Many rules taught in mathematics classrooms "expire" when students develop knowledge that is more sophisticated, such as using new number systems. For example, in elementary grades, students are sometimes taught that "addition makes bigger" or "subtraction makes smaller" when learning to compute with whole numbers,…

For centuries, the basic operations of school mathematics have been identified as addition, subtraction, multiplication, and division. Notably, these operations are "basic," not because they are foundational to mathematics knowledge, but because they were vital to a newly industrialized and market-driven economy several hundred years…

Students with Autism Spectrum Disorders (ASD) have unique educational needs. The concrete representational abstract (CRA) instructional sequence has been shown effective in teaching students with mathematical difficulties. The purpose of this study was to examine the effects of the CRA sequence in teaching students with ASD. A multiple baseline…

This study aimed to create a constructivist learning environment wherein third-grade students talk to problem solve, which is different from traditional approaches to math learning. The study focused on the group talk and discussions to understand the students' actions and interactions during the process of problem-solving. Fifteen students and…

This research shows that people can unconsciously initiate and follow arithmetic rules (e.g., addition). Participants were asked to detect whether a symbol was a digit. This symbol was preceded by 2 digits and a subliminal instruction: "add" or a control instruction. Participants were faster at identifying a symbol as a number when the…

This is a report of a study of students' understanding of infinite series. It has a three-fold purpose: to show that students may construct two essentially different notions of infinite series, to show that one of the constructions is particularly difficult for students, and to examine the way in which these two different constructions may be…

The ability to count has traditionally been considered an important milestone in children's development of number sense. However, using counting (e.g., counting on, counting all) strategies to solve addition problems is not the best way for children to achieve their full mathematical potential and to prepare them to develop more complex and…

The aim of this study was to propose and validate a structural model in fraction and decimal number addition, which is founded primarily on a synthesis of major theoretical approaches in the field of representations in Mathematics and also on previous research on the learning of fractions and decimals. The study was conducted among 1,701 primary…

To better understand the role that ways of reasoning play in students' success on integer addition and subtraction problems, we examined the relationship between students' flexible use of ways of reasoning and their performance on integers open number sentences. Within groups of students in 3 participant groups--39 2nd and 4th graders who had…

We propose learning Matematika GASING to help students better understand the addition material. Matematika GASING is a way of learning mathematics in an easy, fun and enjoyable fashion. GASING is short for GAmpang, aSyIk, and menyenaNGkan (Bahasa Indonesia for easy, fun and enjoyable). It was originally developed by Prof. Yohanes Surya at the…

The authors asked fifth-grade and eighth-grade students to pose stories for number sentences involving the addition and subtraction of integers. In this article, the authors look at eight stories from students. Which of these stories works for the given number sentence? What do they reveal about student thinking? When the authors examined these…

This study examines students' procedural and conceptual achievement in fraction addition in England and Taiwan. A total of 1209 participants (561 British students and 648 Taiwanese students) at ages 12 and 13 were recruited from England and Taiwan to take part in the study. A quantitative design by means of a self-designed written test is adopted…

This paper analyses the strategies used by pre-service primary school teachers for solving simple addition problems involving negative numbers. The findings reveal six different strategies that depend on the difficulty of the problem and, in particular, on the unknown quantity. We note that students use negative numbers in those problems they find…

This study investigated the promotion of children's understanding and acquisition of arithmetic concepts and the effects of inhibitory skills. Children in Grades 3, 4, and 5 solved two sets of three-term addition and subtraction problems (e.g., 3 + 24 - 24, 3 + 24 - 22) and completed an inhibition task. Half of the participants received a…

The present study examined the relations between home numeracy experiences (i.e., parent-child numeracy activities and parents' numeracy expectations) and basic calculation skills (i.e., addition and subtraction) of children with Specific Language Impairment (SLI) and their peers with Normal Language Achievement (NLA), while taking into account…