This qualitative research study uses middle-grades students' numerical reasoning to model their symbolic representations of the relationship between two multiplicatively related unknowns on an algebra task. Students in sixth grade through ninth grade participated in clinical interviews that assessed their numerical reasoning using the Number…

The algorithm for fraction multiplication is relatively easy to memorize and implement with accuracy. The simplicity of the algorithm masks the conceptual complexity involved in making sense of what fraction multiplication means in quantitative situations. One important interpretation of fraction multiplication involves fraction composition,…

This study presents the preliminary qualitative results of a larger mixed methods study. The qualitative phase utilized task-based clinical interviews to examine the non-symbolic and symbolic linear generalizations of middle-grades students. This investigation identified similarities and differences in the students' generalizations, and…

This study aimed to investigate eighth-grade students' mathematical communication competency and mathematical literacy performance in a classroom experiment designed based on the mathematical modeling approach. Accordingly, a teaching experiment methodology was applied. Data were collected from three eighth-grade students through the Mathematical…

Nationally and internationally, teachers are being held increasingly accountable for student achievement, particularly in light of high stakes literacy and numeracy tests. Policies have been implemented that are designed to improve educational outcomes through raising student literacy levels across all school years in all subject areas. This has…

This paper draws on numerous data sources to better understand the shift from additive to multiplicative thinking in years 4 to 9. Research studies that have used the Scaffolding Numeracy in the Middle Years assessment tasks have found that while students can be supported to move through the early and upper zones of the Learning and Assessment…

The purpose of the study was to explore the effects of focused numeracy instruction on the ratio in a middle school mathematics class and the lived experiences of students with special needs as they underwent the intervention. The intervention focused on using numeracy embedded into the intervention, specifically focusing on rational number…

Culture and language play important roles in counting techniques, affecting how students learn math around the globe.

It is well accepted and understood amongst the mathematics education community that numeracy is the responsibility of all teachers, across all levels of schooling. However, the way numeracy is understood and actioned across the Early Childhood, Primary and Secondary contexts is different. This paper reports on a case study of secondary school…

Improving children's "number sense" has been a core component of recent mathematics curricular and instructional reforms (CCSS, 2010; NCTM, 2000, 2014) in the United States. Students with mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly select the most effective and efficient…

Success in math is important to all students; it provides them with college and career options in the fields of science, technology, engineering, and mathematics. In the middle grades, students build upon the critical skills taught in elementary school and prepare for entry into algebra, which is considered a gateway to later achievement in school…

Numerical magnitude knowledge is related to current math abilities and predictive of future math learning. However, this relationship has previously been shown only for knowledge of positive magnitudes; the present study is the first, to our knowledge, to examine the connection between magnitude knowledge and math ability with negative integers.…

The capacity to recognise, represent, and reason about relationships between different quantities, that is, to think multiplicatively, has long been recognised as critical to success in school mathematics in the middle years and beyond. Building on recent research that found a strong link between multiplicative thinking and algebraic, geometrical,…

This paper analyzes factors that affect the numeracy skills of secondary school students from mountainous and ethnic minority regions in Vietnam from the perspective of the students to create suitable strategies for teachers, parents, and the government to enhance their numeracy skills. Data from 755 students in 8 secondary schools in 8 provinces…

If teachers have a deeper comprehension of their students' reading ability, it may lead to students' improved literacy and understanding of the subject. The account presented in this article of the author's growing interest in mathematical literacy specifically involves mathematical reading. This shift in interest began with a six-week…