This design study investigated the use of multiplication and division problems to help 5-year-old children develop an early understanding of multiplication and division. One teacher and her class of 15 5-year-old children were involved in a collaborative partnership with the researchers. The design study was conducted over two 4-week periods in…

Over the last two decades, students in Singapore consistently scored above students from other nations on the Trends in International Mathematics and Science Study (TIMSS; Provasnik et al., 2012). In contrast, students in the United States have not performed as well on international and national mathematics assessments and students with…

The purpose of this study is to determine how Finnish pupils' problem-solving skills develop from the 3rd to 5th grade. As research data, we use one non-standard problem from pre- and post-test material from a three-year follow-up study, in the area of Helsinki, Finland. The problems in both tests consisted of four questions related to each other.…

This study, an education program was developed to improve addition-subtraction skills of 6-year old children using educational toys and smart boards. The program was implemented with children, and its effects on their operational skills were analysed. The study group of the research is composed of 90 children who attended preschool classes in…

PEMDAS is a mnemonic device to memorize the order in which to calculate an expression that contains more than one operation. However, students frequently make calculation errors with expressions, which have either multiplication and division or addition and subtraction next to each other. This article explores the mathematical reasoning of the…

A 3-week problem-solving practice phase was used to investigate concept-procedure interactions in children's addition and subtraction. A total of 72 7- and 8-year-olds completed a pretest and posttest in which their accuracy and procedures on randomly ordered problems were recorded along with their reports of using concept-based relations in…

Action research (AR) is defined by Macintyre to be: "an investigation, where, as a result of rigorous self-appraisal of current practice, the researcher focuses on a problem,or a topic or an issue which needs to be explained, and on the basis of information, plans, implements, then evaluates an action then draws conclusions on the basis of…

Two intervention studies are described. Both were designed to study the effects of teaching children about the inverse relation between addition and subtraction. The interventions were successful with 8-year-old children in Study 1 and to a limited extent with 5-year-old children in Study 2. In Study 1 teaching children about inversion increased…

The present research involved gauging preschoolers' learning potential for a key arithmetic concept, the addition-subtraction inverse principle (e.g., 2+1-1=2). Sixty 4- and 5-year-old Taiwanese children from two public preschools serving low- and middle-income families participated in the training experiment. Half were randomly assigned to an…

This instructional manual consists of 11 competency-based units for a mathematics course for trade and industrial programs in Texas. Each instructional unit includes the following basic components: unit and specific objectives, notes to the instructor (outline of steps to follow in accomplishing specific objectives), information sheets,…

This article explains how to teach long division using hands-on materials (skittles, base ten blocks, colored counters, numeral cards) and investigates reviewing division word problems with middle school students (N=27) with learning disabilities in mathematics by this approach compared to spending the same amount of time on the typical practices…

This study had the purpose of comparing the effects of two approaches in teaching mathematics to secondary special education students. The study attempted to answer the following questions: (1) Were there significant differences between group means of mathematics achievement test scores for students in a diagnostic-prescriptive mathematics program…