On the surface, the number line may seem like a basic tool with obvious applications. However, using a number line is not always intuitive for students. Students may not recognize significant features such as the size of the unit, how units are represented by iterated equal lengths, or that the accumulation of iterated units is a magnitude of…

Contribution: This article compares student success via different pathways in which students take mathematics courses required for engineering degrees. Background: Mathematics courses are an integral part of engineering curriculum. Many institutions require or recommend the order in which students take Calculus II, Multivariable Calculus,…

The ability to interpret mathematical symbols and understand how they capture contextual relationships is a critical element of algebraic thinking. More often than not, students see algebra as merely a list of rules for manipulating abstract symbols, with limited to no meaning. Instead, for students to see algebra as a powerful tool and rich way…

This article describes an instructional sequence used with inservice secondary mathematics teachers as part of a graduate course. The instructional sequence focused on designing tasks using Interactive Geometry Software (IGS). This study answers a call for replication studies to investigate the use of an established instructional sequence. Results…

The current paper overviews a nine-month PhD study that investigated the impact of learning mathematics through sequences of challenging tasks on the mathematical competence and attitudes of Year 2 students (n = 59). Adopting a Self-Determination Theory lens, a pragmatist paradigm and a mixed-method design, the study found that at all levels of…

Learning trajectories (LTs) can inform teaching by contributing a variety of pedagogical and content-related insights and strategies. They support sequencing topic introduction and development. Because ideas evolve gradually and often rely on a careful introduction of new representations, operations, cases of numbers, structures, and definitions,…

Does one approach fit all when it comes to curriculum design? In debates on curriculum design, educators have argued that a curriculum model should take into account the differing knowledge structures of different subjects. Subjects such as maths and science are generally defined as well-structured knowledge domains, characterised by a linearity…

In modern information societies, evaluating information, data, or knowledge claims is crucial. As these activities are influenced by epistemological beliefs, such beliefs are a key element of education in the sense that educational institutions intend to prepare students for professional and social life. Hence, this study aims to examine the…

The aim of this study is to investigate the concept knowledge about the limits of sequences of mathematics teacher candidates. Research is a case study in which qualitative methods are adopted. The first phase of the study was conducted with a total of 45 teacher candidates taking the course of Analysis III. At this stage, the "Limit…

This chapter considers difficulties with traditionally organized developmental math course sequences from the literature and practice. We then report initial student success findings following the system-wide implementation of a corequisite model in developmental math.

The foundation of geometric knowledge and understanding starts in primary school, and in contemporary mathematics education there is an emphasis on identifying learning progressions and trajectories as a way of moving students forward. The van Hiele (1986) theory is well-documented and provides insights into the progression and differences of…

K-12 students are expected to acquire competence in data display as part of developing statistical literacy. To support research, assessment design, and instruction, we developed a hypothesized learning progression (LP) using existing empirical literature in the fields of mathematics and statistics education. The data display LP posits a…

Scholars propose that contextual problems can be used to ground students' understanding of mathematical ideas, and recent curricular trends have resulted in a plethora of resources that introduce and develop new mathematical ideas through contextual problems (CPs). Given the tension between this approach and the traditional role of CPs as…

This article describes features of NAUTeach, a secondary mathematics teacher preparation program that is modeled on the UTeach program at the University of Texas-Austin. NAUTeach is a research-based STEM program that develops the next generation of mathematics and science teachers by engaging them in rigorous content and methodology coursework…

This study highlighted the characteristics and patterns of preservice teachers' informal formative assessment conversations woven into mathematics classrooms. Participants were four preservice teachers from an elementary mathematics methods course whose videotaped lessons were analyzed using an analytic framework based on Initiation, Response and…