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…

Several previous researches showed that students had difficulty in understanding the basic concept of multiplication. Students are more likely to be introduced by using formula without involving the concept itself. This underlies the researcher to design a learning trajectory of learning multiplication using Permainan Tradisional Tepuk Bergambar…

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…

As curriculum scholars in South Africa express concerns about the failures of the outcomes-based curriculum policy that has been introduced post-apartheid it is of increased importance to try and understand the professional development that is required by teachers for its successful implementation. As a contribution to the development of such…

Background: The research on diagrammatic representations highlights their importance for the teaching and learning of mathematics. However, the empirical evidence to support their use in the classroom is mixed and somewhat lacking. Purpose: The aim of this study was to develop the use of diagrammatic representations of mathematical concepts in…

In order to give insights into cross-national differences in schooling, this study analyzed the development of multiplication and division of fractions in two curricula: "Everyday Mathematics" (EM) from the USA and the 7th Korean mathematics curriculum (KM). Analyses of both the content and problems in the textbooks indicate that…

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…

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…

Predictions of the Identical Elements (IE) model of arithmetic fact representation (Rickard, 2005; Rickard & Bourne, 1996) about transfer between arithmetic facts were tested in primary school children. The aim of the study was to test whether the IE model, constructed to explain adult performance, also applies to children. The IE model…

This paper reports on 13 Grade 3 students' approaches to "Equivalent groups" and "Times" as "many" multiplicative word problems. The findings are part of a larger study relating to children's development of multiplicative thinking. Of particular interest was the extent to which task level of difficulty influenced…

Learning the concept of perimeter and area is not easy for students in grade 3 of primary school. A common mistake is that students think that if the area is the same, the perimeter also has to be the same. It is difficult for them to understand that for a given area, there are many possibilities of perimeter and vice versa. When student are not…

The meaning of fractions with integer multiplication is something that is difficult to understand by students. They tend to think that the product it produces a larger number, while the multiplication of fractions with integers, the result can be any number larger or smaller. This study is a research design that aims to develop a local…

This paper discusses the impact of action research methodology used in the teaching and learning process and professional teacher development. In this study are including 58 students of three second grade classes, 3 teachers of those classes and a university professor. Aiming at using a different approach in their teaching of multiplication and…

The main purpose of the present study was to examine the long-term effects of a previous quasi-experiment that used inner speech as a tool to promote appropriate strategies in multiplication. Results one year after the intervention were published by Ostad and Askeland. This is a follow-up study. The 50-week intervention program was conducted in…