Developing both conceptual and procedural knowledge is important for students' mathematics competence. This study examined whether U.S. Grade 9 general education mathematics teachers' self-reported use of concept-focused instruction (CFI) and procedure-focused instruction (PFI) were associated differently with ninth graders' algebra achievement…

This autobiographical study of teaching and learning Algebra 1 was developed to examine classroom experiences through the lens of the researcher and to explore the perceptions of teachers and students involved in the study. The goal was to identify the quality, meaningful educational experiences in the classroom which led to the development of…

There is an ongoing need to support students' learning of linear functions, and the study of slope makes up a foundational component of this learning. We applied techniques from systemic functional linguistics to document the meanings that were established through spoken interaction between a student and her tutors during discussions of slope. We…

We present the results of a research project on arithmetic-algebraic thinking that was carried out jointly by a team in Mexico and another in Quebec. The project deals with the concepts of variable and covariation between variables in the sixth grade at the elementary level and the first, second, and third years of secondary school--namely,…

Fractions are troublesome for many children, especially students with learning difficulties and disabilities in mathematics. To address this serious educational concern, this article recommends the use of number lines to build fraction sense. Math activities that center on the number line build fraction concepts as early as third grade. A number…

Cara, a seventh-grade student with learning disabilities (LD) in mathematics, believes that the ratio 2:3 is equivalent to 4:5 because there is a difference of one between the two numbers in each ratio and there is a difference of two between corresponding numbers in the two ratios (2 + 2 = 4 and 3 + 2 = 5). This misconception affects her ability…

Ratios and proportions are foundational to student understanding across multiple topics in mathematics and science. In mathematics, they are central to developing concepts and skills related to slope, constant rate of change, and similar figures, which are all fundamental to algebraic concepts and skills. This article examines the importance of…

The National Council of Teachers of Mathematics (2012) and the Council for Exceptional Children (CEC; 2012) have stressed the importance of all students learning algebra. CEC stated that there was a crucial need for algebra instruction and intervention that can help students with disabilities in the general education classroom. Algebra is…

The aim of this study was to examine prospective mathematics teachers' proof processes for algebraic concepts. The study was conducted with 10 prospective teachers who were studying at the department of secondary mathematics teaching and who volunteered to participate in the study. The data were obtained via task-based clinical interviews…

This research study investigates how pre-service teachers integrate statistical content, students' thinking, and pedagogy as they examine how 11- to 12-year olds develop mathematically. The findings provide insights into: a) how pre-service teachers identify some of the difficulties that students commonly have, and b) what pedagogical approaches…

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document "Improving Mathematics in Key Stages Two and Three" (Education Endowment Foundation, 2017). The review draws on a substantial parallel study by the same research team, funded by the Nuffield Foundation, which…

The authors completed a narrative review of studies of mathematics interventions from 1996 to 2010 for helping elementary school students with difficulties in mathematics solve word problems. Key instructional components supported by research are teaching cognitive and metacognitive skills; schema-based instruction focusing on semantic analysis,…

This volume, a comprehensive survey and critical analysis of today's issues in mathematics education, distills research to build knowledge and capacity in the field. The compendium is a valuable new resource that provides the most comprehensive evidence about what is known about research in mathematics education. The 38 chapters present five…

Students who have particular difficulty in mathematics are a growing concern for educators. Graphic organizers have been shown to improve reading comprehension and may be applied to upper level secondary mathematics content. In two systematic replications, one randomly assigned group was taught to solve systems of linear equations through direct…

We present a summary of a study carried out with students of the first year of Bachillerato (the first of two pre-university non-obligatory secondary education courses in Spain) to determine and analyse some of their errors and difficulties in learning inequalities with the aim of improving the teaching-learning process of this topic. The study…