This paper draws upon the sociology of numbers, particularly work by Theodore Porter, to reveal the multifarious ways in which numbers actively constitute practices in schools. Drawing upon a case study of one low-performing school in a low-performing region in the state of Queensland, Australia, and theorising into the sociology of numbers, the…

The present study evaluated 626 5-7-year-old children in the UK, China, Russia, and Kyrgyzstan on a cognitive test battery measuring: (1) general skills; (2) non-symbolic number sense; (3) symbolic number understanding; (4) simple arithmetic--operating with numbers; and (5) familiarity with numbers. Although most inter-population differences were…

This study aims to investigate how set model can help students' understanding of addition of integers in fourth grade. The study has been carried out to 23 students and a teacher of IVC SD Iba Palembang in January 2015. This study is a design research that also promotes PMRI as the underlying design context and activity. Results showed that the…

This paper investigates how the selected three East Asian countries--Japan, Korea, and Taiwan-- introduce and develop ideas related to fractions and fraction addition and subtraction compared to the Common Core State Standards of Mathematics and EngageNY. Looking at curricular approaches used across countries can provide a better picture of what…

The three purposes of this study were to (a) describe fraction ordering errors among at-risk fourth grade students, (b) assess the effect of part-whole understanding and accuracy of fraction magnitude estimation on the probability of committing errors, and (c) examine the effect of students' ability to explain comparing problems on the probability…

Algorithms and representations have been an important aspect of the work of mathematics, especially for understanding concepts and communicating ideas about concepts and mathematical relationships. They have played a key role in various mathematics standards documents, including the Common Core State Standards for Mathematics. However, there have…

The ubiquity of the subject of percentages in our everyday life demands that math teachers and pre-service math teachers demonstrate a profound knowledge and thorough understanding of the concept of percentages. This work, which originated from one specific lesson in an 8th grade math class, studies the conceptual understanding and problem-solving…

A "repeating pattern" is a cyclical repetition of an identifiable core. Children in the primary grades usually begin pattern work with fairly simple patterns, such as AB, ABC, or ABB patterns. The unique letters represent unique elements, whereas the sequence of letters represents the core that is repeated. Based on color, shape,…

This chapter situates fraction learning within the integrated theory of numerical development. We argue that the understanding of numerical magnitudes for whole numbers as well as for fractions is critical to fraction learning in particular and mathematics achievement more generally. Results from the Delaware Longitudinal Study, which examined…

We interviewed 40 students in Grade 7 to investigate their integer reasoning. In one task, children were asked to write and interpret equations related to a story problem about borrowing money from a friend. Their responses reflect different perspectives concerning the relationship between this real-world situation and various numerical…

This study tried to explore the degree of representation of math textbooks for grades (4-8) in the Kingdom of Saudi Arabia concerning the key concepts, shape, and levels of questions used in the TIMSS test. The study population of this study includes both students and teachers from fourth grade to eighth grade. The goal of this study was…

These proceedings are a written record of the research presented at the 42nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in Mazatlán, Mexico, virtually beginning May 27, 2021 and in-person June 2-6, 2021. The conference was originally scheduled to take place…

Students with learning disabilities (LD) consistently struggle with word problem solving in mathematics classes. This difficulty has made curricular, state, and national tests particularly stressful, as word problem solving has become a predominant feature of such student performance assessments. Research suggests that students with LD perform…

At the start of the Kindergarten year in New South Wales (NSW) government schools, teachers gather information on several aspects of children's number knowledge to guide their teaching programs. This includes knowledge of the sequence of words used for counting, numeral identification, and using counting to solve problems. This study investigated…

This paper reports on a portion of a research study that examined the development of 43 preservice elementary school teachers' conceptual understanding of place value, and highlights the experiences of one middle-performing preservice teacher. After participating in a research-based constructivist unit of instruction in place value, the findings…