Children's arithmetic performance is dependent on the arithmetic task format, but little is known about how domain-specific and domain-general abilities contribute to solving diverse arithmetic problems. In this study, 145 Italian typically developing children between the ages of five and six, who have not yet received formal schooling, were…

Programming is an interdisciplinary practice with applications in both mathematics and computer science. Mathematics concerns rigor, abstraction, and generalization. Computer science predominantly concerns efficiency, concreteness, and physicality. This makes programming a medium for problem solving that mediates between mathematics and computer…

The ability to recognize one's learning processes is important for learning mathematics as it helps learners to practice the thinking process of how each element works in solving mathematics problems. The K-W-D-L technique has emerged as a technique that could bring about metacognition in learning and it could be beneficial in elementary school…

In this article, we present research on eight kindergarten and eight first-grade students' understandings of the arithmetic properties of commutativity, additive identity, and additive inverse during a classroom teaching experiment, selected from a larger study that included 88 students. In this study, we explore the students' types of…

Symbolic and situational mathematics are the two major representations of mathematical knowledge. Although previous literature has studied the relationship between the two from the perspective of teaching practice, learning effectiveness and behavioural performance, there is still a lack of empirical psychological research on cognitive mechanisms…

What is the nature of the relationship between different lower-level numerical skills and their role in developing arithmetic skills? We consider the hypothesis of a reciprocal relationship between the development of symbolic (e.g., Arabic numerals) and nonsymbolic (e.g., arrays of objects) numerical magnitude processing. Evidence for…

This paper focuses on determining the opinions of primary school third-grade pupils about the conceptual meaning and use of the numbers "0" and "1". The current study employed the case study design, which is one of the qualitative research methods. In the selection of the sample, the criterion sampling method, one of the…

This paper aims to characterise an indicator of the development of the number sequence scheme among students at the level of Compulsory Secondary Education (14-16 years old students). To do so, we use a scheme development proposed by the APOS theory to characterise students' use of relations between mathematical elements when solving a…

This paper resulted from an unfolding of an ongoing doctoral research that deals with the characterization of a specific type of arithmetic in times of Brazilian industrial education, that is, between 1942 and 1968. The objective is to analyze knowledge produced by Roberto Mange for training, aiming not only to recognize them as such, but also to…

The study determined the arithmetic verbal problem solving skills of primary school students and to examine them according to grade level and mathematics achievement variables. The study was designed according to the relational survey model, one of the quantitative research methods. The population of the research consists of students studying in…

Socioeconomic status (SES) has been shown to be associated with children's arithmetic knowledge as early as kindergarten, which is an important issue, given that early numeracy knowledge and skills usually correlate to later academic achievement in arithmetic. In line with recent research, it is argued that the regular practice of exercises…

The aim of this study was to investigate second-grade elementary school students' performance related to their counting skills, place value understanding, and addition operation in natural numbers. A total of 205 second-grade elementary school students from Turkey participated in this study. The data were collected through a 'Personal Information…

This article aims to outline the important role of the summary phase within a mathematics instructional model and provide six strategies to support teachers to move beyond "share time." By drawing upon good teaching strategies during the summary phase, teachers can enhance the learning experience for themselves and for their students.…

Imbalances in problem distributions in math textbooks have been hypothesized to influence students' performance. This hypothesis, however, rests on the assumption that textbook problems are representative of the problems that students encounter in classroom assignments. This assumption might not be true, because teachers do not present all…

In this study we aimed to inquire into the impact of the use of early arithmetic strategies by a group of fifth-grade students, on their solving of equations involving two representations of unknowns. Pre- and post-tests consisting of equation-solving items involving two representations of unknowns (number sentences containing empty 'brackets', as…