Performance tasks enable the development of not just the knowledge but also the skills of students. Unfortunately, teachers find it challenging to prepare their performance tasks. To help teachers, an authentic framework for the preparation of performance tasks should be utilized. GRASPS, as an assessment model, can help teachers develop authentic…

The "Pygmalion effect," is a construct that states that people often rise to the level that is expected of them (Chang, 2011). This is closely related to the "law of expectations," in which individuals receive what they expect to receive. These ideas may be applied to the educational arena when related to teacher perceptions…

Abstract algebra has been identified as an important course for preservice secondary mathematics teachers because much of the abstract algebra content is connected to, and thus relevant for, secondary mathematics teaching (Wasserman et al., 2017). However, many preservice teachers do not recognize the usefulness of an undergraduate abstract…

Private supplementary tutoring (PT) has expanded significantly and attracted widespread public interest in China in recent years. It deserves systematic empirical research and reflection, given its crucial theoretical and practical implications. Based on the data of a large-scale survey and testing project, this study examined its effects on the…

Cognitively demanding tasks have been shown to support students' understanding of mathematics. How a task is launched, or introduced, determines how students engage with the task, as well as the type of work the teacher engages in during the task implementation. The authors designed a unit focused on launching a task where prospective teachers…

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…