Several factors seem important to understand the nature of mathematical learning. Byrnes and Miller combined these factors into the Opportunity-Propensity model. In this study the model was used to predict the number-processing factor and the arithmetic fluency in grade 4 (n = 195) and grade 5 (n = 213). Gender, intelligence and affect (positive…

Previous research has demonstrated how young children can identify the signal in data. In this exploratory study we considered how they might also express meanings for noise when creating computational models using recent developments in software tools. We conducted extended clinical interviews with four groups of 11-year-olds and analysed the…

The authors of this article strongly advocate for a change to the current Australian model of primary education in order to, among other things, establish the concrete practicalities of systematic mathematics thinking thereby limiting the "re-teaching" time required of secondary school mathematics teachers; bring a clear focus to the…

One of the main tasks in teaching mathematics to elementary students is to form calculating methods and techniques. The efforts of teachers and methodologists are aimed at solving this problem. Educational and psychological research is devoted to it. At the same time school teaching experience demonstrates some difficulties in learning methods of…

The following report describes an assessment instrument called the Mathematics Performance and Cognition (MPAC) interview. The MPAC interview was designed to measure two outcomes of interest. It was designed to measure first and second graders' mathematics achievement in number, operations, and equality, and it was also designed to gather…

This report provides an overview of the development, implementation, and psychometric properties of a student mathematics interview designed to assess first- and second-grade student achievement and thinking processes. The student interview was conducted with 622 first- or second-grade students in 22 schools located in two public school districts…

The intention of the present study is to know how the pupils can learn to make a group of ten to understand the idea of unitizing. The pupils were given a contextual problem "Counting the Beads" in order to promote their understanding about the idea of unitizing. The process of designing the problem was based on the 5 tenets of…

In line with design research, the use of Bermain Satu Rumah (BSR) as traditional game to support children's counting classroom wherein students are encouraged to construct mathematical understanding. Number in traditional games is an interesting aspect that is helpful for children to encounter numerous situations that bring them into contact with…

"Number Talks" is: (1) A five- to fifteen-minute classroom conversation around purposefully crafted computation problems that are solved mentally; and (2) The best part of a teacher's day. Whether you want to implement number talks but are unsure of how to begin or have experience but want more guidance in crafting purposeful problems, this…

Theories that explain the gender discrepancy in mathematics almost universally explain why boys are "better at math" than girls while failing to adequately account for girls' higher grades in math classes or better performances on tests of computational ability. This article develops a new, more comprehensive theoretical model that explains girls'…

Proposes a framework that identifies the components of number sense and the attributes of students who possess it. Discusses various aspects of three areas where number sense plays a key role: number concepts, operations with numbers, and applications of number and operation. (MDH)

This article challenges the traditional model for teaching computation in the primary grades. It describes a model in which students are encouraged to invent and use alternative computation procedures.

This report presents a theory of eye movement that accounts for main features of the stochastic behavior of eye-fixation durations and direction of movement of saccades in the process of solving arithmetic exercises of addition and subtraction. The best-fitting distribution of fixation durations with a relatively simple theoretical justification…

Students in grades 1, 3, 4, 5, 6, and college were timed as they produced the answers to simple addition problems or verified a given problem as true or false. First graders clearly relied on a counting process for their performance, as advanced by the Groen and Parkman "min" (for minimum addend) model. Third grade appears to be a…

An intensive, naturalistic study tracked one six year old's learning for six months and more. The study was inspired by the hope that with concepts of Artificial Intelligence and sufficiently detailed observation, the path of knowledge development could be described through observing significant learning experiences. Included is a reasonably…