This paper explores Year 3 Irish students' problem-solving strategies when responding to a skyscraper growing pattern problem. Students' strategies reveal their understandings of multiplicative thinking, pattern, and algebraic reasoning. The version of the growing pattern lesson was that a 'teaching through problem solving' approach was taken,…

This paper reports on 73 Grades 3 to 6 students' written responses to equal groups, arrays, multiplicative comparison and Cartesian product word problems. It is part of a larger study relating to students' development of multiplicative thinking (MT). The potential of using multiplicative word problems as a diagnostic assessment to reveal students'…

In mathematics, there are four basic operations that students must master from the elementary school level, namely addition, subtraction, multiplication, and division. However, some students experience difficulties or misunderstandings in interpreting multiplication as repeated addition. This research aims to improve the learning outcomes of…

When teaching the multiplicative domain in New Zealand primary schools, teachers tend to spend a greater proportion of time on the meaning and processes of multiplication, to the detriment of a specific focus on understanding the concept of division. When division is taught, it tends to be by reversing the context and turning the division…

The Times Tables Drill, in which students recite multiplication facts at high speed, is based on a 200 year-old American military education practice. Emphasising "commands," "obedience," "rules," "silence," "separation," "surveillance," "speed," "competition,"…

The array is a powerful tool that builds students' understanding in multiplication. Students' interactions with the array changes through the course of an instructional sequence, which can be viewed as a process of "reification." In this paper, I report the findings of a research study conducted with 45 Year 5 students in Sydney. The…

Problem solving and reasoning are two key components of becoming numerate. Reports obtained from international assessments show that Australian students' problem solving ability is in a long-term decline. There is little evidence that teachers are embracing problem solving as part of the classroom routine. In this study, we analyse 598 Year 7 to…

Understanding the concept of area requires an understanding of the relationship between geometry and multiplication. The multiplicative reasoning required to find the areas of regular figures is used in many courses in elementary mathematical education. This paper explores various methods in which multiplicative reasoning is incorporated into the…

In the body of knowledge in mathematics education research, fractions are one of the researchers' concerns. The reason is because fractions are very difficult for students to understand. This study explores elementary school students' knowledge and obstacles in dealing with the multiplication of fractions. This study employs descriptive…

In this study we investigated the structure of quantitative competence of kindergartners by testing a hypothesized four-factor model of quantitative competence consisting of the components counting, subitizing, additive reasoning and multiplicative reasoning. Data were collected from kindergartners in the Netherlands (n = 334) and in Cyprus (n =…

Progressing from additive to multiplicative thinking is a key outcome of school mathematics, making ratios an essential topic of study in junior secondary. In this study, 15 Australian Year 8 students were administered a ratio test followed by semi-structured interviews to explore their conceptions of ratio prior to formal instruction. In this…

A one-on-one dialogue-based mathematics intelligent tutoring system (ITS) for learning multiplication and division of fractions was developed and evaluated in this study. This system could identify students' error types and misconceptions in real-time by using a block-based matching method. The adaptive dialogue-based instruction was supported by…

This study aims to develop a conceptual framework regarding practitioner knowledge and describe how one mathematics teacher generates her practitioner knowledge based on the framework. The characteristic of this framework is a combination of static and dynamic aspects of knowledge based on the teacher's perception and interpretation. The research…

The aim in the current study is to examine the conceptualizations of zero in arithmetic operations among students with learning disabilities (LD) and no learning disabilities (N-LD). The similarities and differences in the understandings of students with LD and N-LD of zero in arithmetical operations will be discussed. The study is a multiple case…

In this paper, we have tried to clearly explain the meaning of fractions and operations with fractions. Also, we have tried to illustrate with some examples how to apply the rules of operations with fractional numbers, giving different practical techniques through different figures, visualization methods, and concretizing problems. The paper…