Children learn the cardinalities of the first numbers one, two, three and four before they learn how counting tracks cardinality for all numbers. It may be that when children start to understand counting, they also discover how numbers relate to one another in a structured number system. Do children who understand that the cardinality of a set is…

Early mathematics education presents middle-school students with the challenge of adding and subtracting negative integers. This paper reports on results from the experimental implementation of a proposed educational design for integer arithmetic that utilized the number-line (NL) form as a resource for students to enact simple addition and…

Although absolute value is of interest to mathematics teaching researchers, since many students face problems with it, there does not seem to be an integrated record of students' errors. The present study attempts to conduct a systematic review to identify and categorize errors and misconceptions of secondary school students aged 12-18 concerning…

Experimental research on perception and cognition has shown that inherent and manipulated visual features of mathematics problems impact individuals' problem-solving behavior and performance. In a recent study, we manipulated the spacing between symbols in arithmetic expressions to examine its effect on 174 undergraduate students' arithmetic…

This article analyzes a popular arithmetic textbook, "Arithmetic: For the Use of Schools and Colleges," authored by Jadav Chandra Chakravarti, to examine the contents and pedagogies in the text for how mathematics was taught and learned from the end of the nineteenth century through the first half of the twentieth century in colonial…

Mental brackets constitute an idiosyncratic use of brackets sometimes used to evaluate arithmetic expressions and are closely connected with students' structure sense. The relevant literature describes the use of mental brackets focusing on primary school students and in the context of arithmetic. Using 181 high school students' solutions to seven…

This article presents several mathematics problems on the same theme that can be used in class or for independent study. It is very difficult to show students how mathematics research is done by mathematicians, so the author first introduces a problem that can be tackled solely by arithmetic and then gives an idea of how a mathematician might…

Successful word problem performance often requires understanding the linguistic relations between characters and objects. However, the keyword method promotes associating specific words with mathematical operations while neglecting the situational context. Research has thoroughly investigated the detrimental effects of individuals associating…

Early mathematics plays an important role in introducing foundational concepts for number sense in children. One of the critical areas of learning is the establishment of a linear view of numbers. It is essential to create opportunities for young children to understand that numbers are equally spaced on the number line and that they increase in…

The goal of the present study was to test theories about the extent to which individual differences in word reading align with those in spelling and the extent to which other cognitive and linguistic skills play different roles in word reading and spelling. Using data from 1,116 children ranging from 8 to 17 years, we modeled word reading and…

Problem-solving is a key aspect of mathematics instruction. Although it is part of several national curricula, its implementation is still being vastly explored. The present research, which is part of a larger project, aimed to investigate the effect of using problem-oriented instruction in grade 3 of primary school on students' mathematical…

Primary school textbooks can enhance the acquisition of arithmetic word problem solving skills by offering diverse problems based on their semantic-mathematical structure with targeted reasoning aids, including schematics highlighting their mathematical structure. While certain countries, such as the USA and Singapore, have made progress in…

Although there have been a huge number of attempts to improve school algebra teaching, several countries are still struggling to improve students algebraic skills. In this study, we focus on the specific case of Sweden where students for several decades have had major problems mastering algebra. In order to get a better understanding of the…

Early arithmetic skills, and in particular the understanding of the part-whole relationship, are currently considered crucial for future arithmetic achievement. They are complex skills extending far beyond the mastery of counting procedures. In order to develop these arithmetic skills in kindergarten children, we developed a game-based approach…

This article reports on an empirical study that investigates the way students' performance in solving arithmetical tasks may be related to their performance in solving algebraic tasks. The sample consisted of 203 Grade 6 students. The arithmetical tasks involved arithmetical expressions with known quantities, whereas the algebraic tasks involved…