This study focuses on a case study that highlights the mathematical discourse developed by two pairs of students when dealing with a specific transition task, i.e., an activity leading to the construction of a graph of a function based on the exploration of another representation of the same function. Such a task was designed to work on the…

Taylor series play a ubiquitous role in calculus courses, and their applications as approximants to functions are widely taught and used everywhere. However, it is not common to present the students with other types of approximations besides Taylor polynomials. These notes show that polynomials construed to satisfy certain boundary conditions at…

The mathematics education community has affirmed the importance of writing in the mathematics classroom for a long time (e.g., National Council of Teachers of Mathematics [NCTM], 2000, 2014), and many examples exist of writing strategies or activities in mathematics learning (e.g., Altieri, 2009; Bixby, 2018; Carter, 2009; Gunter, 2016; Linhart,…

In this article, the authors share the story of Diego, a kindergarten student, navigating issues of mathematical identity and competence--his own and those of his kindergarten classmates. The authors are a team of educators, including a kindergarten teacher (Sara) and a math teacher educator (Jody) who worked together on a quality improvement…

Action-Process-Object-Schema (APOS) theory and the triad of schema development are used as the framework in this study to investigate students' understanding of the concept of "circle." In this report, results are presented from the data analysis of responses to questions in semi-structured interviews of 15 students enrolled in a college…

A productive understanding of rate of change concept is essential for constructing a robust understanding of derivatives. There is substantial evidence in the research that students enter and leave their Calculus courses with naive understandings of rate of change. Implementing a short unit on "what is rate of change" can address these…

Coordination of theoretical probability and relative frequency estimates is challenging in probability teaching and learning. Modeling is one of the ways of teaching and learning that facilitates inquiry between these two perspectives. Given that, we designed a modeling activity to support fifteen secondary students in investigating theoretical…

Creating sustained, transformative change within and across organizations is challenging, particularly when those undertaking change act as individuals. COMmunities of Practice (CoPs) are organically created collaborations among like-minded participants, working toward a common set of goals (Lave & Wenger, 1991; Wenger-Trayner &…

The relationship Terry and I developed as colleagues and friends illustrates elements of the legacy she leaves. Our overlapping research interests stimulated conversations about synergies and differences between our theoretical perspectives. Depending on the situation and purpose, these interactions possessed different characteristics. Terry…

Researchers have identified many ways that students think about rectangular area. However, research about students' understanding of triangle area is relatively scarce. Although it may seem simple to apply the triangle area formula, there is more to students' understanding of triangle area. In this dissertation, I obtained data to help answer the…

The National Council of Teachers of Mathematics (NCTM) promotes creating resources that build procedural fluency from conceptual understanding through intentionally sequenced tasks that draw on students' prior knowledge and move from simple, concrete representations to more complex and abstract representations (Boston et al., 2017). Liljedahl…

This paper reports on university students' responses to an inverse proportion question. The authors conclude that inverse proportion is a difficult concept that requires constant reinforcement, using approaches to teaching that facilitate deeper conceptual understanding.

Many states use research-based mathematics curricula as an instructional tool to improve mathematics performance outcomes on state assessment scores. The problem was that despite the implementation of a research-based curriculum, students at XYZ Elementary School (pseudonym) had underperformed on the Partnership for Assessment of Readiness for…

This study aims to examine the opinions of the pre-service teachers, who are studying in the department of mathematics, on creativity and the concept of mathematical creativity. The study group of the study consisted of 32 pre-service teachers studying in the 4th grade in the department of mathematics teaching in a province located in the southern…

This paper presents methodology aimed at developing a rich understanding of the interplay of mathematical progress in the different social settings in which learning in inquiry-oriented classrooms occurs: individually; in small groups; and as a whole class. For this purpose, we enhance a theoretical-methodological approach of coordinating…