic numbers is about 15 ms slower when naming trials are interleaved with simple multiplication (e.g., state product of 2 x 3) than when naming digits is interleaved with magnitude comparison (e.g., state larger; 2 [arrow up] 3). To explain this phenomenon, J. I. D. Campbell and A. W.…

We present the findings of a study on prospective elementary teachers' proportional reasoning. After describing some of the teachers' performance in solving multiplicative structure problems that involve ratios and relations of direct proportionality between quantities, we were able to establish classifications of their answers according to…

Combinatorial scientific computing plays an important enabling role in computational science, particularly in high performance scientific computing. In this thesis, we will describe our work on optimizing matrix-vector multiplication using combinatorial techniques. Our research has focused on two different problems in combinatorial scientific…

These days, multiplying two numbers together is a breeze. One just enters the two numbers into one's calculator, press a button, and there is the answer! It never used to be this easy. Generations of students struggled with tables of logarithms, and thought it was a miracle when the slide rule first appeared. In this article, the author discusses…

This study aimed at investigating the progress of students' learning on multiplication fractions with natural numbers through the five activity levels based on Realistic Mathematics Education (RME) approach proposed by Streefland. Design research was chosen to achieve this research goal. In design research, the Hypothetical Learning Trajectory…

The maturation of multiplicative thinking is key to student progress in middle school as rational number, ratio, and proportion concepts are encountered. But many students arrive from the intermediate grades and falter in developing this essential disposition. Elementary students have historically learned multiplication and division as operation…