This qualitative exploratory case study delves into learners' understanding of differentiation through the first principle and power rule. The study adopted the action, process, object, and schema (APOS) theory as a lens to track learners' understanding of these concepts using the activities, classroom discussion, and exercise (ACE) teaching…

The anthropological theory of didactics (ATD) provides a lens to view mathematics education by placing mathematical practices within socio-cultural and historical contexts. The significance of institutions, in what regards with educational establishments, societal structures, cultural norms, and historical contexts, influences the perception and…

This article presents a simple, fast, and equally accurate technique for measuring the area of a circle and of an ellipse without using geometric formulas. This therefore, together with the known radius of the circle and the semi-major and semi-minor axes of the ellipse, allows for the calculation of [pi]. The experiment is easy, thrilling, and…

Daily plans are the key tool for teachers to ensure their delivery meets the expectations of the programme, and math activities are one of the important activities required to be offered daily in the early years to form the foundations of future math knowledge. As outdoor environments provide various learning opportunities, assessing the math…

In this study we aimed to capture the characteristics of Chinese high-quality lessons from a lesson structure perspective, specifically addressing the elements of teaching activity and their sequence. Sixteen videotaped middle school mathematics lessons were selected from 224 daily lessons collected from urban districts in five cities located in…

The author presents a child-centered approach to teaching, developed through longtime connections with colleagues, which concentrates on the children and provides them time to make their own connections, to learn, to think, and to develop at their own pace with the support of their classmates. Two examples of how mathematics interlaced into…

This qualitative case study of four middle school and secondary school mathematics teachers examines how teachers' reflective practice supported their selection of strategies that align with the needs of current mathematics education according to the 10 dimensions of mathematics education. The findings suggest that teachers' reflection practice,…

Understanding a mathematical concept in real-world situations is of practical importance and would be helpful to learn the concept in depth. One potential way to help students learn mathematical concepts in real-world situations would be to engage them with contextual problems. Exponential and logarithmic concepts are essential topics in higher…

Teachers are increasingly adopting flipped instruction for individual lessons or even entire courses. Typically, flipped instruction involves a teacher assigning videos for homework and then using in-class time for students to solve problems--that is, the settings for content delivery and completing assignments have "flipped." In…

Successful integration of problem-solving in mathematics classrooms lies mostly with the assistance and support teachers get. Many studies have been conducted on the strategies teachers can use to integrate problem-solving in their teaching of mathematics, however, few studies have been conducted on frameworks/models that can assist teachers and…

Although geometric shape content should be mastered by early high school, many pre-service teachers (PSTs), particularly those in elementary and special education, have limited yet deeply engrained shape concepts. This poses challenges for how to teach shape concepts in content courses for PSTs. Thus, this study tested an approach atypical for a…

Teachers' noticing of classroom activity shapes who is invited to participate, who is valued, and whose forms of knowing are included in mathematics classrooms. We introduce a framework for multidimensional noticing for equity that captures the stretch and expanse of teachers' attention and sense making of the local, sociocultural, and historical…

Shifting classroom discourse to be more student-centered has become an integral part of reform-oriented instructional practices. At the same time, shifting discourse can open up opportunities for inequity to occur in the immediate learning environment as both the quantity and quality of mathematical talk changes. In this project, I examined…

"High Yield Routines 2nd Edition, Grades K-8," is an essential resource for elementary and middle school mathematics teachers seeking to enhance their instructional practices and optimize classroom time. Authored by experienced educators, this book presents effective mathematical routines designed to integrate seamlessly into everyday…

We describe a method that instructors can use to grade tests and assignments that can be used in follow-up inquiry-based activities in class to review material. The grading process is essentially a sorting of student assignment/test responses based on the instructor's conception of what makes responses acceptable. The instructor can assign a grade…