Quantitative reasoning is defined as reasoning about relationships between items, measurements of objects, and quantities rather than numbers. Both in the transition from arithmetic to algebra and in the problem-solving process, quantitative reasoning is seen as a critical instrument for the development of students' mathematical skills. In the…

The overarching aim of this article is to exemplify and analyse how some algebraic aspects of equations can be theoretically explored and reflected upon by young students in collaboration with their teacher. The article is based upon an empirical example from a case study in a grade 1 in a primary school. The chosen lesson is framed by the…

Teaching students with Intellectual Disability (ID) is a relatively new endeavor. Beginning in 2001 with the passage of the No Child Left Behind Act, the general education curriculum integrated algebra across the K-12 curriculum (Kendall, 2011; National Governors Association Center for Best Practices & Council of Chief State School Officers,…

Practitioner research is in progress at a Further Education college to improve the motivation of vocational students for numeracy and problem solving. A framework proposed by Tang, Sui, & Wang (2003) has been adapted for use in courses. Five levels are identified for embedding numeracy applications and modelling into vocational studies:…

This paper provides a method for analysing undergraduate teaching of proof-based courses using Toulmin's model (1969) of argumentation. It presents a case study of one instructor's presentation of proofs. The analysis shows that the instructor presents different levels of detail in different proofs; thus, the students have an inconsistent set of…

University mathematics education (UME) is considered, in this paper, as a kind of "didactic practice"--characterised by institutional settings and by the purpose of inducting students into "mathematical practices." We present a research programme -- the anthropological theory of the didactic (ATD)--in which this rough…

This study investigated the ways in which four K-12 teachers, following professional development in blended learning, designed the online portion of their blended learning courses and how these online components were ultimately enacted with students. Specifically, the study investigates what kind of content, resources, or activities were developed…

This paper discusses the results of a three-year mixed methods study into the effectiveness of a mathematics education unit. This was written for both pre-service primary education students and re-training in-service teachers, to prepare them for the teaching of pre-algebra and early algebra. The unit was taught rom 2013 to 2015 inclusively in a…

This study addresses the problem of mathematics teachers' resistance to problem-solving models that align with constructivist perspectives because they feel pressure to utilize more teaching approaches that focus on preparing students for high-stakes tests. The purpose of this qualitative study was to explain how ninth grade mathematics students…

This paper discusses upper primary school teachers' perspectives on changes to their knowledge and practice through participation in a design-based research project. It analyses their experiences using Clarke and Hollingsworth's (2002) empirically-founded model for professional growth to understand more about the mechanisms for change that might…

Fostering algebraic thinking is an important goal for middle-grades mathematics teachers. Developing mathematical reasoning requires that teachers cultivate students' habits of mind. Teachers develop students' understanding of algebra by engaging them in tasks that involve modeling and representation. This study was designed to investigate how…

With passage of The No Child Left Behind Act in 2001, the nation's schools have been under pressure to bring all students to a proficient level as defined by their state. The State of California currently uses a status model accountability system to measure whether a student, school, or district is proficient. Other states such as Arizona,…

This paper examines the way two 10th graders cope with a non-standard generalisation problem that involves elementary concepts of number theory (more specifically linear Diophantine equations) in the geometrical context of a rectangle's area. Emphasis is given on how the students' past experience of problem solving (expressed through interplay…

Using a qualitative case study approach, this research explored the perceptions of middle school students on the role of their mathematics teacher in their success or failure to achieve in his mathematics classroom. Also, the study examined the teacher's perceptions of his role in the students' achievement. Further, the research explored the…

The Carnegie Learning Cognitive Tutor curricula are based on cognitive models, which include a representation of the learner's thinking, strategies, and misconceptions. The Cognitive Tutor curricula typically speed up learning and yield greater learning as compared to traditional math curricula (Morgan & Ritter, 2002; Sarkis, 2004; Koedinger,…