Mastering single-digit arithmetic during school years is commonly thought to depend upon an increasing reliance on verbally memorized facts. An alternative model, however, posits that fluency in single-digit arithmetic might also be achieved via the increasing use of efficient calculation procedures. To test between these hypotheses, we used a…

In guiding students to construct a mathematical concept themselves, learning process should be started by a context which is suit with the concept. In this research, we focused on structured arrangement which was believed to be able to support students ages 8-9 years old developing splitting strategy in doing multiplication. This study was a…

The purpose of the present study was to examine the effectiveness of a constructive strategic training program on improving students' performance in solving multiplication problems. The participants were three third graders with math learning difficulties. In this teaching experiment design study, microgenetic approach was employed to analyze…

This project had two major goals: to determine the usefulness of individually-administered interview process to access elementary students' fluency with basic multiplication facts, and to determine whether a developmental sequence found in Australian mathematics education literature applied to elementary students in the United States. Students in…

Derivation of the law of radioactive decay is considered without prior knowledge of calculus or the exponential series. Calculus notation and exponential functions are used because ultimately they cannot be avoided, but they are introduced in a simple way and explained as needed. (Contains 10 figures, 1 box, and 1 table.)

We examined the effects of the Concrete-Representational-Abstract Integration strategy on the ability of secondary students with learning disabilities to multiply linear algebraic expressions embedded within contextualized area problems. A multiple-probe design across three participants was used. Results indicated that the integration of the…

The purpose of this study is to demonstrate how virtual manipulatives, designed to provide multimodal interactions, support richer perceptual experiences that promote conceptual learning. To study this phenomenon, a virtual manipulative called, "Puzzle Blocks," was developed by the researcher. "Puzzle Blocks" introduces the…

The "Extending Mathematical Understanding" (EMU) Program is a specialised mathematics program that aims to accelerate the learning of Grade 1 students who struggle with learning school mathematics. Forty-two students participated in an EMU Program in 2010 as part of the "Bridging the Numeracy Gap" (BTNG) project. Analysis of…

This article describes a pilot study in which pre-service elementary teachers (PSTs) used rectangular area models on base-10 grid paper to begin making sense of multiplication of decimal fractions. Although connections were made to multi-digit whole number multiplication and to the distributive property, the PSTs were challenged by interpreting…

The data used for the qualitative analysis reported here were generated as part of a larger study to understand and characterize teacher practice related to engaging students in algorithmic thinking associated with the fraction operations of addition, subtraction, multiplication and division. This paper presents ways in which teachers used…

I explore the impact of ambiguous referral to the unit on understanding of decimal and fraction operations during episodes in two different mathematics courses for pre-service teachers (PSTs). In one classroom, the instructor introduces a rectangular area diagram to help the PSTs visualize decimal multiplication. A transcript from this classroom…

What does it look like to "understand" operations with fractions? The Common Core State Standards for Mathematics (CCSSM) uses the term "understand" when describing expectations for students' knowledge related to each of the fraction operations within grades 4 through 6 (CCSSI 2010). Furthermore, CCSSM elaborates that…

Deficiencies in mathematics standardized test scores prompted school district policymakers to consider implementing a program designed to increase students' basic multiplication fact skills. This study was an evaluation of the Math Factual Operations for Understanding program. The program, marketed with a martial arts theme, was intended to…

Usually, multiplication is introduced to students to represent quantities that come in groups. However there is also rectangular array model which is also related to multiplication. Barmby et al. (2009) has shown that the rectangular model such as array representations encourage students to develop their thinking about multiplication as a binary…

We examined how a student with learning disabilities (SLD) in mathematics constructed a scheme for differentiating, selecting, and properly operating on/with units that constitute a multiplicative situation, namely, singletons ('1s') and composite units (abbreviated UDS). Conducted as part of a larger teaching experiment in a learning environment…