We present an external close replication of the 1985 Fischbein et al. study about intuitive models of multiplication and division. We administered two batteries of mathematics items developed in the original study, via a spiralling process, to a quota sample of 903 students attending grade 7. Compared with the analytic strategy based on the count…

Visuospatial representations of numbers and their relationships are widely used in mathematics education. These include drawn images, models constructed with concrete manipulatives, enactive/embodied forms, computer graphics, and more. This paper addresses the analytical limitations and ethical implications of methodologies that use broad…

Mathematical definitions are central to learning and doing mathematics. Research has uncovered significant differences between how mathematicians and non-mathematicians construct, reason about, and refine mathematical definitions. Various strands of research provide insight into the development of definitional practices, yet an integrated approach…

Early years mathematics textbooks are support material for teachers and learners as they contain visual representations which communicate and clarify mathematical concepts. In this paper, we report on the types and functions of visual representations of multiplication and division in South African early years mathematics textbooks. There seems to…

This study aims to investigate the effect of history-of-mathematics activities on the development of mental computation of middle-grade students and to determine the students' views on the history of mathematics. This study was carried out as an action research project. The participants of the study consisted of 19 seventh-grade students studying…

In the current study, it is aimed to determine the activities that need to be done to eliminate the mistakes made by primary school fourth grade students in multiplication and division operations and to present solution suggestions for eliminating these mistakes. The study employed action research, one of the qualitative research methods. The…

The aim of this study is to investigate Danish pre-service teachers' (PSTs) mathematical and didactical knowledge of operations with rational numbers. This knowledge is studied through their collaborative activities to certain tasks related to the teaching of operations with rational numbers. An explicit model of the teachers' mathematical and…

The aim of this study was to determine learning difficulties and misunderstanding in multipliers and factors of middle school students in Kayseri, Turkey. One hundred and seven students from 6th grade and 48 students from 8th grade were selected randomly from three middle schools for the study. A questionnaire, which was developed by the first…

Many educators face the challenge of engaging students in science and mathematics, often struggling to bridge the gap between theoretical concepts taught in classrooms and their real-world applications. This disconnect can lead to disinterest and disengagement among students, hindering their learning outcomes. "Cases on Informal Learning for…

Elementary number theory is a standard topic in the mathematical preparation of preservice elementary teachers. To understand elementary number theory, a student must be comfortable with the representation of natural numbers as the product of primes. This paper discusses methods for accomplishing this goal in a mathematics course. It also…

Presents an analysis of young students' development of multiplication and division concepts based on a multimodal Structure of the Observed Learning Outcome (SOLO) model. Describes a SOLO developmental model for multiplication and division in terms of developing structure and associated counting and calculation strategies. Contains 48 references.…

A model for fractions derived by an operation of "scattering into subunits" is hypothesized. Five stages in the model are discussed. Assumptions underlying the development of the model, features of the model, and disadvantages of the model are listed. (DT)

Proposes a four-category classification of semantic structures of one-step word problems involving multiplication and division: forming the n-th multiple of measures, combinatorial multiplication, composition of operators, and multiplication by formula. This classification is compatible with semantic structures of addition and subtraction word…

The effects of several variables on the ability of students to solve open sentences involving multiplication and division were examined. The variables considered were sex, grade level, position of the unknown in the sentence, and operation. (SD)