We investigated the influence of self-efficacy beliefs and working memory capacity on mathematical problem-solving performance, response time, and efficiency (i.e., the ratio of problems solved correctly to time). Students completed a letter-recoding task (Experiment 1) or an operation span task (Experiment 2), rated their self-efficacy for…

This paper presents the row-column multiplication of rhotrices that are of high dimension. This is an extension of the same multiplication carried out on rhotrices of dimension three, considered to be the base rhotrices.

When the word problems of forty-five sixth-grade students were examined, multiple levels of understanding and misunderstanding multiplication were exposed. The purpose of this article is to demonstrate the potential of problem writing as a technique for assessing the depths of students' mathematical understandings. Discussions include sample…

In line with current efforts to understand the piece-by-piece structure and articulation of children's mathematical concepts, this case study compares the reversibility schemes of two eighth-grade students. The aim of the study was to identify the mechanism through which students reverse their thought processes in a multiplicative situation. Data…

Children's understanding of the inversion concept in multiplication and division problems (i.e., that on problems of the form "d multiplied by e/e" no calculations are required) was investigated. Children in Grades 6, 7, and 8 completed an inversion problem-solving task, an assessment of procedures task, and a factual knowledge task of simple…

This experimental mixed method study examined the effect of memorization of multiplication tables on students' performance in math at the high school level. Students took a diagnostic multiplication test and a comprehensive assessment in various mathematics topics. The study used two methods of testing and similar instruments. In the first,…

This quasi-experimental study aims to streamline cognitive models on fraction multiplication and division that contain the most worthwhile features of other existing models. Its exploratory nature and its approach to proof elicitation can be used to help establish its effectiveness in building students' understanding of fractions as compared to…

Can teachers contact the inner coherence of mathematics while working in a context fragmented by always-new objectives, criteria, and initiatives? How, more importantly, can learners experience the inner coherence of mathematics while working in a context fragmented by testing, modular curricular, short-term learning objectives, and lessons that…

Introduction: In the present-day didactic process of transition from natural numbers to integers, a certain kind of measure is involved which is neither easy nor appropriate to integrate into the familiar numerical systems. We refer to measures and comparisons for which we need a third numerical system--what we will call "relative…

Adaptive learning techniques have typically scheduled practice using learners' accuracy and item presentation history. We describe an adaptive learning system (Adaptive Response Time Based Sequencing--ARTS) that uses both accuracy and response time (RT) as direct inputs into sequencing. Response times are used to assess learning strength and to…

This article shows how a matrix can be used to represent a food chain and how the square of this matrix represents the indirect food sources for each animal in the chain. By exploring, through mathematics, the implications when the bottom of the food chain is destroyed, students will see an important connection between mathematics and science.…

In this third of a series of four articles, the author deconstructs the primary national strategy's approach to written multiplication. The approach to multiplication, as set out on pages 12 to 15 of the primary national strategy's "Guidance paper" "Calculation" (DfES, 2007), is divided into six stages: (1) mental…

This study examined effectiveness of simultaneous prompting system in teaching students with cognitive impairment to automate recall of multiplication facts. A multiple probes design with multiple sets of math facts and replicated across multiple subjects was used to assess effectiveness of simultaneous prompting on recall of basic multiplication…

Ways of teaching multiplication to elementary school students. (CK)

An important issue in knowledge acquisition is how children generate concepts from the stream of regularities in the environment. One theoretical approach to this issue (theory-revision) proposes that children generate initial hypotheses about relations in the environment and modify those hypotheses in response to error. A second approach…